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This is the first of two courses designed to emphasize topics which are fundamental to the study of calculus. Emphasis is placed on equations and inequalities, functions (linear, polynomial, rational), systems of equations and inequalities, and parametric equations. Upon completion, students should be able to solve practical problems and use appropriate models for analysis and predictions. This course has been approved to satisfy the Comprehensive Articulation Agreement general education core requirement in natural sciences/mathematics
Elementary Linear Algebra 9780030973543 ISBN: 0030973546 Edition: 5 Pub Date: 1994 Publisher: Thomson Learning Summary: Intended for the first course in linear algebra, this widely used text balances mathematical techniques and mathematical proofs. It presents theory in small steps and provides more examples and exercises involving computations than competing texts. Grossman is the author of Elementary Linear Algebra, published 1994 under ISBN 9780030973543 and 0030973546. Four hundred six Elementary Linear Algebra textbooks ...are available for sale on ValoreBooks.com, one hundred forty used from the cheapest price of $35.95, or buy new starting at $120Intended for the first course in linear algebra, this widely used text balances mathematical techniques and mathematical proofs. It presents theory in small steps and provide [more] Intended for the first course in linear algebra, this widely used text balances mathematical techniques and mathematical proofs. It presents theory in small steps and provides more examples and exercises involving computations than competing texts
Calculus For Dummies Book InformationWell, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus. Calculus For Dummies is intended for three groups of readers: Students taking their first calculus course – If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series. Students who need to brush up on their calculus to prepare for other studies – If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course. Adults of all ages who'd like a good introduction to the subject – Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth. This is a user-friendly math book. Whenever possible, the author explains the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. Then, you'll see how the calculus concepts work in concrete examples. All explanations are in plain English, not math-speak. Calculus For Dummies covers the following topics and more: Real-world examples of calculus The two big ideas of calculus: differentiation and integration Why calculus works Pre-algebra and algebra review Common functions and their graphs Limits and continuity Integration and approximating area Sequences and series Don't buy the misconception. Sure calculus is difficult – but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off – it's simply the next step in a logical progression. Related Books About : Calculus For Dummies This... View detail "Flower Therapy" is the art of working with flowers, flower essences, and angels for healing, manifestation, and abundance. With flowers as your allies, your dreams really can come true, and you'll see that nature truly has the ability to heal! In this book, Doreen Virtue... View detail... View detail Before Jane Austen, William Deresiewicz was a very different young man. A sullen and arrogant graduate student, he never thought Austen would have anything to offer him. Then he read Emma—and everything changed. In this unique and lyrical book, Deresiewicz weaves the misadventures... View detail MARTY WILL DO ANYTHING TO SAVE SHILOH When Marty Preston comes across a young beagle in the hills behind his home, it's love at first sight — and also big trouble. It turns out the dog, which Marty names Shiloh, belongs to Judd Travers, who drinks too much and has a gun — and abuses
At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After calculus, he takes a course in analysis and a course in algebra. Depending on his interests (or those of his department), he takes courses in special topics…The exciting revelations that that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. And the following passage is contained in the preface of the book under review: Too often in an undergraduate mathematics curriculum, each course or sequence is taught as a discrete entity, as though the intersection of its content with the content of other courses or sequence were empty. So, after a period of 44 years, it seems that the problem of the compartmentalized mathematics curriculum is still a cause of concern for at least a few of those involved in the teaching of the subject. The authors of this book clearly belong to this minority. But the contents of this book are very different to that written by Singer and Thorpe — although the underlying philosophy is the same. Here, the foundations are provided for the later study of topics such as algebra, analysis and topology, and readers are simultaneously led to see mathematics as a way of knowing. In other words, there is a good balance between process and content. The content is centred upon logic, proof, sets, relations and functions. Methods of proof are explored, and deeper ideas such as cardinality and infinity introduced. The book concludes with a short chapter called 'Algebraic Systems', with the notion of binary operation being introduced by means of examples previously discussed. These include logical connectives, set operations, function composition and the number operations. The text is nicely balanced between expository narrative, examples, illustrations and exercises, and the book as a whole is not overloaded with content. Consequently, it makes for pleasurable and informative reading. In general, I think that this book provides a very useful first step into 'abstract mathematics', because many essential concepts, and the vocabulary and notation that represent them (e.g., quantifiers), are systematically developed. The exercises are of varying degrees of difficulty, but the authors have deliberately provided no solutions or hints. In conclusion, I would like to make two minor observations regarding the contents. Firstly, as with many books that introduce symbolic logic, I could find no explicit discussion of the validity of an argument. That is to say, an argument is valid if the conjunction of the premises implies the conclusion, which is a very useful framework in which to embed ideas of mathematical proof. Secondly, the concepts of binary operation and algebraic systems require a wider range of examples than is possible to provide in a book of this size. However, when students subsequently encounter topics like geometric transformations, matrices and vector spaces etc, they will have a much wider range of examples to draw upon. Overall, I feel that this book is highly suited to the purpose referred to in its title. As an undergraduate student in 1962, Peter Ruane greatly benefitted from a book with a similar aim to this one. It was Finite Mathematical Structures, by Mirkil, Kemeny, Snell and Thompson — possibly the first ever text written for foundation course.
Course Information Ahead of the Curve: Exponential and Other Functions for Grades 6-8 Course Description: Help middle school students function with functions. Study strategies for teaching exponential functions and growth, and solve a range of mathematical problems to understand the underlying mathematics of functions. Collaborate with peers online to find ways to recognize and address students' misconceptions. Create a lesson plan that prepares students for the type of function problems they will encounter in your curriculum. If you like this course, you may also like: * MATH136 Pattern and Relations for Grades 6-8 (15 hours) * MATH150 Making Comparisons with Data Analysis (30 hours) * MATH186 Math in Everyday Life for Grades 6-8 (15 hours) Note: This is a facilitated course. Learners submit coursework and participate in asynchronous discussions throughout the course term, and receive graded feedback. The number of hours identified for each course reflects time spent online, but does not reflect the total time spent completing offline coursework and assignments. All learners are different and you will likely spend double the indicated number of hours completing all coursework depending on your learning style and work habits. Graduate Credit Information: Graduate credit may be obtained from the provider(s) listed below, for an additional fee after the course begins.
More About This Textbook Overview This Student Solution Manual provides complete solutions to all the odd-numbered problems in Essential Mathematical Methods for the Physical Sciences. It takes students through each problem step-by-step, so they can clearly see how the solution is reached, and understand any mistakes in their own working. Students will learn by example how to select an appropriate method, improving their problem-solving skills. Related Subjects Meet the Author K. F. Riley read mathematics at the University of Cambridge and proceeded to a Ph.D. there in theoretical and experimental nuclear physics. He became a Research Associate in elementary particle physics at Brookhaven, and then, having taken up a lectureship at the Cavendish Laboratory, Cambridge, continued this research at the Rutherford Laboratory and Stanford; in particular he was involved in the experimental discovery of a number of the early baryonic resonances. As well as having been Senior Tutor at Clare College, where he has taught physics and mathematics for over 40 years, he has served on many committees concerned with the teaching and examining of these subjects at all levels of tertiary and undergraduate education. He is also one of the authors of 200 Puzzling Physics Problems. M. P. Hobson read natural sciences at the University of Cambridge, specialising in theoretical physics, and remained at the Cavendish Laboratory to complete a Ph.D. in the physics of star-formation. As a Research Fellow at Trinity Hall, Cambridge, and subsequently an Advanced Fellow of the Particle Physics and Astronomy Research Council, he developed an interest in cosmology, and in particular in the study of fluctuations in the cosmic microwave background. He was involved in the first detection of these fluctuations using a ground-based interferometer. Currently a University Reader at the Cavendish Laboratory, his research interests include both theoretical and observational aspects of cosmology, and he is the principal author of General Relativity: An Introduction for Physicists. He is also a Director of Studies in Natural Sciences at Trinity Hall and enjoys an active role in the teaching of undergraduate physics and
Quoted from the site: This Web site contains a page for each section of the book Principles of Calculus Modeling, an... see more Quoted from the site: This Web site contains a page for each section of the book Principles of Calculus Modeling, an Interactive Approach. A section page includes a summary of the section, an on-screen applet demonstrating the key point of the section, and what you should know after studying the material of the section. It also includes links to * additional in-depth applets, * worked examples, * videos of problems being worked out by students and teachers, * a quiz (with answers) that you can take to test your knowledge, * a link to a PDF document with of all the exercises of the section, * a link to these same exercises in interactive form with answer feedback, and * hypertext links to other supplementary materials on the Web that you might find useful, such as sample exams. This helps one to sketch equations, and calculate statistical parameters of Central Tendency, Skewness, Quartiles,... see more This helps one to sketch equations, and calculate statistical parameters of Central Tendency, Skewness, Quartiles, Correlation, Simple Regression, etc.... It will enable students to see the meaning of math expressions by using graphs.
Introduction To Graph Theory 9780073204161 ISBN: 0073204161 Pub Date: 2004 Publisher: McGraw-Hill College Summary: Written by one of the leading authors in the field, this text provides a student-friendly approach to graph theory for undergraduates. Much care has been given to present the material at the most effective level for students taking a first course in graph theory. Gary Chartrand and Ping Zhang's lively and engaging style, historical emphasis, unique examples and clearly-written proof techniques make it a sound yet acc...essible text that stimulates interest in an evolving subject and exploration in its many applications.This text is part of the Walter Rudin Student Series in Advanced Mathematics. Chartrand, Gary is the author of Introduction To Graph Theory, published 2004 under ISBN 9780073204161 and 0073204161. One hundred thirty eight Introduction To Graph Theory textbooks are available for sale on ValoreBooks.com, eleven used from the cheapest price of $47.88, or buy new starting at $136.22.[
Mathematics GLmath is a highly optimized, OpenGL-compatible C++ math library. The package offers developers several types of 2d and 3d math primitives to ease development efforts while maintaining a high level of computational efficiency
This course is a standard second semester Calculus course covering methods of integration, applications of the integral, differential equations, parametric and polar equations, and sequences and series. Sect# Type Room Instructor Units Days Time Start-End Footnotes 2136 LEC PH102 LOCKHART L 4.0 TuTh 0630P - 0820P Math 8A prepares the student for the study of calculus by providing important skills in algebraic manipulation, interpretation, and problem solving at the college level. Topics will include basic algebraic concepts, complex numbers, equations and inequalities of the first and second degree, functions, and graphs, linear and quadratic equations, polynomial functions, exponential and logarithmic functions, systems of equations, matrices and determinants, right triangle trigonometry, and the Law of Sines and Cosines. Math 8B prepares students for the study of calculus by providing important skills in algebraic manipulation, interpretation, and problem solving at the college level. Topics will include trigonometric functions, identities, inverse trigonometric functions, and equations; applications of trigonometry, vectors, complex numbers, polar and parametric equations; conic sections; sequences, series, counting principles, permutations, mathematical induction; analytic geometry, and an introduction to limits. Sect# Type Room Instructor Units Days Time Start-End Footnotes 0545 LEC LS102 DACHKOVA E 4.0 TuTh 1110A - 1225P DACHKOVA E 4.0 F 1110A - 1200P MATH 12: Mathematics for Elementary Teachers Prerequisite: Mathematics 208, or successful completion of a high school geometry course and Mathematics 233This course is the first half of the Elementary Algebra course. It will cover signed numbers, evaluation of expressions, ratios and proportions, solving linear equations, and applications. Graphing of lines, the slope of a line, graphing linear equations, solving systems of equations, basic rules of exponents, and operations on polynomials will be covered. This course contains the material covered in the second half of the Elementary Algebra Course. It will cover factoring, polynomials, solving quadratic equations by factoring, rational expressions and equations, complex fractions, radicals and radical equations, solving quadratic equations by completing the square and the quadratic formula. Application problems are integrated throughout the topics. Sect# Type Room Instructor Units Days Time Start-End Footnotes 0554 LEC LS102 DACHKOVA E 2.5 F 1210P - 0100P DACHKOVA E 2.5 TuTh 1245P - 0200P MATH 233: Intermediate Algebra Prerequisite: Mathematics 205 or Mathematics 205A and 205B or Mathematics 206 with a grade of 'C' or better. Prerequisite: Completion of Math 400 with a 'C' or better, or assessment test recommendation. Transferable: No This course covers operations with integers, fractions and decimals and associated applications, percentages, ratio, and geometry and measurement, critical thinking and applications. Elementary algebra topics such as variables, expressions, and solving equations are introduced. This course is a remedial, modular, self-paced course. Application similar
Good QuestionsPaperback– Apr 13 2010 More Good Questions, written specifically for secondary mathematics teachers, presents two powerful and universal strategies that teachers can use to differentiate instruction across all math content: Open Questions and Parallel Tasks. Showing teachers how to get started and become expert with these strategies, this book also demonstrates how to use more inclusive learning conversations to promote broader student participation. Strategies and examples are organized around Big Ideas within the National Council of Teachers of Mathematics (NCTM) content strands. With particular emphasis on Algebra, chapters also address Number and Operations, Geometry, Measurement, and Data Analysis and Probability, with examples included for Pre-Calculus. To help teachers differentiate math instruction with less difficulty and greater success, this resource: Most helpful customer reviews This book was recommended to me by one of the authors ... so I may be a bit biased. However it was money well spent. I teach grade 8 math in Ontario and although the title is "Secondary Mathematics" there is almost equal weight given to grade 7 and 8 level material. Not only is the theory sound, but the authors have compiled many many sample problems that are ready to use with a class. They are even organized by the strands used in the Ontario curriculum. This will certainly be a part of my teaching this year and in the future. Most Helpful Customer Reviews on Amazon.com (beta) Amazon.com: 6 reviews 8 of 9 people found the following review helpful Not just for high school - Grade 6 and up!Nov. 24 2010 By SarahQuilts - Published on Amazon.com Format: Paperback I love this book! I will admit to a slight bias - I met one of the authors, Amy Lin because she worked at my school board and she suggested I buy this book. It is money well spent. I really like that there are many many practical suggestions and example questions that you can use in the classroom right away. The questions are divided by strand, and there are enough that you could use them weekly through an entire year. I wish that the grade level was indicated in the title. Half of the content is geared towards grades 6-8 (and many of the lower grade questions would be good for high school classes too) There are two types of activities "open questions" that let students participate in a mathematical discussion at multiple levels, and "parallel tasks" that give student choice, but achieve the same big picture understandings. The authors even included scaffolding questions or prompting questions to help re-start a discussion that has stalled or help a student get started. Finally, there is a clear index organized by topic that lets you flip straight to the page that has the questions you need for today's lesson. 3 of 4 people found the following review helpful There are NO questions.March 22 2013 By Janet Orloski - Published on Amazon.com Format: Paperback Verified Purchase This book addresses generalities about differentiation and does not include specific lessons that differentiate mathematics. I do not recommend this book. Great Common Core resource!Dec 22 2013 By Emily Y. - Published on Amazon.com Format: Paperback I have used the questions and parallel tasks for math journals. My students love them because they can think outside the box, and there are no wrong answers. I especially appreciate the sample teacher questions that the authors provide to help facilitate class discussion. I would recommend this book to math teachers looking for a way to incorporate more writing and discussion in their class. ExcellentOct. 23 2013 By Freedomite - Published on Amazon.com Format: Paperback Verified Purchase Very useful in developing good questions to facilitate student centered talk that is needed to support student competencies for the Math Common Core Curriculum. Great Book!Jan. 8 2013 By Catwoman - Published on Amazon.com Format: Paperback Verified Purchase This book has lots of applicable ideas for teaching secondary level mathematics. I read the hints when putting together Lesson Plans. I have two copies one for my personal library and one as a reference in the classroom.
This is a free textbook offered by BookBoon.'The success of Group Theory is impressive and extraordinary. It is, perhaps, the... see more This is a free textbook offered by BookBoon.'The success of Group Theory is impressive and extraordinary. It is, perhaps, the most powerful and influential branch of all Mathematics. Its influence is strongly felt in almost all scientific and artistic disciplines (in Music, in particular) and in Mathematics itself. Group Theory extracts the essential characteristics of diverse situations in which some type of symmetry or transformation appears. Given a non-empty set, a binary operation is defined on it such that certain axioms hold, that is, it possesses a structure (the group structure). The concept of structure, and the concepts related to structure such as isomorphism, play a decisive role in modern Mathematics.The general theory of structures is a powerful tool. Whenever someone proves that his objects of study satisfy the axioms of a certain structure, he immediately obtains all the valid results of the theory for his objects. There is no need to prove each one of the results in particular. Indeed, it can be said that the structures allow the classification of the different branches of Mathematics (or even the different objects in Music (! )).The present text is based on the book in Spanish "Teoría de Grupos: un primer curso" by Emilio Lluis-Puebla, published by the Sociedad Matemática Mexicana This new text contains the material that corresponds to a course on the subject that is offered in the Mathematics Department of the Facultad de Ciencias of the Universidad Nacional Autónoma de México plus optional introductory material for a basic course on Mathematical Music Theory.This text follows the approach of other texts by Emilio Lluis-Puebla on Linear Algebra and Homological Algebra. A modern presentation is chosen, where the language of commutative diagrams and universal properties, so necessary in Modern Mathematics, in Physics and Computer Science, among other disciplines, is introduced.This work consists of four chapters. Each section contains a series of problems that can be solved with creativity by using the content that is presented there; these problems form a fundamental part of the text. They also are designed with the objective of reinforcing students' mathematical writing. Throughout the first three chapters, representative examples (that are not numbered) of applications of Group Theory to Mathematical Music Theory are included for students who already have some knowledge of Music Theory.In chapter 4, elaborated by Mariana Montiel, the application of Group Theory to Music Theory is presented in detail. Some basic aspects of Mathematical Music Theory are explained and, in the process, some essential elements of both areas are given to readers with different backgrounds. For this reason, the examples follow from some of the outstanding theoretical aspects of the previous chapters; the musical terms are introduced as they are needed so that a reader without musical background can understand the essence of how Group Theory is used to explain certain pre-established musical relations. On the other hand, for the reader with knowledge of Music Theory only, this chapter provides concrete elements, as well as motivation, to begin to understand Group Theory.' Analysis of Bach's Fugue No 1 in C minor (WTC Book 1, BWV 847)This material is part of the teoria.com website which was... see more Analysis of Bach's Fugue No 1 in C minor (WTC Book 1, BWV 847)This material is part of the teoria.com website which was reviewed here: " target=״_blank״In four voices fugues there are 24 possible combinations in the order of voice entries in the exposition. This system of... see more In four voices fugues there are 24 possible combinations in the order of voice entries in the exposition. This system of classification according to the order of voice entries in the expositions summarizes all possible combinations using a few simple circles. An interactive music theory quiz that helps students improve their ability to identify errors in pitch or time. A piece of... see more An interactive music theory quiz that helps students improve their ability to identify errors in pitch or time. A piece of music is displayed and students must press the play button to hear the correct way it is played. They must select the measure number in which the written error occurs. A 'Show Answer' button can help them.
Group theory is an important subject that has come a long way in recent years. Introduction to Group Theory presents the fundamentals of both finite and infinite group theory, with a focus on finite groups. It provides students with the ability to prove the Thomas normal p-complement theorem and to classify simple finite groups. A large portion of the text is devoted to general linear groups. Additional topics covered include the construction of BN pairs, Coexeter groups, Hall–Higham theory, and Bender results. The text also offers an in-depth exploration of the complex relationship between groups, coding, and cryptography.
... More About This Book directions, answer key, and reproducible student activity sheets. Activities in sections 1-6 are presented in order of difficulty within each section while those in Part 7, "A Potpourri of Geometry," are open-ended and may be used with most middle and high school classes. Many activities throughout the book may be used with calculators and computers in line with the NCTM's recommendations
Synopses & Reviews Publisher Comments: This volume contains the proceedings of a highly successful AMS Short Course on Chaos and Fractals, held during the AMS Centennial Celebration in Providence, Rhode Island in August 1988. Chaos and fractals have been the subject of great interest in recent years and have proven to be useful in a variety of areas of mathematics and the sciences. The purpose of the short course was to provide a solid introduction to the mathematics underlying the notions of chaos and fractals. The papers in this book range over such topics as dynamical systems theory, Julia sets, the Mandelbrot set, attractors, the Smale horseshoe, calculus on fractals, and applications to data compression. The authors represented here are some of the top experts in this field. Aimed at beginning graduate students, college and university mathematics instructors, and non-mathematics researchers, this book provides readable expositions of several exciting topics of contemporary research
Summary: Susanna Epp's DISCRETE MATHEMATICS: AN INTRODUCTION TO MATHEMATICAL REASONING provides a clear introduction to discrete mathematics and mathematical reasoning in a compact form that focuses on core topics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision, helping students develop the ability to think abstractly as they study each topic. In doing so, the book provides students with a strong foundation both for computer scienc...show moree and for other upper-level mathematics courses. ...show less New Hardcover. TEXTBOOK ONLY 1st Edition Ships same or next day. Expedited shipping takes 2-3 business days; standard shipping takes 4-14 business days. $150.47 +$3.99 s/h New Texts Direct Lexington, KY 2011 Hardcover BRAND NEW! Ships same or next business day. NO INTERNATIONAL ORDERS PLEASE. $159.60 +$3.99 s/h Acceptable TEXTBOOKFETCHER! Cortland, NY 0495826170 This is a used item. $162.22 +$3.99 s/h New Jeff's books Mayfield village, OH Hardcover New 0495826170 Your book ships within 24 hours of ordering. $167.07 +$3.99 s/h Good Facetextbooks Pittsburg, KS Hardcover 1st Edition text. Hardcover. NO WRITING /HIGHLIGHTING Used in book Used tems may have stickers on cover. May have writing/underlining or highlighting, and varying degrees of wear.. Ships fas...show moret
Mathematical Thinking Problem-Solving and Proofs 9780130144126 ISBN: 0130144126 Edition: 2 Pub Date: 1999 Publisher: Prentice Hall Summary: For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematicsskills vital for success throughout the upperclass mathematics curriculum. The text offers both discrete an...d continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality. D'Angelo, John P. is the author of Mathematical Thinking Problem-Solving and Proofs, published 1999 under ISBN 9780130144126 and 0130144126. Five hundred sixty Mathematical Thinking Problem-Solving and Proofs textbooks are available for sale on ValoreBooks.com, one hundred fifty one used from the cheapest price of $49.98, or buy new starting at $117.22.[read more Acceptable condition. Will show clear signs of use may contain damage to the binding, cover and/or pages. 2nd day shipping offered. Ships same or next day!!! Used book [more] Book in Acceptable condition. Will show clear signs of use may contain damage to the binding, cover
Programs and resources for educators, schools, students, and "lifelong learners" of science, technology, engineering, and mathematics Your First Step to STEM Success is exclusively for community/technical college and primary/secondary school teachers who want to make a difference in their classrooms. If you teach a STEM subject like math, physics, biology, or chemistry, this program can give you the tools to engage your students and increase their understanding of the concepts you're teaching... with Mathematica. Buy Mathematica for only £75excl. VAT Get Started Now This content requires JavaScript and Adobe Flash Player 10 or higher. If you are using a browser with JavaScript or Flash disabled, please enable them now. Otherwise, please install the latest version of the free Flash Player.
This unit consists of two computer programs. The first teaches X,Y plotting; the second is a demonstration of coordinate transformations, matrices, vector equations of lines and perspective and will draw a picture of... This mathematics tutorial gives users an introduction to functions, functional notation and terminology. The site explains how a function is defined, and the correct way to read and write functional notation. Resources... Based at the University of Plymouth, the Centre for Innovation in Mathematics Teaching has developed many instructional materials designed to help both novice and experienced math teachers. This particular area of their... The Open University had long been dedicated to the proposition of providing high-quality educational materials for persons all over Britain and the world. They were one of the first universities to place such materials... Created by Alexander Bogomolny, this site is a clearinghouse of fun and engaging mathematics exercises, puzzles, and other such activities that teachers can utilize in their classrooms. Of course, students might happen...
Shipping prices may be approximate. Please verify cost before checkout. About the book: Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problemssome computational and some classical, many original, and some with complete solutions. The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat's and Wilson's theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and answers to selected exercises and problems. Hardcover, ISBN 0716704382 Publisher: W.H.Freeman & Co Ltd16704382 Publisher: W.H.Freeman & Co Ltd, 197016704382 Publisher: W.H. Freeman & Company, 1969 Used - Good. Former Library book. Shows some signs of wear, and may have some markings on the inside. Shipped to over one million happy customers. Your purchase benefits world literacy! Hardcover, ISBN 0716704382 Publisher: W.H.Freeman & Co Ltd, 1970 Used - Good, Usually ships in 1-2 business days, Hardcover with fair dust jacket. W. H. Freeman & Company, Ltd, publisher. 1969 Edition. Printed in the USA. The boards are a nice green with a lighter lime green with letters. There is black lettering on the front cover and the spine. Underwood Dudley, author. Total 262 pages. Approximate size, 6.25 x 9.50. The spine is tight and straight, the pages are clean of markings with exception of an old sales price stamped on the front endpage. There...
Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources. less
I think 'step by step solutions' is the only feature which is limited to three times a day. Feels like you're complaining a bit much. WA developed that feature and then made it free-use for 3X a day, which seems like an improvement on what came before- i.e. nothing. WA will still give you the solutions (an unlimited number of times each day). Is that not enough to get you going? Does it really have to do all your homework for you as well? You're right, It doesn't have to do all the work for me, and It really shouldn't. I just find it help full to check over my work/find out what I did wrong when I face a problem. Also I am sorry if I came off as complaining, definitely wan't trying to do so. Well, is it not enough that WA will find you the correct solutions for most problems you're likely to encounter? That seems like a pretty sweet deal to me, and I would have loved to have a program like that when I was studying math in high-school. Not only do you have WA, but you the internet contains thousands of pages of worked examples of practically every type of problem you could run into.
Calculus With Finite Mathematics - 2nd edition ISBN13:978-0618372133 ISBN10: 061837213X This edition has also been released as: ISBN13: 978-0618539611 ISBN10: 0618539611 Summary: The Second Edition of this engaging text for the two-semester applied calculus and finite mathematics course continues to use intriguing, real-world applications to capture the interest of business, economics, life, and social science majors. This practical approach to mathematics, along with the integration of graphing calculators and Excel spreadsheet explorations, exposes students to the tools they will encounter in future careers. Summaries and reviews ...show moreappear frequently throughout the text to support students' mastery of mathematical concepts. A wealth of pedagogy includes the following distinctive features: detailed Worked-out Examples with Annotations help students through more challenging concepts; Practice Problems are offered to help students check their understanding of concepts presented in the examples; Section Summaries briefly restate essential formulas and key concepts; Chapter Summary with Hints and Suggestions unify chapter themes, give specific reminders, and reference problems in the review exercises suitable for a practice test; and Cumulative Review Exercises appear at the end of groups of chapters to reinforce previously learned concepts and skills. Graphing Calculator Examples and Exercises located throughout the text explore new topics, guide students through "messy" calculations, or show technology pitfalls. These are optional and may be omitted without disrupting the flow or cohesion of the text. Application Previews place mathematics in a real-world context and motivate students' interest in the material. Some examples of the diversity of applications covered include sports, genetic engineering, spread of disease, gambling, business, and environmental issues. Annotations beside many formulas and solution steps emphasize the importance of being able to "read mathematics" by restating much of the mathematics in words10.3007 +$3.99 s/h New Letusbegin Ossining, NY 2004-02-23 Hardcover New New Hardcover! Pristine unmarked pages, may have very slight warehouse wear, no remainder marks, still a great buy straight from book warehouse unread, sealed in plastic, e...show morexact
salam i wanted some help regarding applied math sub ,i have seen many posts all discussing about the books ,and other things about the subject but heavent seen any about the composition of the paper and distributions of different sections i shall be highly thankful if any body helped
Mathematics: Linear Programming eBooks Linear programming is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. Linear programming can be applied to various fields of study. It is used most extensively in business, economics, and engineering. Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proved useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design. Linear programming eBooks are available for download here at eBookMall. There are currently 24 eBooks in the category Mathematics: Linear Programming.
Discrete Mathematics With Graph Theory 9780130920003 ISBN: 0130920002 Edition: 2 Pub Date: 2001 Publisher: Prentice Hall Summary: For one or two term undergraduate courses in Discrete Mathematics for students of Mathematics and Computer Science. Adopting a user-friendly, conversationaland at times humorousstyle, these authors make the principles and practices of discrete mathematics as stimulating as possible while presenting comprehensive, rigorous coverage. Examples and exercises integrated throughout each chapter serve to pique student inter...est and bring clarity to even the most complex concepts. Above all, the book is designed to engage today's students in the interesting, applicable facets of modern mathematics. Goodaire, Edgar G. is the author of Discrete Mathematics With Graph Theory, published 2001 under ISBN 9780130920003 and 0130920002. Twenty seven Discrete Mathematics With Graph Theory textbooks are available for sale on ValoreBooks.com, twenty three used from the cheapest price of $0.08, or buy new starting at $24.17
This learning object from Wisc-Online covers simplifying algebraic expressions using addition and subtraction. The unit's activities include defining the terminology associated with algebraic expressions, using the... This learning object from Wisc-Online covers simplifying algebraic expressions using division. The unit's activities include defining the terminology associated with algebraic operations, using the fundamental laws of... This lesson from Illuminations teaches students to use a computer algebra system to determine the square root of 2 to a given number of decimal places. Students will learn how utilizing technology makes an algorithm... This lesson from Illuminations asks students to use a geometry applet to analyze the characteristics of a square. Graphs are created to show relationships between characteristics (side length, diagonal length, perimeter... This lesson from Illuminations asks students to look at different classes of polynomial functions by exploring the graphs of the functions. Students should already have a grasp of linear functions, quadratic functions,...
Learning of physics concepts often requires fluency with the underlying mathematics concepts. Only a few studies in physics education research (PER) have investigated connections between student difficulties with physics concepts and those with either the mathematics concepts, application of those concepts, or the representations used. One mathematical concept that is widely used across a broad spectrum of disciplines such as physics, chemistry, biology, economics, etc., is the definite integral. We studied the extent to which the conceptual understanding of definite integrals affects the understanding of physics concepts that involve definite integrals. We also identified specific difficulties that students have with definite integrals, particularly with graphical representations. One strong focus of this work was how students reasoned about integrals that yield a negative result. Many of our findings corroborate previous results reported in the literature, including students' using the area under the curve to reason about definite integrals, and ensuing difficulties generalizing area as always being a positive quantity. Additionally, novel results in this work include: multiple student difficulties in applying the Fundamental Theorem of Calculus in graphical situations; difficulties determining the signs of integrals that are carried out in the "negative direction" (i.e., from a larger to a smaller value of the independent variable); and student success invoking physical context to interpret certain aspects of definite integrals. Furthermore, we find that although students dominantly use area under the curve reasoning, including unprompted invocation of the Riemann sum, when contemplating definite integrals, their reasoning is often not sufficiently deep to help think about negative definite integrals. Overall, our results serve as one example that the connections between mathematics and physics are not trivial for students to make, and need to be explicitly pointed out. Implications for additional research as well as for instruction are discussed.
Summary: Syllabus for Math 107, Fundamentals of Mathematics I, Fall 2010 Instructor: Dr. Elizabeth Arnold e-mail: arnoldea@math.jmu.edu Phone: 568-6532 URL: Office: Roop 111 Office Hours: MWF 12:10-1:10pm, and by appointment. COURSE DESCRIPTION: This course is the first in a series of three that are required for the IDLS major. Topics covered include number systems, number operations, fractions, quantitative reasoning and number theory. This course partially fulfills the requirements for licensure of prospective early childhood, elementary, and middle school teachers. TEXT: Reconceptualizing Mathematics for Elementary School Teachers, by Sowder, Sowder and Nickerson. We will cover Chapters 1-11 in Math 107. MathPortal: You should purchase this subscription from the bookstore. For $10, you will have access to the MathPortal for 2 years. After you purchase the registration, go to and click on "register". This is where you will see your grades, assignments and supplementary materials. Please register before coming to class the first day. SUPPLIES: Clear plastic ruler with both metric and American units, pencil, Calculator, 3 ring notebook. SPECIAL COURSE REQUIREMENTS: IDLS Assessment Test: All IDLS majors are required to take a mathematics assessment test at the begin-
Geared to preparing students to make the transition from solving problems to proving theorems, this text teaches them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5 Systematic and thorough, shows how several techniques can be combined to construct a complex proof Selected solutions and hints now provided, plus over 200 exercises some using Proof Designer software to help students learn to construct their own proofs Reviews & endorsements "The prose is clear and cogent ... the exercises are plentiful and are pitched at the right level.... I recommend this book very highly!" MAA Reviews "The book provides a valuable introduction to the nuts and bolts of mathematical proofs in general." SIAM Review "This is a good book, and an exceptionally good mathematics book. Thorough and clear explanations, examples, and (especially) exercised with complete solutions all contribute to make this an excellent choice for teaching yourself, or a class, about writing proofs." Brent Smith, SIGACT News
General Math Workbook This workbook consists of practice problems based on essential fundamental math concepts focusing primarily on number sense standards from grades one through six. The 80 problem... More > sets are designed to work in tandem with our General Math Curriculum but can also be utilized to remediate basic math ideas. For curriculum information, please contact us at info@ssformath.com< study guide provides parents, teachers and students with multiple opportunities to practice and master the math content areas on the CAHSEE. The lessons use plain language to define academic... More > concepts and simplify seemingly complicated ideas within the California state standards. The topics covered within the workbook mirror the test itself: number sense, statistics, data analysis and probability, measurement and geometry, algebra and functions, mathematical reasoning and algebra I. All questions are formatted to match the CAHSEE and there are three complete practice tests included. This is the ideal solution for tutorial, home study or independent study students " and also discusses the continuum hypothesis. Invites the reader to form his own unbiased opinion based on his own thinking and understanding and expresses an interest in the general consensus of opinion on this issue.< Less THE present work is essentially one of constructive criticism. It is, we believe, the first attempt made on any extensive scale to examine critically the fundamental conceptions of Mathematics as... More > embodied in the current definitions. The purpose of our examination is not solely or even chiefly to show the presence of error, but to pro mote the development of a more scientific doctrine. In expounding our own views we have often been obliged to find fault with those of others; but we have not gone out of our way for the sake of mere criticism; we have merely cleared away false doctrine preparatory to replacing it with true.< Less From the PREFACE: ""The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and... More > philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation examination, and, despite clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation." -Albert Einstein< Less
Math Art Computer Graphics Math Art Grades 7-12 Colette Stemple Coral Reef High School Miami, Florida Math Art Contents Page Teacher Statement 1. Course Overview Adobe ® Photoshop™ proves that Math is Beautiful Course description Course Goals 2. Summary of State Standards 3. Technology Specifications 4. Lesson Plan Table 5. Detailed Lesson Plans 6. Evaluation Form 7. Lesson Ideas 8. Bibliography 9. Tutorials and Gallery of Projects Math Art Computer Graphics Photoshop Mathematical Visualization Colette Stemple Coral Reef High School Miami, Florida TEACHER STATEMENT The connection between Photoshop and Math became apparent to me when I launched the first version of Photoshop in the middle school art program. Students began experimenting with actions, paths, and filters and began applying "visual math" to their imaging projects. Because they were working on Art projects and could see the concepts, and watch changes as they altered curves and percentages or worked with graphs, they were able to apply math concepts with ease without really knowing that Math was what they were doing. Even though these exercises were not formal math projects math scores improved for each of these students as a result of their visual experimentations. This course will introduce a series of Math Art exercises that have been formalized by International Baccalaureate students at Coral Reef High School. The messages of these exercises is that reinforcing lessons from any discipline by creating hands on visuals with the Art teacher Colette Stemple and approaching the process through play, imagination Reviewing Math Art Project Digital Compass and creative exploration, is a wonderful extension of any subject or discipline. Math Art ART AS THE HUB If teachers from other disciplines will let the art teacher aware of the mathematical principles inherent in the creation know what they are teaching, all concepts can be of visual images. With Adobe Photoshop, these principles reinforced through visual exercises. This has been are inherent in the process of creating art on the computer. demonstrated for centuries by actual man made objects as evidenced in cave paintings, arts and crafts and Adobe Systems software used across the curriculum in all of architecture throughout history. Now we also have the the classrooms and computer labs helps administrators, option of using the computer to help achieve these goals. teachers, parents, and the students to cooperatively get And, in the art classroom, the actual creation of an art work more out of, and put more into learning. Adobe software can often spontaneously spark the "genius "core in each offers a cohesive visual language and form of expression child that applies to every classroom situation. It "De-isolates", teachers and their subjects, it makes everyone's job easier In many schools, students move from one room, one and more fun. subject, and one teacher to another all day long, and never see connections from one subject to another. Most states have Math Rubrics and a Curriculum that teachers must follow. By working with the math teacher and applying these requirements to art exercises, the Art teacher can demolish the erroneous, long held, idea that Art is a frivolous elective and establish the art curriculum as the core of any discipline. The Art classroom is the place where all disciplines can and should all come together. As an Art teacher I have shown how this can happen by helping the Math teachers bring concepts to life and improving math comprehension by simply giving students some examples of how to be Math Art COURSE OVERVIEW The students were not obliged to get their creations "OK'd" by the Math Coarse Description: teacher, although that could certainly be a wonderful way for the Math These lessons and exercises are not meant to be Math Workbook teacher to connect to the creative core of the person they are trying to Lessons, though some could be used as such. Some of these teach. Exploring images made by students could indicate a "thinking" examples illustrate actual math concepts literally and accurately, pattern in a student's mind that the teacher could tap into and exploit. others are uninhibited play based in diverse mathematical themes or Also, art works could start lively discussion about Math principles in the focusing on the "MATH TOOLS" inherent in Photoshop. The lessons Math Room and not just in the Art Room. Math Art lessons should were created for use by Art Teachers, to allow them to use art to trigger the heart and imagination of each student and allow them to reinforce mathematical concepts, rules and explorations. This course share those qualities in the Math classroom. If the Math teacher doesn't module was designed for artistic explorations in the realm of have the skills to create these opportunities for visual learning, then the mathematical structures, laws, deviations and explorations. Art should be called upon to help. The course module I created is a nine week project for students from all academies, on each level of mathematical and artistic expertise. The only instructions they needed was to remind them of the incredibly diverse amount of information they have learned in Math classes and also Science classes and then challenge them take one or more principles or theories and create a simple work of visual art that reflects these principles and theories. This made it possible for students to take one discipline, Art and another discipline, Math, and put them together to see that they were inseparable. Of course, this leads too a great deal of lively discussion and collaboration among the students which also sparks learning. No emphasis was placed aesthetics. In some exercises it is easy to that this was not stressed. However, some students started to see it themselves as artists as their "Math ideas" became pictures and this sparked the wonderful result of making them want to keep working on to achieve an aesthetic that they considered acceptable. Course Goals: This workbook is intended to encourage all teachers to share their Digital Compass Project comprehensive tests, standards and lessons with the art teacher. Though it is not the Art teacher's job to teach Math, Science, Language Arts or Computer Literacy but that is exactly what happens when art class is combined with any other discipline. Math Art State Standards Florida State Standards Technology Specifications Florida Department of Education Sunshine State Computer Specifications: Standards-Visual Arts 9-12 20 PC computers, Pentium III Processors, 128.0 MB RAM 2 HP Deskjet 870 CXI color Printers Skills and Techniques: 1 HP Deskjet 1600 CM Color Printer Standard 1: The student understands and applies media, 2 HP Scanjet 6100 C Flatbed Scanner techniques and processes. VA.A.1.4 2 Epson Stylus Photo 1270 Inkjet printers 1 Fuji FUJIX 3000 Dye Sublimation Printer 2 Canon CanoScan FS 2710 negative & transparency scanners Cultural and Historical Connections 20 12" Wacom Tablets Standard 1: The student understands the visual arts in relation to history and culture. VA.C.1.4 Adobe Software List: Aesthetic and Critical Analysis Adobe Photoshop 7.0 Standard 1: The student assesses, evaluates, and Adobe® GoLive ™ responds to the characteristics of works of art. VA.D.1.4 Adobe® Illustrator ™ Applications to Life Adobe® Atmosphere ™ Adobe® Acrobat™ Standard 1 The student makes connections between the visual arts, other disciplines and the real world. VA.E.1.4 For more information about the Florida Sunshine State Competency Based Standards go to: Math Art Lesson Plan Table 1. Review Math Concepts and Visualization See Bibliography** Start with the BLACK HOLE Review Photoshop Tools Photoshop & Photoshop by O'Connor Elements Tutorials* Photoshop or Elements* 2 Simple Algebraic Graphing Graphing Equations from any See DIGITAL COMPASS Creating a simple x axis and y axis graph and elaborate Algebra book. Exercise by Marraccini 3. Review Perspective (as in the Renaissance), Foreshortening and Atmospheric 1, 2, & 3 point perspective 3D transform tool 9th Perspective (as in Photo Realism) samples Grade samples using & from Art texts Sample PHOTOGRAPHS by Curtis Chan 4. 2D Design as defined in Abstract Art Art History texts & URLs G. Yap & C. Chan samples. 5. Saturation and the Properties of Color and Light (as in Impressionism), Value Color Theory, Intensitiy, Christina Jay and 9th grade Scale Saturation, Scales Sample Color 6. Pattern and Symmetry (as in Islamic Art) Art History texts & URL's N. Salz Formal Symmetry samples 7. Digitization (as in Photo Imitation), Computer Graphics, The Art of Chuck Close & Enlargements of any Computer Engineering and Photo Realism Rasterization, Pixels etc. Rasterized Image Computer Engineering Photos by J. Jing Zeng 8. Geometric Abstracts using all types of Angles The Art of Richard "Propriano", Mortensen's Basic laws of motion in physics Mortensen. S. Delauney, M. abstract painting; study of the Weber measurement of angles. Sample & Natural Elements by G. Obermeier (9 gr.) Math Art Detailed Lesson Plans THE VISUAL ARTS LESSON PLAN Show Art and Mathematical examples of both. LEVEL 1 Discuss OP ART, Convergence, Performance Assessment: Vortex, Perspective, Emphasis, Depth of Field, Observation: All Lessons illustrated in this workbook Concentricity, Space, Unity, were developed by the students in Illusory Motion, & Space Final Project: Visual Arts Level I. Group Critique of individualized re- interpretation of the Vocabulary: Assignment Each student was evaluated and All of the words in Procedures with emphasis Observation of student working graded according to the components on the correlation of Mathematics with the Self - assessment by the student shown below for this course. Elements of Visual Composition Journal Entries Sketches Materials: Photoshop or Photoshop Elements Sketchbook/ Journal or Homework: Base Assessment: Do sketches in the Journal of the Vocabulary test Media: concepts introduced. Design creation Computer Imaging List possible Design Applications List possible Mathematical Applications Visual Resources: Photoshop or Elements tool tutorial if necessary. See Evaluation Form following page. Show examples from the imagination, nature and existing Art and Mathematical forms or functions. Procedures: Show students how to open Photoshop and Show how a simple concept can lead to instruct with handout a basic diagram of the advanced theories in Physics, Calculus, tools. Geometry, and Algebra Give a background with Art History examples Show where Symmetry both Radial and of Formal and Radial Symmetry and discuss Formal have dominated centuries of Design in the concept of Compositional Centering different cultures and religious iconography. Math Art Florida Sunshine State Standards for Teacher and Student Evaluations. Course Name___________________________________________________________________________________ Student Name__________________________________________________________________________________ Student State Standards-Performance Assessment Teacher Grade Evaluation evaluation I. Skills and Techniques: Standard 1: The student understands and applies media, techniques and processes. VA.A.1.4 II. Cultural and Historical Connections Standard 1: The student understands the visual arts in relation to history and culture. VA.C.1.4 III. Aesthetic and Critical Analysis Standard 1: The student assesses, evaluates, and responds to the characteristics of works of art. VA.D.1.4 IV. Applications to Life Standard 1 The student makes connections between the visual arts, other disciplines and the real world. VA.E.1.4 V. Observation: Math Art MATH LESSON IDEAS 1. Analytic Geometry, Bi Lateral Symmetry, Rotational Symmetry, Curves 2. Graphs: Equations and Slopes of Lines, Tessellations or Tiling, Perspective, Histograms, Scale, Pattern _ Rhythm, Sierpinski Triangles, Fractals, 3. Tangents, 2D & 3D Geometric Shapes, Saturation, Spherical Coordinates, 4. Parametric Equations, Tangents, Drag: (e.g. Marine objects with least drag are torpedo shaped and are ¼ wide as they are long.) 5. Area & Perimeter, Diameter and Radii, Segments, Transformations, Rotations, Reflections, Positive vs. Negative, Bezier Curves, Mandalas, 6. Contours, Values, Shades, Series, Syncopation, Perimeter, Area, Volume Graphing, Histograms. LESSONS WITH FOUNDATIONS IN ART AND CULTURES 1. Perspective (as in the Renaissance) 2. Value Scale 3. 2D & 3D Design, (as in Abstract Art) 4. Saturation, and the Properties of Color and Light, (as in Impressionism) 5. Pattern and Symmetry (as in Islamic Art) 6. Foreshortening and Atmospheric Perspective (as in Photo Realism) 7. Digitization (as in Photo Imitation) 8. Geometric Abstracts (as in Rayonism) 9. Mathematical Languages ( as in Abstraction, Symbolism, Architectural Construction, Cubism) 10. Proportion and Distortion and Illusion (as in Surrealism). 11. The SUMBA CULTURE of Indonesia 12. WESTERN APACHE CRAFTS and all Native American & African Crafts Math Art 13. HELLENISTIC POTTERY of Greece 14. LANDSCAPE & STILL LIFE PAINTING from any period & place 15. MASTERS OF LIGHT DEFINITION from the Renaissance to the Present 16. CUBISM Its masters, prototypes, and imitators 17. OP ART 18. TROMPE L'OEIL especially in French & Dutch Art of the Renaissance 19. RAKED GARDENS OF JAPAN 20. ARCHITECTURE from any time and place 21. FUTURISM, DE STIJL, CONSTRUCTIVISM, SURREALISM, SUPREMATISM 22. NEOCLASSICISM especially Jacques Louis David & Jean Auguste Ingres 23. POST IMPRESSIONISM especially Paul Cezanne 24. EXPRESSIONISM especially Henri Matisse & Wassily Kandinsky Math Art BIBLIOGRAPHY 1. Art & Physics Parallel Visions in Space, Time & Light, by Leonard Shlain, Quill William Morrow New York, 1991 2. Exploring The Invisible (Art, Science And The Spiritual,) by Lynn Gamwell, Princeton University Press, 2002 3. Schoolworks Photoshop Elements , for Teachers, by Barbara and Nickolas Delikaris, Schoolworks, 2003 4. Discovering Geometry, An Inductive Approach, by Michael Serra, Key Curriculum Press 5. The Genesis of Form, From Chaos to Geometry, by Mark Verstockt, Muller, Blond & White 6. Symmetry in Chaos, A Search for Pattern in Mathematics, Art, & Nature, by Michael Field & Martin Golubitsky, Oxford Press 7. Visualization, The Second Computer Revolution, by Richard Mark Friedhoff and William Benzon, W.H. Freeman & Co. 8. Cellular Automata and Complexity, Collected Papers, by Stephen Wolfram, Westview Press, 1994 9. Algebra to Go, A Mathematics Handbook, by Great Source Education Group, Houghton Mifflin Co., 2000 10. Key to Geometry Skillbook Series # KJ100, by Lakeshore Basics ON-LINE RESOURCES Integrating Technology in Science & Math Instruction Yahooligans! Arts & Entertainment: Art Welcome to Integer Jim's Math Squad Index Vance & Art's Spell Bound Game and Math Puzzles and Games ADOBE EDUCATION SITE, wwwladobe.com/education Math Art Mathematics – k – 12 Internet Sites PiRanch Math Camps, Unique Art, Algebra Camp, Geometry Camp etc. dvdream.com art instruction catalog Kathy Schrock's Guide for Educators – Mathematics Resources school.discovery.com/schrockguide/math.html Art Links 2002 AMTNJ Symposium: Using Computers to Enhance Math Instruction mathforum.com/~shelly/presentations/AMTNJ/10.2002.html Art Instruction Books Cool Math Sites Fun Math Deliberately Distorting The Digital Mechanism Site 404.jodi.org, wrongbrowser.com & mirapaul@nytimes.com Math Art TUTORIALS Adobe Photoshop 7.0 M. O'Connor Template Project TEMPLATE TUTORIAL Copy Layer Photoshop 7.0 Rotate New Layer 90 degrees 1. Pull down the File menu and select new. Copy Layer In the dialogue box set Rotate New Layer 90 degrees 50 Pixels/inch 5 in x 5 in 2. In the toolbox select the Geometric Lasso Tool Create a spiral in towards the center, and then follow it back out. 3. Double click the foreground color box in the Color Picker at the bottom of the toolbox and select the color Red as the foreground color 4. Pull down the Edit menu and select Fill In the dialogue box select foreground color The will fill selection with red. 5. Pull down the Filter menu and select Distort>Twirl In the dialogue box set the Amount to –150 to –100 or 100 to 150 depending on the direction of the twirl you want to create Select OK and the lines on the image will twirl into a spiral 6. In the Layer menu select New Layer A new layer will appear in the Layer window 7. In the Layer menu select Layer Properties In the dialogue box Add drop Shadow seta t 120 degrees TEMPLATE Copy Layer M. O'Connor Rotate New Layer 90 degrees Math Art BLACK HOLE TUTORIAL BLACK HOLE Photoshop 7.0 File Menu: M. O'Connor New Image 150 pixels/inch 5 inches x 5 inches Edit Menu: Fill Fill Layer with Black Image Menu: Mode Screen Filter Menu: Add Noise… Gaussian Monochrome Image menu: Adjustments: Adjust levels Drag Far Left (Black) Arrow Right. Filter Menu: Blur> Radial Blur Amount: 25 Math Art Tessellation Tutorial Layer Menu: Photoshop 7.0 Copy Layer. Fill Selection with black. File: New Image Edit Menu: 150 Pixels/inch Fill, Fill background with white. 5 in x 5 in Layer menu: Edit: Align black and red selections. Merge Layers. Fill >Background with black Edit Menu: Toolbox: Copy Layer with black and red. Paste Rectangular Marquee Continue copying until image is full. In foreground, create a square that Is approximately 1/16th of the screen size Fill Background with black Edit: TESSELATION Fill>Fill Square with color (red) M. O'Connor Toolbox: Lasso tool: Create a selection including only parts from the right size of the square. Rectangular Marquee: Select half of square Edit Menu: Copy Selection Paste selection on a new layer Move selection until it is flush with opposing side. Layer Menu: Merge New layer with square layer Repeat process for top and bottom. Do not cross outside of the square when making selection. Math Art Cage and Curl Tutorial 7. In the toolbox select the Rectangular Selection Tool Photoshop 7.0 Make Vertical selections that extend from the top to the bottom of the image area 1. Pull down File Menu and create a New Image file In the dialogue box, use the following parameters 8. Pull down the Edit Menu and select Fill: 150 pixels/inch Fill each selection with 100% Black. 5 inches x 5 inches Each rectangle should look like a line Repeat Process with Horizontal Lines 2. Select the Paint Brush from the Toolbox and the Airbrush tool from the These lines will form boxes that indicate a cage menu bar Choose Color: Black The boxes should look tilted because of the swirl behind them. Set the brush size to Size: 35 (Soft) CAGE CURL 3. On the blank image Create Lines Create several Vertical Lines and Several Horizontal Lines. M. O'Connor Do not make them completely straight. 4. Pull down the Filter menu and select Distort>Pinch Set the Pinch to 100% 5. Pull down the Filter menu and select Distort>Twirl Set the Twirl to 72% Select OK and the original pinched lines will twirl 6. In the Layer menu Create a New Layer. Be sure this layer is selected in the Layer Window Math Art TUTORIAL PHOTOSHOP 7.0 UNRAVELLING UNRAVELLING M. O'Connor File Menu: New>New Image 150 Pixels/inch 5 Inches x 5 inches Toolbox: Paintbrush tool Color: Black Size: 35 (Soft) Create Lines Create several Vertical Lines and Several Horizontal Lines. Do not make them completely straight. Filter Menu: Polar Coordinates:>Rectangular to Polar Math Art TUTORIALS PHOTOSHOP 7.0 MATHEMATICAL DISTORTION R. Fackler Science Major In this exercise, I took a photo of my brother, added mathematical principles of geometry and algebraic graphing and turned the picture into a work of art. I believe you can make any subject fun by applying basic math principles to photographic images. This project allowed me to use my creativity while using the math concepts I have learned over the last four years. Rendered Brother- applied to a photograph based on the geometric principles Head embellished by using a sphere shape on a 35-degree angle field of view: 1. Pull Down the filter menu> Render>3-D transform. 2. Choose the sphere shape from the toolbox 3. Draw around the head 4. Tilt the sphere at a 35 –degree angle. This made the head almost look 3-D while the rest of the picture was flat. I thought about using other shapes to accent his body shapes, however it drew away from the essence of the geometric figures. POLAR COORDINATES R. Fackler Math Art MATHEMATICAL DISTORTION R. Fackler Polar Coordinate Brother- Modifications to a photographic image using mathematical concepts of algebraic graphing. Distortion One: 1. Start with the equation x = y 2. Set the image on a vertical slope at the points (0.0) on the x/y axis. This pulled the picture into the center of the graph distorting the picture into an oval shape. Distortion Two: 1. Select the Filter Menu>Distort> polar coordinate. 2. Choose the option rectangular to polar. Mathematical Distortion R. Fackler Math Art Math Concepts Polar Coordinates-Graphs: Illustrating Geometric Shapes: R. Fackler Centering equidistant to the midpoint: Filter/Render/3D Images Science Major Pulled image area into 0-0 on x-y axis Selected Cube Created an Oval of the original shape Tilted Axis by 15 degrees Math Art DIGITAL COMPASS P. Marriccinni Step 1. Open a new file that is 1200 by 1600 pixels and make a graph that ranges from at least 6 to –6 on the x and y axis using the line tool. Make a mark the x-axis and y-axis every 100 pixels. Make sure you use the rulers to make sure the space between each number is exact. Step 2. Draw the line y=x using the line tool. Start at point (-5, -5) which is 1300 pixels on the vertical line and at 100 pixels on the horizontal ruler. Then draw the line to point (5,5) which is 300 pixels on vertical ruler and 1100 pixels on the horizontal ruler. Draw the line y=-x, which starts at (- 5,5) which, is 300 pixels on vertical and 100 pixels on the horizontal ruler. Then end at point (5, -5) which is 1300 pixels on the vertical and 100 pixels on the horizontal ruler.. Math Art Step 3. Draw the line y=0 and the line x=0. They are on your axis but only draw them from 6 to –6. Math Art Step 4. Select the pen tool and make 3 anchor points on the line y=-x. One at where it started, one on the origin (0,0) which is 800 pixels on the vertical and 600 pixels on the horizontal ruler. Math Art Step 5. Hold down shift and click on the anchor point at the origin. Then move the mouse to make a curve. Then let go of the shift key and the mouse. Math Art (Step 5. Hold down shift and click on the anchor point at the origin. Then move the mouse to make a curve. Then let go of the shift key and the mouse.) Step 6. Repeat Steps 5 except make the curve the opposite way Math Art Step 7. Repeat step 6 for new curve (Step 6 Go to the anchor point on the end of the line that does not have the curve hold down shift and click on it. It will automatically make the curve for you.) Math Art Step 8. Repeat for line y=x Math Art Step 9. Repeat for line y=0 Math Art Tutorials Step 10. Finish line y=0 Math Art Tutorials Step 11. Make curves on line x=0 Math Art Step 12. Make a new layer with 30% opacity. Then write in the equations for some of the lines used next to them to label them. Math Art Step 13. Make new layer 100% opacity and label the units on the graph. Math Art Final Step. (Optional) Color in graph and add filter. Math Art STEP BY STEP THROUGH THE HISTORY PALLETTE History: - paint bucket - ellipse - ellipse - ellipse - ellipse - pattern fill 1 - liquefy - liquefy - line - line - line - line - line - line - line - line - pattern fill 1 - lens flare Math Art History: - pen - pen - pattern fill - ellipse - ellipse - pattern fill - ellipse - pattern fill - liquefy - liquefy - 3D transform Math Art Math Art TUTORIALS Adobe Photoshop 7.0 The figure above was drawn with the polygonal and the elliptical selection tools. The Foreground and Background colors were set to Black and White and the Gradient Tool was used to fill in the shapes. The letters were created by hand using the Pencil Tool, working with black in the white areas and white in the black areas for visibility. The figure above illustrates a surprising fact about triangles and circles. Given any triangle, within the A, B, C, points there is a circle that contains all of the following nine points: 1. The midpoints K, L, and M of the sides of the triangle ABC. 2. The points X, Y, and Z, where AX, BY, and CZ are the altitudes of triangle A, B, C. 3. The points R, S, and T, which are the midpoints of the segments AH, BH, and CH that join the vertices of triangle ABC to the point H where the lines containing the altitudes intersect. Math Art GALLERY OF STUDENT PROJECTS J. Williams To create this image I used the ellipse tool, the rectangle tool, the custom shape tool, the rounded rectangle tool and the polygon tool. I duplicated the shapes and used the Emboss Filter tool in the Stylize section of the Filters menu. Math Art This image was inspired by the lesson in geometric relationships on the classifications of quadrilaterals. It was created with the polygonal lasso, the gradient tool, the rectangular selection tool and the paint brush tool. Math Art This painting was done with the Adobe Photoshop. Tools used were the Paintbrush, Pencil, Polygonal lasso tool, Paint Bucket and Color Selection Tools. The Lasso was used to draw the shapes and the Paint Bucket and Brush Tools were used to fill in the colors. The paint Brush and the Pencil were used to draw in the lines and details. This lesson was designed to teach Mathematical Concepts using Art History for inspiration, in this case Richard Mortensen's work, and Adobe Photoshop for execution. Math Art To make the picture above: 1. Create a background with the gradient tool 2. Use the Filter Menu to create and color shapes: - Create shapes with the 3D Transform filter and the Cutout filter - Create effects with the Glass filter and the Lighting Effects filters. Math Art Math Art Math Art Math Art Shapes One Shapes Two Math Art Math Art Math Art STELLAR NAVIGATION G. Yap
Calculus is one of the greatest achievements of the human intellect. Inspired by problems in astronomy, Newton and Leibniz developed the ideas of calculus 300 years ago. Since then, each century has demonstrated the power of calculus to illuminate questions in mathematics, the physical sciences, engineering, and the social and biological sciences. Calculus has been so successful both because its central theme—change—is pivotal to an analysis of the natural world and because of its extraordinary power to reduce complicated problems to simple procedures. Clearly written and comprehensive, the tenth edition of Gustafson/Frisk/Hughes' popular book provides in-depth and precise coverage, incorporated into a framework of tested teaching strategy. The authors combine carefully selected pedagogical features and patient explanation to give students a book that preserves the integrity of mathematics, yet does not discourage them with material that is confusing or too rigorous. Long respected for its ability to help students quickly master difficult problems, this book also helps them develop the skills they'll need in future courses and in everyday life. This new edition has the mathematical precision instructors have come to expect, and by bringing in new co-author, Jeff Hughes, the authors have focused on making the text more modern to better illustrate to students the importance of math in their world
MicroComputers and Mathematics - J. W. Bruce - Hardcover 9780521375153 ISBN: 0521375150 Publisher: Cambridge University Press Summary: The interaction between computer and mathematics is becoming more and more important at all levels as computers become more sophisticated. This book shows how simple programs can be used to do significant mathematics. The purpose of this book is to give those with some mathematical background a wealth of material with which to appreciate both the power of the microcomputer and its relevance to the study of mathematic...s. The authors cover topics such as number theory, approximate solutions, differential equations and iterative processes, with each chapter self-contained. Many exercises and projects are included giving ready made material for demonstrating mathematical ideas. Only a fundamental knowledge of mathematics is assumed and programming is restricted to 'basic BASIC' which will be understood by any microcomputer. The book may be used as a textbook for algorithmic mathematics at several levels, with all the topics covered appearing in any undergraduate mathematics course. Bruce, J. W. is the author of MicroComputers and Mathematics - J. W. Bruce - Hardcover, published under ISBN 9780521375153 and 0521375150. Six MicroComputers and Mathematics - J. W. Bruce - Hardcover textbooks are available for sale on ValoreBooks.com, five used from the cheapest price of $22.20, or buy new starting at $229.30.[read more]
More About This Textbook Overview The History of Mathematics: An Introduction, Seventh Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools. Elegantly written in David Burton's imitable prose, this classic text provides rich historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social context behind mathematics' greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Seventh Edition a valuable resource that teachers and students will want as part of a permanent library. Editorial Reviews Booknews New edition of a text for junior and senior undergraduate students, and accessible to general readers. Provides an introduction to the achievements, prominent people, and development of concepts connected with math over the past 5,000 years. Interspersed throughout the text are problems of varying degrees of difficulty which typify a particular historical period and require the procedures of the time; working the problems teaches math as well as history. Annotation c. by Book News, Inc., Portland, Or. Booknews This account of the history of mathematics for junior and senior undergraduates highlights the lives of major mathematicians and uses math problems as an integral part of the text. Chapters chronicle different periods in the development of mathematics and discuss number and probability theory and non-Euclidean geometry. This third edition contains a new chapter on extensions and generalization, and adds material on several figures who were neglected in previous editions, including female mathematicians 25, 2011 MISSING LETTERS This was the hardest book to read on NOOK. If the woird had an i,f together then it wasn't there. This might not have been an issue if I had been READING it, but since I was listening to it every thir the word first or field or confirm was in the book it just read off the letters. was very confusing!!!! Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
Michael Geisen M.A., Southern Oregon University National Teacher of the Year Professor Michael Geisen was selected from among millions of public-school educators to serve as the National Teacher of the Year in 2008. In this position, he traveled nationally and internationally as an ambassador for the teaching profession, helping educators, policymakers, and community members meet the needs of high-school students in a rapidly changing 21st-century world. Professor Geisen was a middle-school science teacher at Crook County Middle School in Prineville, Oregon, for 10 years. He has received numerous other teaching awards and accolades. He was selected as the 2009 Outstanding Teacher in K-12 Education by the Oregon Academy of Sciences and was named the Toshiba Innovator in Education in Tokyo, Japan, and the 2007-2008 Oregon Teacher of the Year. How to Become a SuperStar Student, 2nd Edition ProfessorTransform your students' lives and give them the keys to success with this two-course set. Students will learn vital skills that will carry them through high school, college, and well into the challenges of adult life with How to Become a SuperStar Student, 2nd Edition. And they'll finally grasp all the major concepts of first-year algebra—including variables, order of operations, and functions—with the engaging and accessible Algebra I. Give your students the keys to success in high school and beyond with this engaging two-course set. They'll learn vital skills about everything from homework to class presentations to exam preparation with How to Become a SuperStar Student, 2nd Edition. And in The Secrets of Mental Math, they'll discover tips and tricks for enhancing their ability to solve a range of mathematical problems—right in their heads. Give your students the keys to lasting success with this engaging two-course set that gives them effective study skills—and places them inside the minds of their teachers. First, they'll get advice, tips, tricks, and resources for everything from homework and class participation to group presentations and test preparation in How to Become a SuperStar Student, 2nd Edition. Then, they'll explore education from the other side of the classroom by learning what makes for an effective and influential teacher in The Art of Teaching: Best Practices from a Master Educator.
Matlab is one of the most popular programs for quantitative analysis. This book introduces you to the basics of Matlab without requiring any previous experience of programming. About the book Description Matlab is one of the most popular programs for quantitative analysis. This book introduces you to the basics of Matlab without requiring any previous experience of programming.Through a series of easily followed examples, the book builds your knowledge step-by-step so that, at the end, you will master all the fundamentals of the program. Topics include how to import data, mathematical operations, graphics, and programming. Special attention has been given to debugging techniques and how to find further help. Examples include linear regressions, solving equations, and numerical integration. Content - An Introduction to Matlab Introduction Preliminaries and a map of the book - Features of Matlab The Desktop Some basics of using Matlab The order of precedence Some algebraic functions, special characters, and tips The syntax of functions Variables Different types of variables A note on interpretation and error messages How Matlab "searches for meaning" Matrices, vectors and scalars Creating matrices Addressing parts of matrices Changing parts of a matrix Some special commands for handling matrices The Workspace Browser and the Variable Editor More about matrices Mathematical operations with matrices Functions that operate element-by-element Elementary mathematical functions that operate columnwise Matrix algebra Solving systems of linear equations Finding linear regression coefficients Importing and exporting data The Current Folder Problems with importing formatted data Preparing data to import Copy-and-paste importing Importing using the Import Wizard Importing using commands Exporting to Excel files with commands More about importing and exporting data Graphics Useful commands for two-dimensional plotting Time series plotting Plotting a function Several graphs in one window and other types of graphs Other two-dimensional graphs Plotting tools More about graphics - Programming in Matlab Scripts The Editor Writing a script The search path User interaction with the script User defined functions About the differences between scripts and user defined functions More about functions Flow control Loops Relational and logical operators Conditional statements More about flow control Numerical analysis and curve fitting Solving equations Finding a function minimum point Numerical integration Curve fitting More about numerical analysis - Debugging and Help Debugging The Code Analyzer Executing part of the code with F9 Using breakpoints Checking programs for correct input Use comments More on debugging Help To find specific information on functions To find general information Online documentation from MathWorks The internet Appendix; Commands used in this book Endnotes About the Author Krister Ahlersten has a PhD in Finance from the Stockholm School of Economics and work with quantitative analysis, asset pricing, and risk assessment in the banking industry
Lake Station TrigonometryStructural systems are constantly modeled as matrices, i.e. the structural matrix, an applied force matrix, and the reaction matrix. I also took an advanced engineering mathematics course which focused a lot on matrix calculus and other advanced matrix operations. Linear programming is also som...
Introduction to Ordinary Differential Equations 9780486659428 ISBN: 0486659429 Pub Date: 1989 Publisher: Dover Pubns Summary: A thorough, systematic 1st course in elementary differential equations for undergraduates in mathematics and science, requiring only basic calculus for a background, and including many exercises designed to develop students' technique in solving equations. With problems and answers. Index. Landin, Joseph is the author of Introduction to Ordinary Differential Equations, published 1989 under ISBN 9780486659428... and 0486659429. Four hundred eighty four Introduction to Ordinary Differential Equations textbooks are available for sale on ValoreBooks.com, one hundred twenty four used from the cheapest price of $4.73, or buy new starting at $9
This is a free, online textbook that is a wikibook. "This book will help you learn how to do mathematics using Algebra. It... see more This is a free, online textbook that is a wikibook. "This book will help you learn how to do mathematics using Algebra. It has chapters (parts of the book) with lessons (parts of the chapter about one idea). A lesson has five parts: 1.Vocabulary - gives special words you need for the lesson. 2.Lesson - gives a new idea and how to use this idea. 3.Example Problems - gives the steps to do problems using the new idea. 4.Practice Games - gives places for amusement where you do problems. 5.Practice Problems - You do problems.״ This is a free online textbook from the Saylor Foundation.״This book is suited for Business Communication courses, but is... see more This is a free online textbook from the Saylor Foundation.״This book is suited for Business Communication courses, but is also appropriate for Business English, Business Presentation, Professional Communication courses. Scott McLean brings his authoring expertise to this new communications textbook. Scott has authored textbooks in the areas of Speech Communication, Interpersonal Communication and Public Speaking. Business Communications for Success benefits from Scott's extensive understanding of how students learn the art of effective communication. Students are provided ample opportunity to engage with the concepts, vocabulary and models covered in the text, including role-playing exercises, journal writings, case studies, small-group activities, games, and self-assessment activities.״ This is a free textbook offered by BookBoon.'Modern microeconomics book explains the advanced version of traditional... see more This is a free textbook offered by BookBoon.'Modern microeconomics book explains the advanced version of traditional microeconomic theories. It provides the explanation from consumer utility to general equilibrium in economy. This book therefore explains the economic units such as consumers and producers and their economic behaviors. The utility maximization of these units is subject to different constraints. The utility maximization approach of consumer and firm is different but it is complementary with each other. The main emphasis in this book is given on the game theory where producer and consumer play different type of games to get high payoffs. This book covers four distinct parts of microeconomic theory. This book is written as per the syllabus of master degree in economics. In addition to postgraduate course, it is also useful to the students pursuing their doctorate in economics. They could make use of this text to explain theoretical concepts to practical analysis of different microeconomic phenomena. The author has taken help of three methods such as theoretical explanation of concepts, diagrams and equations to illustrate microeconomics models. This book is different because of number of points.- This book provides the explanation of modern theories with simple examples. The consumer equilibrium, production function, game theory, information economics and social welfare are the major topics of this book.- This book provides the systematic analysis of the consumer utility and behavior. It is most relevant topic to the decision making of consumer. The revealed preferences, rational choice, utility maximization, indirect utility function, Roy's identity, Expenditure minimization function are the important topics of this book.- This book provides an explanation of modern theory of production function. There are different types of production functions and technology is used in each production function. Input output analysis, cost minimization, short run and long run costs, homogenous and heterogeneous production function, duality of costs and different types of technology in production function is strength of this book. The theory of Kalecki and kaldor of factor share in production function is also part of this book.- The game theory explains that every individual play a game to maximize payoff. But every game has certain rules. Nash equilibrium is explained with different examples in this book. There are co-operative and non-cooperative games which are again explained with different examples in this book. Welfare game is explained with the example of government and poor in rural economy. Both are maximizing their payoff subject to different constraints. Production related game of firm is explained as Bertrand, Cournot and Stackelberg model. These are the games related to market share of firms.- Information economics describes the applications of game theory. Moral hazard with hidden information is an important topic and it is explained with salesman game. Similarly adverse selection is explained with Lemon theory. There are different parts of Lemon theory and it gives brief idea of behavior of seller and buyer of lemon car. Adverse section under uncertainty explains the insurance game. Signaling and screening in relation to labor market is the advantage of this book.- The general equilibrium and social welfare is comprehensive part of this book but it is also basic strength of this book. It explains the welfare functions and the Pareto criterion. First and second theorem of welfare economics, market failure and second best is an important topic. Market failure is explained with different examples. Lastly coase theorem is explained with example.' This is a free textbook offered by Saylor Foundation.'According to Jack Lule, the world did not need another introductory... see more This free, online textbook "gives a self-contained introduction to quantum game theory, and is primarily oriented to... see more This free, online textbook "gives a self-contained introduction to quantum game theory, and is primarily oriented to economists with little or no acquaintance with quantum mechanics. It assumes little more than a basic knowledge of vector algebra. Quantum mechanical notation and results are introduced as needed. It is also shown that some fundamental problems of quantum mechanics can be formulated as games.״ ״In this text, we present various mathematical models of games and study the phenomena that arise. In some cases, we will be... see more ״In this text, we present various mathematical models of games and study the phenomena that arise. In some cases, we will be able to suggest what courses of action should be taken by the players. In others, we hope simply to be able to understand what is happening in order to make better predictions about the future.״ ״This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on... see more ״This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values, plus analyzes of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles.״ ״Games of Strategy: Theory and Applications, originally published by Prentice Hall in 1961, was written by Melvin Dresher, a... see more ״Games of Strategy: Theory and Applications, originally published by Prentice Hall in 1961, was written by Melvin Dresher, a RAND research mathematician, during the heyday of Game Theory at RAND. This book introduced readers to the basic concepts of game theory and its applications for military, economic, and political problems, as well as its usefulness in decisionmaking in business, operations research, and behavioral science. More than forty years after its first publication as a RAND research study, and to celebrate RAND's 60th Anniversary, RAND is proud to bring this classic work back into print in paperback and digital formats.״ ״These are lecture notes for a course in game theory which the author taught at the University of Kaiserslautern. Game Theory... see more ״These are lecture notes for a course in game theory which the author taught at the University of Kaiserslautern. Game Theory is a formal approach to study games: conflicts where some number of players take part and each one tries to maximize his utility in taking part in the conflict. This text covers general concepts of two person games, Brouwer's fixed point theorem and Nash's equilibrium theorem, more general equilibrium theorems, cooperative games and differential games.״ This is a free textbook offered by BookBoon.'How do team games make you feel; horrified, skeptical, apprehensive,... see more This is a free textbook offered by BookBoon.'How do team games make you feel; horrified, skeptical, apprehensive, embarrassed, excited?The benefit of team activities is seen when they are; well facilitated, congruent with learning outcomes, on going, proactive, well debriefed & followed up. This ensures they provide an influence long after the activity has concluded.This book explains 60 activities, facilitator skills & approaches, post activity debrief and follow up options and suggestions for debrief models, theories & concepts that will add depth and insight and ensure activities are more than a standalone 'game'.
"If you honor growth, you will consistently do what is best for all kids." What are NWEA Integrated Math assessments? Integrated Math assessments are part of the Upper Math test packages include in your MAP license. Integrated Math does not observe the traditional boundaries between algebra and geometry. Integrated Math courses may vary in the order in which topics are taught, but their one common feature is that algebra and geometry are not taught as separate components. Generally, more emphasis is placed on coordinate geometry and transformations and less is placed on formal axiomatic geometry in Integrated Math courses. It's also common for Integrated Math courses to include a substantial component of statistics and probability, which is not usually found in traditional algebra courses. The goal structures for NWEA's Integrated Math tests are very similar to the MAP 6+ goal structures for many states.
Rabu, 24 Juni 2009 silabus matematika kelas 8 SILABUS School Subject Grade/Semester Standard Competence Basic Competency 1.1 Solving Algebraic Forms Main Material Algebraic Form : SMP N 2 Cileunyi : Mathematics : VIII/1 : 1. To undestand of algebraic form, relation, function, and equation of straight line Learning Experience Using books, pencils, pens, and erasers that student have, to under stand the meaning of algebraic form Indicator a. to explain the notation of monomial, binomial, polynomial in one or more variables b. to solve operation of addition, subtraction, multipication, and power of monomial, binomial and polynnomial c. to factorize the term of algebraic forms up to a trinomial d. to solve the operation of addition, subtraction, multipication, division, of algebraic fraction with a denumerator of one term, two terms or the same term e. to simplify algebraic fraction Assesment Technic written test Form of quis Instrument 1. Give the example of monomial, binomial, trinomial, and other polynomial 2. Determine the result of a. 3x(2x + 5) b. (2x - 3)(3x + 5) Time Alocation 13 period written test essay 1.2 Analizing the Algebraic form into its factors written test essay 3. Factorize the following algebraic form 3x - 5x + 4 4. Look at the lesson plan written test essay written test essay 5. Look at the lesson plan 1.3 Understanding the relation and the function Function 1.4 Determing the value of a function Solve the daily problem a. describe the definition related to a function of a function b. explain whether a rela tion is a function c. explain in words daily problems related to a function d. determine the domain codomain, and range of a function e. explain a map form the element of a range f. explain a function using the arrow diagram, the Cartesian diagram and ordered pair g. explain the rule of a function h. mention the independent variable and dependent variable in a function i. express the graph of a function j. calculate the value of a function k. make a tabel of a function l. determine the arrow diagram of an enable function between two sets that have element i.e 1, 2, or 3 oral test oral test oral test quis quis quis 1. What is function? 2. What the condition of a relation which is a function? 3. Give the three examples of daily rpoblem are related to function. 4. Look at the lesson plan 16 period written test essay oral test written test essay essay 5. Look at the leson plan 6. Look at the lesson plan written test oral test essay quis 7. How is the relation to be a function. 8. f(x) = 2x - 7 What is the independent and the dependent variable of the function 9. Express f(x) = 3x + 4 in graph 10. Known: f(x) = 4x - 1 and x ∈ {1, 2, 3, 4, 5}. Calculate the vale of f for each x. 11. Write the result in no. 10 by a table 12. Draw the arrow diagram of a function of two sets that have 2 elements oral test written test essay essay written test written test esay essay m.determine the amount of function between two sets that have element n. mention the definition of one-one coresponden ce between two sets o. determine the existance of one-one corespon dence between two sets that have been known 1.5 Determining the slope, equation, and the graph of straight line The Equation Draw a kinds of straight a. determine the slope line of Straight Line on the Cartesian diagram oral test essay oral test quis 13. How many function of two will forming that the sets have 3 elements. 14. Write the example of one-one correspondence between two sets 15. Look at the leson plan written test essay written test essay 1. Determine the slope of line that through to points (5,2) and (9,4) 15 period g. graph the line if the slope and a point are known written test essay 7. Graph the line that through to point (3,-2) and the slope is -2. Standard Competency Basic Competency 3.1 Finding Pythagorean Theorm Main Material : 3. using Pythagorean Theorm on Problem Solving Learning Experience Indicator a. find the pythagorean theorm b. determine the length of side of a right triangle if the length of the other of two side is known c. determine ratio of sides of the special right triangle a.determine the length of the diagonal of the 2 dimention such as quare, rectangle, kite, rhombus, etc a. To define the Pythagorean numbers b. To classify triangles on the basis of the lengths of their sides Assesment Technic written test written test Form of quis essay Time Instrument Alocation 1. Write down the Pythagorean 12 period theorm. 2. What the length of hypotenuse of a rigth triangle if the others side are 6 cm and 8 cm? 3. Look at the lesson plan find the Pythagorean Theorm using models Pythagorean Theorm written test essay 3.2 Using Pytharean Theorm written test essay 1. The length of the sides of a square is 6 cm. What is the length of the diagonal? 3.3 Determine the converse of the Pythagorean theorm written test written test quis essay 1. Write three difference Pythagorean numbers. 2. The length of the sides of a triangle are 4 cm, 6 cm, and 7 cm. Is it the rigth triangle? SILABUS School Subject Grade/Semester Standard Competency Basic Competency 4.1 Determine the elements of a circle and parts of a circle Main Material : SMP N 2 Cileunyi : Mathematics : VIII/2 : 4. To understand the caracteristic of a corcle and using its on the problem solving Learning Experience Indicator a. determine the elements of a circle b. drawing the elements of a circle on a circle known Technic oral test written test Form of quis essay Assesment Instrument 1. Te cord is passing through the centre point of a circle is …. 2. Draw a segment of the circle Time Alocation 48 period Find the elements of a circle using models Elements of of a circle a Circle 4.2 Counting the Perimeter and the Area of a Circle The Perimeter and the Area of a Circle a. find the formula of perimeter of a circle b.discovering the formula of the area of a circle using models c. using the formula of the perimeter and the area of a circle to problem solving a. discription of a central angle b. determine the relation of central angle, arc, and sector c. calculate the area of a oral test oral test quis quis 1. What is the formula of the circumference of a circle? 2. What is the formula of the area of a circle? 3. The radius of a circle is 10 cm, what is the circumference and the area of a circle? 1. Explain the central angle of a circle. 2. What is the realtion of central angle, arc, and a sector of a circle? 3. The diameter of a circle is 14 cm, written test essay 4.3 Determine the relation between the central angle, the length of arc, the area of sector Central Angle, oral test written test quis esssay written test essay Arc, and Sector sector, the length of an arc calculate the area of a sector and the length of an arc if the central angle of the circle is 60 degree. 4.5 Find the Incircle and the Circumcircle of a triangle The Incircle and the Circumcircle a. drawing the incircle of a triangle b. drawing the circumcircle of a triangle a. to know the properties of tangent of a circle. b. To draw a tangent of a circle. c. to calculate the length of tangent of a circle. written test written test essay essay 1. Construct an incircle of a triangle 2. Construct a circumcircle of a triangle. 1. What are the properties of a tangent of a circle? 2. Draw the inner common tangents 3. The radius of circle A is 24 cm, and the radius of circle B is 14 cm The distance of A and B is 46 cm, what is the length of outer common tangents. 4.6 To calculate the length of the Com mon Tangents of Two Circles The Common Tangents of Two Circles oral test written test written test quiz essay essay Standard Competency Basic Competency 2.1 To solve the linear equation system with two variables 2. To undestand of algebraic form, relation, function, and equation of straight line Main Learning Experience Material Simultaneous solve the daily proof blem which connected Linear Equation with with Two Variableslinear equation with two variable Indicator a. review the linear equation with one variable Assesment Technic oral test Form of quis Instrument 1. x + 5 = 7 is called Linear Equation with one variable. Why? 2. Write 2 examples of linear equation with one variable 3. Siena have a box of books, then her mother give her 7 books. And now, Siena have 24 books. Write the problem in LEOV 4. Write 2 examples of Linear Equation with Two Variables. Time Alocation 24 period written test quiz written test quiz b. to state the definition of a linear equation with two variable c. to state whether or not a pair of numbers is a solution of a linear equation with two variables d. to state the difference between a linear equation with variable and a linear equation system with two variables e. to determine the solution or solution set of a written test quiz oral test essay 5. State the pairs of the numbers are the solution of x + y = 8 written test quiz 6. Explain the differences of Linear Equation with One Variable and Linear Equation with Two Variables. 7. Determine the solution set of Linear Equation system written test essay linear equation system with two variables x+y=7 x-y=3 by graph method 2.2 to make the mathematic model of the relalife problem are related to Linear Equation System with Two Variables f. to make the mathematic model of the real life problem are related to Linear Equation System with Two Variables written test quiz 8. The difference of two numbers is 8. Write it in the Linear Equation with Two Variables 9. The sum of two numbers is -5, and the product is 6. Write it in Linear Equation with Two Varia bles. 10. The sum of two numbers is 8, and the product is -20. What are the numbers? oral test quiz 2.3 To solve mathema tics model of the daily problem are related to Linear Equation System with Two Variables g. to determine the solution of a story problem related to a linear equation system with two va- written test esay Standard Competency Basic Competency 5.1 Determine the value on the three dimention Main Material Cubes and Cuboids : 5. Determining the elements and caracterisstic of a line and the shape of three dimention Learning Experience Indicator a. to identify the elements of cube and cuboids b. to draw cube and cuboid nets c. to state the formula of the surface areas of a cube and a cuboids d. to calculate the surface areas of a cube and a cuboids e. to find the formula of the volume and to calculate the volume of a cube and a cuboids f. to design a cube and a cuboid with particular volume g. to calculate the quantity of volume change of a cube or a cuboid if the edge measurement changes h. to solve a problem involAssesment Technic oral test written test oral test essay written test essay written test essay written test essay 6. The volume of a cuboid is 96 cm cubic. Make a design of the cuboid. 7. The length of edges of cuboid are p = 6 cm, l = 4 cm, and t = 3 cm. Calculate the quantity of volume change if the length changes to be 9 cm. Form of quis essay Instrumens 1. Mention the elements of a cube. 2. Draw 3 possible nets of cuboid 3. What is the surface area of cube and cuboids 4. The length of the edges of cube is 5 cm. What is the surface area of cube? 5. What is formula of volume of a cube? Time Alocation 52 period Find the area and the volum of a cylinders, cones, and spheres using models written test esssay written test essay ving a cube and a cuboid. Prisms a. to label a prism b. to state the formula of the volume of a prism c. to calculate the volume of a prism oral test oral test written test Pyramids a. to find the surface area of a pyramid b. to find the volume of a pyramid c. to recognizing and show faces, edges, face disgonal, and height of a pyramid d. to draw a pyramid e. to draw a pyramid nets and finding the area of a pyramid oral test oral test oral test 2. What is the formula of the volume of a prism 3. The area of the base of a prism is 45 cm square, what the volume of the prism if the height of the prim is 21 cm? 1. Make a discuss to find the formula of the surface area of pyramids 2. What is the formula of the volume of the pyramids? 3. Show and explain the element of pyramids written test written test 4. Draw a pyramid with 4 cm in heigth 5. Draw a pyramids nets on no. 4 then calculate the surface area of a pyramids. SILABUS Source Students Book at page 1 - 73 Source Students Book at page 105 127 SILABUS Source Students Book at page145 191 Source Students Book at page 75 - 103 Source Students Book at page 193 - 211 DISTRIBUTION TIME ALOCATION No 1 Standard Competence To understand of algebraic form, relation, function, and equation of straight line To understand sistem of linear equation with two variables and to used it in problem solving To used Pythagorean theorm on problem solving To understand the characteristic of a circle and used it on problem solving To understand the characteristics and the elements of cube, cuboids, prism, pyramid, and to determine the measurements Time Aloc 44 July Augst 55555 Semester 1 September October 555 4 November December January February March Semester 2 April May 2 24 155553 255 3 12 4 48 5555555553 5 52 2555 555555 : MOPD : Pasting Month and Idul fitri : : General Examination : Raport Preparation : Holydays : UAN The Principal Bandung, July Math Teach Drs. Tantan Rustandi NIP : 130678374 Kristiana Sili P NIP : 131879 June July 5 andung, July 2008 Math Teacher ristiana Sili P, S.Pd NIP : 131879319 PROGRAM SEMESTER GANJIL Mata Pelajaran : Matematika Kelas : VIII Tahun Pelajaran : 2008 - 2009 A. Perhitungan Alokasi Waktu 1. Banyaknya pekan Nama Bulan Juli Agustus September Oktober Nopember Desember Jumlah 2. Banyaknya pekan tidak efektif Kegiatan MOS + Rapat kerja Libur puasa + Idul Fitri Ulangan Umum Persiapan Raport Libur semester ganjil Jumlah 3. Banyaknya pekan efektif ( 24 - 8 ) pekan = 16 pekan 4. Banyaknya jam pelajaran 16 pekan x 5 jam pelajaran = 80 jam pelajaran Banyak pekan 1 3 1 1 2 8 Banyak pekan 3 4 4 5 4 4 24 PROGRAM SEMESTER GENAP Mata Pelajaran : Matematika Kelas : VIII Tahun Pelajaran : 2008 - 2009 A. Perhitungan Alokasi Waktu 1. Banyaknya pekan Nama Bulan Januari Pebruari Maret April Mei Juni Juli Jumlah 2. Banyaknya pekan tidak efektif Kegiatan UN kelas IX Ulangan Umum Persiapan Raport Libur Semester Genap Jumlah 3. Banyaknya pekan efektif ( 28 - 6 ) pekan = 22 pekan 4. Banyaknya jam pelajaran 22 pekan x 5 jam pelajaran = 110 jam pelajaran Banyak pekan 2 1 1 2 6 Banyak pekan 5 4 4 5 4 4 2 28 PROGRAM TAHUNAN Rincian Minggu Efektif dan istribusi Alokasi Waktu A. Rincian Minggu Efektif 1.a. Semester Ganjil Bulan Jumlah Minggu Hari Juli 3 17 Agustus 4 31 September 4 30 Oktober 5 31 Nopember 4 30 Desember 4 31 Jumlah 24 170 b. Minggu Tidak Efektif Minggu Keterangan 1 MOPD 1 libur awal puasa 2 libur idul fitri 4 akhir semester c. Minggu Efektif Jumlah Minggu tersedia tdk efktf efektif 2 1 1 5 5 4 1 3 5 2 3 4 4 4 2 24 6 16 B. Distribusi Alokasi Waktu No Standar Kompetensi, Kompetensi Dasar No 1 2 3 4 5 6 Bln Jul Sep Okt Des ALJABAR 1 Memahami bentuk aljabar, relasi, fungsi, dan persamaan gari lurus. 1.1 Melakukan operasi aljabar 1.2 Menguraikan bentuk aljabar ke dalam faktor-faktor nya. 1.3 Memahami relasi dan fungsi 1.4 Menentukan nilai fungsi 1.5 Membuat sketsa grafik fungsi aljabar sederhana pada sistem koordinat Cartesius 1.6 Menentukan gradien, persamaan dan grafik garis lurus. 2 Memahami sistem persamaan linear dua variabel dan menggunakannya dalam pemecahan masalah 2.1 Menyelesaikan sistem persamaan linear dua variabel 2.2 Membuat model matematika dari masalah yang berkaitan dengan sistem persamaan linear dua variabel 2.3 Menyelesaiakan model matematika dari masalah yang berkaitan dengan sistem persamaan linear dua variabel dan penafsirannya GEOMETRI DAN PENGUKURAN 3 Menggunakan teorema Pythagoras 3.1 Menggunakan teorema Pythagoras untuk menentukan panjang sisi-sisi segitiga siku-siku 3.2 Memecahkan masalah pada bangun datar yang berkaitan dengan teorema Pythagoras 4 Menentukan unsur, bagian lingkaran serta ukurannya 4.1 Menentukan unsur dan bagian lingkaran 4.2 Menghitung keliling dan luas lingkaran 4.3 Menggunakan hubungan sudut pusat, panjang busur luas juring dlam pemecahan masalah 4.4 Menghitung panjang garis singgung persekutuan dua lingkaran 4.5 Melukis lingkaran dalam dan lingkaran luar suatu segitiga 5 Memahami sifat-sifat kubus, balok, prisma, limas, dan bagian-bagiannya, serta menentukan ukurannya 5.1 Mengidentifikasi sifat-sifat kubus, balok, prisma, dan limas serta bagian-bagiannya 5.2 Membuat jaring-jaring kubus, balok, prisma, dan limas 5.3 Menghitung luas permukaan dan volume kubus, balok, prisma, dan limas Bln Jul Ags Sep Okt Nop Des JML No 2.a Semester Genap Bulan Jumlah Minggu Hari 1 Januari 5 31 2 Pebruari 4 28 3 Maret 4 31 4 April 5 30 5 Mei 4 31 6 Juni 4 30 7 Juli 2 14 Jumlah 28 194 b. Minggu Tidak Efektif Minggu Keterangan 1 lib smt ganjil 2 UAN/US 2 Ulum dan raport 2 libur smt genap c. Minggu Efektif Jumlah tersedia tdk efktf efektif 5 1 4 4 4 Bln Jan Apr Juni Juli Bln Jan Peb Mar Apr Mei Jun Jul JML 4 5 4 4 2 28 2 2 2 8 4 3 4 2 21 Alokasi Waktu 9 jp 8 jp 6 jp 4 jp 2 jp 15 jp 10 jp 6 jp 8 jp 6 jp 6 jp 5 10 15 10 8 20 10 22
Academic Literacy Mathematics Academic Literacy Mathematics It is extremely important that all new undergraduate students entering UIW begin their academic careers with a strong foundation. To ensure this, UIW requires new students to take a placement exam, which is a series of assessments in Reading, Writing, and Mathematics, to determine their readiness to succeed in college. These assessments identify students' academic strengths and also any needs that must be addressed in order to build a solid educational plan to gain full benefit of the UIW learning experience. Academic Literacy Math I ( ALMA 0318 ) is required of those students whose assessment scores in mathematics are below college level and indicate a need for development of basic algebraic skills normally associated with Algebra I. Academic Literacy Math II ( ALMA 0319 ) is required of those students whose assessment scores in mathematics are below college level and indicate a need for development of intermediate algebraic skills usually associated with Algebra II. Students required to take ALMA 0318 ( Math I ), must also take ALMA 0319 ( Math II ), unless they take and pass a challenge test administered by the Testing Center. They may also take a challenge test if they fail to satisfactorily pass an ALMA course. A grade of C or better is required to satisfactorily pass each course. All students must be continuously enrolled in an Academic Literacy Math course each semester until they have satisfactorily completed all requirements. Only then will they be allowed to take college-level mathematics courses, such as MATH 1304 ( College Algebra ). Course Description, ALMA 0318 ( Math I ): This course is a review of math topics from Algebra I: basic concepts of arithmetic and algebra, including number systems, expressions, and order of operations; integer and rational numbers, operations with real numbers and their properties; understanding and solving problems using ratios, proportions, decimals, and percents; exponents and their properties; solving linear equations and linear inequalities; problem solving techniques and word problems; and finally, polynomial operations. Course Description, ALMA 0319 ( Math II ): This course is a continuation of an extensive review of basic algebra skills. It focuses on operations with polynomials, factoring, fractional expressions, linear equations and their graphs, expressions and equations involving roots and radicals, solving quadratic equations, and an introduction to functions and functional notation. A structural approach to solving word problems is utilized throughout the course. Prerequisite: ALMA 0318 or satisfactory placement test score.
ISBN: 0321758951 / ISBN-13: 9780321758958 Introductory Algebra for College Students The Blitzer Algebra Series combines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum appeal. Blitzer's ...Show synopsis synopsis Introductory Algebra for College Students (Pearson) – Hardcover (2011) by Robert F. Blitzer Hardcover, Pearson 2011 6th edition. 768 pages ISBN: 0321758951 ISBN-13: 9780321758958 100% BRAND NEW ORIGINAL US HARDCOVER STUDENT 6th Edition / Mint...100% BRAND NEW ORIGINAL US HARDCOVER STUDENT 6th Edition / Mint condition / Never been read / ISBN-13: 9780321758958 / Shipped out in one business day with free trackingReviews of Introductory Algebra for College Students tHIS IS NOT THE COVER Of the book. Its orange and has a bottle cap on the cover. BUUT this book is great. It clearly lists the steps and reasons for the math eq. and such. Although I DESPISE the ANSWER KEY in the back because it only lists the answers for ODD NUMBERS. Other than that, the condition is great and the text is as well Unfortunately, this text was required for my class. I got to use the Lial series for PreAlgebra, and I will get to for Intermediate as well. They are much better for those who need more examples, description, worked problems, etc. This one assumes you know a lot
0133173inite Mathematics and Its Applications This text presents topics with straightforward, interesting applications intended to improve students' mathematical maturity while giving them an appreciation for the usefulness of mathematics. It includes many updated examples and over 200 new exercises. Recent Book Searches: ISBN-10/ISBN-13: 0597710368 / 978-0597710360 / 2000 Import and Export Market for Aluminium in India / Inc Icon Group International 0597709211 / 978-0597709210 / 2000 Import and Export Market for Unwrought Nickel and Nickel Alloys in China / Inc Icon Group International 0597709238 / 978-0597709234 / 2000 Import and Export Market for Unwrought Nickel and Nickel Alloys in Czech Republic / Inc Icon Group International 0597709246 / 978-0597709241 / 2000 Import and Export Market for Unwrought Nickel and Nickel Alloys in Denmark / Inc Icon Group International 0597709343 / 978-0597709340 / 2000 Import and Export Market for Unwrought Nickel and Nickel Alloys in Japan / Inc Icon Group International 0597709521 / 978-0597709524 / 2000 Import and Export Market for Unwrought Nickel and Nickel Alloys in United States / Inc Icon Group International 0597709556 / 978-0597709555 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Albania / Inc Icon Group International 0597709653 / 978-0597709654 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Czech Republic / Inc Icon Group International 059770967X / 978-0597709678 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in France / Inc Icon Group International 0597709785 / 978-0597709784 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Malaysia / Inc Icon Group International 059770984X / 978-0597709845 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Qatar / Inc Icon Group International 0597710007 / 978-0597710001 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Vietnam / Inc Icon Group International 0597710295 / 978-0597710292 / 2000 Import and Export Market for Aluminium in Ghana / Inc Icon Group International 0597710341 / 978-0597710346 / 2000 Import and Export Market for Aluminium in Hungary / Inc Icon Group International 059770905X / 978-0597709050 / 2000 Import and Export Market for Nickel in Sweden / Inc Icon Group International 0597709149 / 978-0597709142 / 2000 Import and Export Market for Nickel in Venezuela / Inc Icon Group International 0597709440 / 978-0597709449 / 2000 Import and Export Market for Unwrought Nickel and Nickel Alloys in Spain / Inc Icon Group International 0597709750 / 978-0597709753 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Israel / Inc Icon Group International 0597710139 / 978-0597710131 / 2000 Import and Export Market for Aluminium in Canada / Inc Icon Group International 0597710333 / 978-0597710339 / 2000 Import and Export Market for Aluminium in Hong Kong / Inc Icon Group International 0597710376 / 978-0597710377 / 2000 Import and Export Market for Aluminium in Indonesia / Inc Icon Group International 0597709084 / 978-0597709081 / 2000 Import and Export Market for Nickel in Thailand / Inc Icon Group International 0597709548 / 978-0597709548 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Denmark / Inc Icon Group International 0597709580 / 978-0597709586 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Austria / Inc Icon Group International 0597709599 / 978-0597709593 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Bahrain / Inc Icon Group International 0597709610 / 978-0597709616 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Bulgaria / Inc Icon Group International 0597709858 / 978-0597709852 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Russia / Inc Icon Group International 0597709955 / 978-0597709951 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in Tunisia / Inc Icon Group International 059770998X / 978-0597709982 / 2000 Import and Export Market for Worked Nickel and Nickel Alloys in United States / Inc Icon Group International 059771004X / 978-0597710049 / 2000 Import and Export Market for Aluminium in Argentina
Find more:Highlights: The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom.Texas Instruments : TI-34 MultiView Scientific Calculator Find more: Highlights: Texas Instruments TEXTI34MV TI-34 MultiView is ideal for middle school math, pre-Algebra, Algebra I and II, trigonometry, general science, geometry, and biology. MultiView display shows fractions as they are written on paper. View multiple calculations on a four-line display and easily scroll through entries. Enter multiple calculations to compare results and explore patterns on the same screen. Simplify and convert fractions to decimals and back again. Integer division key expresses results as quotient and Highlights: Free Shipping Highlights: The TI-34 MultiView scientific calculator was designed with educators in mind. It's ideal for use in these middle grades math and science classes: Middle School Math, Pre-Algebra, Algebra I & II, Trigonometry, General Science, Geometry and Biology. View multiple calculations on a four-line display and easily scroll through entries. See math expressions and symbols, including stacked fractions, exactly as they appear in textbooks. Highlights: The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom.Find more: Highlights: The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom.
MathsWorks is a series of teacher texts covering various areas of study and topics relevant to senior secondary mathematics courses. The series has been specifically developed for teachers to cover helpful mathematical background, and is written in an informal discussion style. The series consists of six titles: ? An Introduction to Functional... more... Sharkovsky's Theorem, Li and Yorke's "period three implies chaos" result, and the (3x+1) conjecture are beautiful and deep results that demonstrate the rich periodic character of first-order, nonlinear difference equations. To date, however, we still know surprisingly little about higher-order nonlinear difference equations. During the last ten years,... more... The Eighth International Conference on Difference Equations and Applications was held at Masaryk University in Brno, Czech Republic. This volume comprises refereed papers presented at this conference. These papers cover all important themes, conjectures, and open problems in the fields of discrete dynamical systems and ordinary and partial difference... more... Representing an introduction to tensor analysis, this book introduces tensors in symbolic notation and in Cartesian and curvilinear co-ordinates, amongst other things, as well as the algebra of second stage tensors. It imparts the required algebraic aids; and is directed at students on various engineering study courses. more... The book provides the reader with the different types of functional equations that s/he can find in practice, showing, step by step, how they can be solved. A general methodology for solving functional equations is provided in Chapter 2. The different types of functional equations are described and solved in Chapters 3 to 8. Many examples, coming from... more... Say goodbye to dry presentations, gruelling formulas, and abstract theories that would put Einstein to sleep, now there's an easier way to master the disciplines you really need to know Everyday Math Demystified has everything you need to know about essential mathematics, including arithmetic, ratios, and proportions, working with money, the International... more... This textbook, deals with tensors that are treated as vectors, and has a practical orientation. In addition to dealing with the classical topics of tensor books, new tensor concepts are introduced, such as the rotation of tensors, the transposer tensor, the eigentensors, the permutation tensor structure, etc. The book covers an existing gap between... more... Presents a series of analytic and numerical methods of solution constructed for important problems arising in science and engineering, based on the powerful operation of integration. This volume is meant for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students. more... Extending and generalizing the results of rational equations, Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures focuses on the boundedness nature of solutions, the global stability of equilibrium points, the periodic character of solutions, and the convergence to periodic solutions, including their periodic trichotomies.... more...
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From inside the book Review: Math Through the Ages: A Gentle History for Teachers and Others, Expanded Edition (Mathematical Association of America Textbooks) User Review - Lillian - Goodreads Great overview, not too heavy, and fed to you in short chapters on widely varying topics. It includes some problems and projects to further investigate at the end of each chapter. Great for teachers. This may be inspiring to me for programs or just outreach to people facing math homework.Read full review Review: Math Through the Ages: A Gentle History for Teachers and Others, Expanded Edition (Mathematical Association of America Textbooks) User Review - Brian Carpenter - Goodreads The collection of sketches on mathematical history contained in this book were, for the most part, interesting to read. Many of them provoked additional thoughts or drove me to look up new sources ...Read full review
12,033including precalculusincluding precalculus precalculus
College Mathematics offers a refreshing approach to the traditional content of the course. Presented in worktext format, Basic College Mathematics focuses on basic number skills: operations and problem-solving with whole numbers, fractions, and decimals. Other topics include geometry, measurement, ratios, proportions, percents, and the real number system (with an introduction to algebra). The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of developmental level students.
Synopses & Reviews Publisher Comments: Whether you're a science major, an engineer, or a business graduate, calculus can be one of the most intimidating subjects around. Fortunately, Calculus for the Utterly Confused is your formula for success. Written by two experienced teachers who have taken the complexity out of calculus for thousands of students, this book breaks down tough concepts into easy-to-understand chunks. Calculus for the Utterly Confused shows you how to apply calculus concepts to problems in business, medicine, sociology, physics, and environmental science. You'll get on the road to higher grades and greater confidence, and go from utterly confused to totally prepared in no time! Inside, you'll learn about Calculus problems with applications to business and economics How to use spreadsheets for business analysis Growth and decay models including exponential and logarithmic models for biology How to integrate algebra into business analyses Synopsis: "Synopsis" by McGraw,
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Elementary and Inter. Algebra : Graphs and Models - 4th edition Summary: TheBittinger Graphs and Models Serieshelps readers learn algebra by making connections between mathematical concepts and their real-world applications. Abundant applications, many of which use real data, offer students a context for learning the math. The authors use a variety of tools and techniques-including graphing calculators, multiple approaches to problem solving, and interactive features-to engage and motivate all types of learners32346-5-0 $33.87 +$3.99 s/h Good SellBackYourBook Aurora, IL 0321726340 Item in good condition. Textbooks may not include supplemental items i.e. CDs, access codes etc... All day low prices, buy from us sell to us we do it all!!46 +$3.99 s/h Good TextbookBarn Woodland Hills, CA 032172634087
Mathematics Department Student Learning Outcomes The mathematics faculty at Seattle University aims to prepare students to use and continue their study of mathematics after graduation. Graduates should have the knowledge and skills needed to succeed in appropriate employment in teaching, business, or industry or to enter a graduate program in mathematics, statistics, mathematics education, or related field. They should possess the confidence, independence, and knowledge base to learn new mathematical ideas and skills. To this end, mathematics majors who complete any of the three mathematics programs at Seattle University will: Possess breadth of mathematical knowledge. Students will demonstrate an understanding of foundational mathematics in calculus, linear algebra, and differential equations. Possess depth of mathematical knowledge.Building upon a solid foundation, students will demonstrate a depth of understanding in advanced mathematical topics. Develop algorithms and use computation proficiently. Students will possess strong algorithmic reasoning skills and be able to analyze and solve a wide variety of mathematical and real-world problems either exactly or approximately. They will know when and how to use software or programming languages in their analysis of these problems. Understand and write rigorous proofs for theorems. Students will be skilled in a variety of proof methods and have strong axiomatic reasoning skills. They will be able to apply these skills creatively to make persuasive logical arguments in various contexts. Communicate mathematical ideas effectively in speech, writing, and collaborative groups. Students will use precise mathematical language and express results verbally and in writing. They will be capable of working collaboratively to frame and solve complex problems.
More About This Textbook Overview Math Connects: Concepts, Skills, and Problem Solving was written by the authorship team with the end results in mind. They looked at the content needed to be successful in Geometry and Algebra and backmapped the development of mathematical content, concepts, and procedures to PreK to ensure a solid foundation and seamless transition from grade level to grade level. The series is organized around the new NCTM Focal Points and is designed to meet most state standards. Math Connects focuses on three key areas of vocabulary to build mathematical literacy, intervention options aligned to RtI, and a comprehensive assessment system of diagnostic, formative, and summative
Introduction to Graph Theory (Dover Books on Mathematics) for an Amazon Gift Card of up to £1.43, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more Book Description Publication Date: 17 Mar 2003 \| Series: Dover Books on MathematicsAlthough it's an "introduction", this gem of a book ends up in some quite deep territory. Trudeau starts off with some basic definitions of set theory concepts and then moves forward to define graphs in those terms. Concepts such as planarity, connectedness, polygonality and colourings are quickly and smoothly reached, and the back end of the book covers genuses (which I thought was pretty incongruous for an "introduction"). Proofs of the Five Colour Theorem and the Heawood Colouring Theorem are included, as well as demonstrations of Euler's Formulae and Kuratowski's Theorem. Trudeau's style is completely non-indimidating and patient - almost conversational - and he conveys a real enjoyment of the subject. Non-mathematicians will be able to follow almost all of his arguments quite easily and, for this reason above all others, he deserves 5 stars. P.S. I spotted quite a large howler towards the end of the book: the Four Colour Theorem is stated as having "just been proved" - it was proven in 1977, which goes to show how old this book is! Having never encountered graph theory before, I decided to purchase this book. It is a delight to read, and progresses very gently through the subject. The author has targted this book at people who don't necessarily want to get bogged down with heavy math jargon, and any jargon delivered is introduced very nicely with great explanations. The book is a small paperback so very transportable. A dedicated reader could probably swallow the contents of this book in a few days. Not for the faint hearted or novice but good for someone trying to get beyond novice or A level graph theory. Having some knowledge of proofs and undergrad discrete maths will help.However, when I revisit my graph algorithms in computer science I found I had a better understanding than before purchasing the book. Graph theory normally receives little if any attention at school but is an interesting subject with a range of practical applications. This is an extremely lucid introduction, requiring very little previous mathematical knowledge - just elementary arithmetic - and is readily comprehensible to non-specialists. Thoroughly recommended.
Introductory Algebra - 2nd edition ISBN13:978-0077281120 ISBN10: 0077281128 This edition has also been released as: ISBN13: 978-0073406091 ISBN10: 0073406090 Summary: Introductory Algebraoffers a refreshing approach to the traditional content of the course. Presented in worktext format,Introductory Algebrafocuses on solving equations and inequalities, graphing, polynomials, factoring, rational expressions, and radicals. Other topics include quadratic equations and an introduction to functions and complex numbers. The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of dev...show moreelopmental level students. ...show less499.00 +$3.99 s/h Good Lucky's Textbooks Dallas, TX 0077281128
*Please note that this may be stricter when compared to your other classes. An absence is defined as failure to be present for a scheduled class meeting, arriving for the class more than ten minutes after the scheduled time for the class to begin, missing ten or more minutes during the middle of class, or leaving class early. 2.Absences are counted from the first day of class. 3.Three tardies are considered as one absence. A tardy is defined as "arrival in class after the instructor has taken attendance and before ten minutes after the scheduled time for the class to begin." If you are tardy, it is your responsibility to inform the teacher that you came in late. 4.You are responsible for all material/announcements presented whether you are present or absent. If you are more than 10 minutes late, you are officially absent. Students who exceed the allowed number of absences will be dropped from the course and receive a grade of W if passing or WF if failing after midterm. Students who drop a course, or are withdrawn from a course are responsible for any impact concerning Financial Aid. Course average will be determined by counting 75% of your final exam grade and 25% of your quiz/homework grades. A satisfactory grade will be required to enroll in Mat-101 and unsatisfactory will require you to enroll in Mat-100. You should not retake the College's Placement Test once you begin this course. Date Assignment Orientation & Assessment Test TBA TBA TBA TBA TBA TBA Final Exam Course Topic Outline/Course Calendar with Assignments: Airport Campus Date Assignment Orientation & Assessment Test TBA TBA TBA TBA TBA TBA Final Exam PLEASE NOTE: Should change become necessary, the instructor reserves the right to adjust the requirements, pace, or scheduling of this course. Any change will be announced in class before it becomes effective. Mat 010 Fast Track Dev Math CATALOG COURSE DESCRIPTION: This course serves as an intensive refresher course that helps students develop the basic skills needed to be successful in curriculum-level Mat-101. TEXTBOOK(S):No book required. Students will receive hand-outs from instructor. Purchase MyMathLab/CourseCompass software. EQUIPMENT: Scientific Calculator GRADING SCALE: 75% or above Satisfactory Below 75% Unsatisfactory COURSE OBJECTIVES:Upon completion of this course the student will be able to: demonstrate understanding of basic order of operations, use exponent rule, perform operations with polynomials, and solve algebraic equations. COURSE OUTCOMES AND COMPETENCIES: Intended Course Outcome:Students will demonstrate an overall knowledge of the learning objectives for introductory algebra including order of operations, integers, expressions, equations, and factoring Course Competency:Students will be able to: 1.Demonstrate understanding of basic order of operation 2.Use exponent rules 3.Perform operations with polynomials 4.Solve algebraic equations Performance Measurement Instrument and Success criteria:Students will meet the course competency by responding to questions on the standardized final exam which includes the following individual competencies: 1. Demonstrate understanding of basic order of operation 2.Use exponent rules 3.Perform operations with polynomials 4.Solve algebraic equations College Policies and Expectations Students are expected to read the MTC Student Handbook and abide by its policies. Some of the more important policies that impact your academic work are below. The Handbook is located on the web: . Copies of the handbook are also available at various locations on campus. Academic Integrity – The students of MTC have adopted the following Honor Code: As a member of the Midlands Technical College community, I will adhere to the college's Student Code. I will act honorably, responsibly, and with academic integrity and honesty. I will be responsible for my own academic work and will neither give nor receive unauthorized or unacknowledged aid. I will behave courteously to all members of the MTC community and its guests and will respect college property and the property of others. The Student Code addresses what constitutes academic dishonesty. All forms of dishonesty including, but not limited to, cheating on tests, plagiarism, collusion and falsification, will result in discipline. CHEATING ON TESTS includes: .Copying from another student's paper. .Using materials during a test not authorized by the person giving the test. .Collaborating with any other person during a test without permission. .Knowingly obtaining, using, buying, selling, transporting, or soliciting in whole or part the contents of any un-administered test. .Bribing any other person to obtain information about tests. .Substituting for another student, or permitting another student to substitute for oneself. PLAGIARISM is taking another person's work and using that work without giving the source credit in any assignment turned in for credit. For more information, see Appendix I at the end of MTC Student Handbook. .If a college-wide emergency occurs, the college will use a variety of methods to communicate additional information and instructions including the MTC Information Centers, campus loud speakers, MTC Alerts!, voice mail, email, college Intranet, and the MTC website homepage. (Sign up for MTC Alerts! at Inclement Weather Policy: In the event that weather conditions or other emergencies cause the closing or a delayed start of Midlands Technical College, announcements will be made over local radio and TV stations, on the MTC Web site, and on the college's information line (803-738-8324). .Notices will be sent to students via Campus Cruiser Mail when applicable. Separate announcements may be made for day and evening classes as weather conditions change during the day. .If the college closing or reopening means that there is at least 30 minutes of a class remaining, plan to attend that class. For example, if the college opens at 10:00 a.m., in TTH, classes that normally meet at 8:00 a.m. will not meet, but classes beginning at 9:30 a.m. will meet. If the college closes at 8:00 p.m., 6:00 p.m. classes will meet for their regular time, but 7:35 p.m. classes will not meet since there are fewer than 30 minutes remaining in class. Student E-Mail Accounts: All MTC students are assigned a college e-mail account upon admission to the college. This account is called "Campus Cruiser Mail." Follow the link on the Enrolled Students page or go to .Campus Cruiser Mail is the primary mode by which the college communicates with students. Students are responsible for checking their college e-mail on a regular basis for important information and announcements about registration, financial aid, cancelled classes, emergency announcements and other notices. .Students can use their college e-mail accounts to communicate with faculty, staff, fellow students, and others, on college-related activities. In addition to e-mail, students can maintain personal calendars and "tasks lists" through their Campus Cruiser e-mail account. MTC Online: The college conducts business with students and has many services and resources for students through MTC Online. Follow the link on the Enrolled Students page or go to midlandstech.edu/mtconline. Student Evaluation of Instruction: Toward the end of the semester, students will have the opportunity to evaluate this course. The confidential evaluation process is conducted through MTC Online using the individual student's username and password. Announcements will be made during the term concerning how and when to complete the online evaluation. Students are encouraged to participate in this process. Students Requiring Special Accommodations: .If special accommodations are needed for a student with a disability, the student should go to Counseling Services in the Student Center on Beltline or Airport Campus for assistance. Documentation regarding a specific disability is required in order for special arrangements to be made. Confidentiality of information received will be maintained. .For more information, go to the Counseling and Career Services link on the Enrolled Students page.
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STUDENTS' ATTiTUDE TOWARDS THE USE OF SCIENTIFIC CALCULATORS IN MATHEMATICS EXAMINATION BY SANI SAIDU DEPARTMENT OF MATHEMATICS FEDERAL COLLEGE OF EDUCATION ZARIA BEING PAPER PRESENTED AT A WORKSHOP ORGANISED BY NATIONAL MATHEMATICAL CENTRE ABUJA NIGERIA FROM 20 TH -25 TH JUNE, 2010 Abstract Literatures have shown that calculators and computers have been integrated into the mathematics curriculum of many countries in the world, but in Nigeria the story is different. The aim of this paper was to find the students views on the usage of scientific calculators in public examination such as UTME, NECO SSCE. Sixty candidates were randomly sample in four different examination centers during 2010 Unified Tertiary Matriculation Examination. Data was collected using questionnaires. Both descriptive and inferential statistics were used to analyze the result. The findings of the study include the following: The candidates' posses' scientific calculators; they can also use scientific calculators well. However the findings showed that candidates always device other means of checking how reasonable the answer given by calculators is, before they use it. Finally some recommendations were given. 2 Introduction The invention of Logarith m tables, slide rule, calculators and computers is meant to make computations easier. However, the introduction of calculators in teaching and learning of mathematics in many countries generated a lot of debates and controversies. Despite these debates and controversies there are evidences which show that calculators and computers are used in teaching and learning as well as examinations in many education systems in the world, Kiano& Salani (2004). In addition to this, Waits & and Bert (1994) reported that the use of hand held calculators has forever changed the way students are taught and forever changed the way students learn mathematics. Computing quickly and accurately is very essential in solving mathetimatical problems. The method may be mental mathematics, paper and pencil, calculator or computer but this is just one part of problem solving process. Students must also know what kind of operation to perform and be able to identify the appropriate numb er to use. In other words Hembree and Dessart (1986) assert "real mathematics means knowing a variety of strate gies for problem solving and having the ability to apply them appropriately . 3 Professional Mandates for Using Calculators (NCTM, 2000) declared that calculators should be used in school at all levels. NCTM expected that the tool would aid algorithmic instruction, support concept development, reduce demand for memorization, enlarge the scop e of problem solving, provide motivation and encourage d iscovery, exploration and creativity. Similarly, the Australian Association of Mathematical Teachers has a policy on students' use of calculators. It suggests that scientific calculators should be used in the early secondary schooling both as instructional aids and as a learning tool. (R eys, & Senuma, 1996) reported that current course of study in Japan permits the use of calculators after grade 3. That is from Grade 4 up-ward. The situation is different in Nigeria where the use of scientific calculators is no t allowed in most public examinations. In examination such IJMBE, NECO SSCE, WASSCE and UTME students are not allowed to use scientific calculators. Why is our policy different from that of the developed countries? This paper is aimed at finding the students reaction to this development in 4 Nigeria and consequently to find out their general attitude towards the use of calculators in public examinations. Research Questions The following questions were asked in o rder to tackle the problem at hand. What are the students views on:- i. The accessibility of scientific calculators by th e students ii. The usage of scientific calculators by the students iii. The level of dependence on calculators by the student s Hypotheses The following hypotheses were formulated based on the above research questions: (i) Students do not have access to scientific calculators (ii) Students do not enjoy the use of scientific calculators in examinations. (iii) Students do not depend completely on the answers produce by scientific calculators during examinations . 5 Literature Review Due to the debates on the use of calculato rs in schools, there exist a lot of literatures on the topic. One of the most famous researches is that of Hembree and Dessarts (1986) who conducted a Meta-analysis of the effects of pre-college calculators' use. They analyzed the results of seventy-nine research reports on student's achievement and attitude towards mathematics. Each study involved on group of students using calculators and another group having no access to calculators. Hambree and Dessart (1986) concluded that the calculator "did not delay student acquisition of conceptual skill and that it significantly improved their attitude and self concept. Also Mc Cauliff (1994) quoted Hembree and Dessart (1986) saying that in general, research found that students using calculators possessed a better attitude towards mathematics than the students who are not using calculators. Similarly Mccauliff (2002), cited Smith (1997) who analyzed twenty four research studies conducted from 1984 to 1995, asking questions about attitude and achievement due to use of 6 calculators, Smith compared students using calculators with students not using calculators. Smith study showed that calculators had positive effects on increasing conceptual knowledge and positive attitude toward mathe matics. In an article on choosing the proper calculator for classroom, Denama and Osborne (1988) argue that classrooms should use scientific calculator which will perform operation in the correct order, rather than commercial calculator, which will perform operations as they are entered. For example, a scientific calculator will correctly evaluate 3x4+5x2 as 2 2, while most commercial calculators will display 34. More so, Bert & Denama (1998) stated that the use of calculators provide an unparalleled opportunity to deliver better mathematics education than we have ever thought possible. And it can be delivered to all students because of the rapid expansion of inexpensive powerful calculator and computer technology all over the world. Infact with less than N 200 a student can purchase a scientific calculator. 7 Methodology The target of the study was the candidates of Unified Tertiary Matriculation Examination (UTME 2010 ). The study was carried out in four examination centers at Federal College of Education, Zaria. Data was collected using a questionnaire. The questionnaire was validated by a chief lecturer in the above named college. The data was analyzed using the statistical package for social science (SPSS). The questionnaire consisted of 4-point Likert scale. I.e. Strongly Agreed (S.A), Agreed (A) Disagree (D) strongly Disagree (S.A) . The Quantitative variables in the study are as follows: Accessibility to scientific calculator (i) I can afford to buy a scientific calculator (ii) I have a scientific calculator Usage of Scientific Calculator (iii) I can use scientific calculator well (iv) I enjoy using calculators in learning and during examination (v) I use only calculators in the classroom 8 (vi) I use both four figure table & calculators in the classroom Dependence on Calculators (vii) Anything that calculator can be use for; I can do it using four figure tables. (viii) I feel handicapped in examination without a calculator (ix) I accept any answer that appears on the screen of my calculator without checking (x) I always find other means of checking how reasonable an answer given by a calculator is, before I use it. Findings As presented earlier, the variable s in the questionnaires are grouped as follows; V 1 and V 2 are tie together under accessibility; while calculator usage comprised of V 3 , V 4 , V 5 and V 6 , lastly V 7 , V 8 , V 9 and V 1 0 are put together under dependence on calculators. The result were summarize in the table below. 9 Summary of't' test students attitude towards the usage of calculators Source N df t-value Decision Accessibility 60 59 12.236 Rejected to calculators Usage of 60 59 4.649 Rejected calculators Dependence 60 59 2.579 Retained on calculator Accessibility to calculator: Results from the descriptive statistics on V 1 and V 2 shows that the means are 3.77 and 3.27 respectively. Which implies th at majority of the candidates can afford to buy scientific calculators and they also posses' scientific calculator. Furthermore, the hypothesis which says students do not have access to calculators is rejected as it ca n be seen above. Usage of calculators: The results obtained from the descriptive statistics on V 3 , V 4 , V 5 , and V 6 are as follows: First, majority of the students indicated that they can use scientific calculators very well, with mean 3.33; they also said 10 that they enjoy using scientific calcul ators with mean 3.03. However, the candidates answered that they don't use only calculators in the classroom and also during examination with mean of 2.47, which means they can use both calculators and four figures tables with mean of 3.10. The t-test result for the hypothesis which says students do not enjoy the use scientific calculators in examination is also rejected. Dependence on calculators: Results from descriptive statistics on V 7 showed that candidates can use other means such as four figures tables in the absence of calculators yet the out come of V 8 indicated that majority feel handicap in examination in the absence of scientific calculators. V 8 and V 9 results showed that students do not solely depend on answers produce by their scientific calculators they always find other means of verifying the answer. Finally the hypothesis which says students do not solely depend on calculators is retained. 11 Conclusion Problem solving in mathematics is not only performing calculations rather calculations are only part of problem solving. Since scientific calculators are cheap and affordable by student; and they are use in teaching and learning in different countries. There is need for our policy makers to reexamine the policies on the usage of scientific calculators in senior secondary schools and public examinations. Recommendations (1) Government should redesign the senior se condary school curriculum to incorporate the use of scientific calculators (2) Examination bodies such as JAMB , NECO and WAEC should allow students to use scientific calculators in examinations. 12 References Bert, K.W, & Demana F. (1998). The Role of Hand -Held computer symbolic Algebra in Mathematics Education in the Twenty-First century: A call for Action.Retrievedfrom:httR/ ard.org/ Q/math/htm/indica Danama, R.& Obsborne, F (1986). The Role of Hand - Held Calculators in Mathematics Education: A meta - Analysis. Journal for Research in Mathematics Education,17(2)83-89 Hembree, R. & Dessarts, D. (1986). Effects of Hand held calculators in Pre-college mathematic education: A meta Analysis. Journal for Research in Mathematics Education. 17 (2), 83-89. McCauliff, R. (2002). The Calculator in the Elementary Classroom. Making a Useful tool out of ineffective crutch Retrieved from http/ National Council of Teachers Mathematics, NCTM (2000): Principles and standard for school mathematics, April 2000 Kiano L.M and Salani E.B. (2004), Gender a ttitude in the use of calculators in junior secondary in Botswana. Proceeding of the 28 t h Conference of the International Group for the Psychology in Mathematic Education. Reys,B & Senuma,F (1996).The Development of Computation In Three Japanese School. The Elementary School Journal,98 -24
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
Product Description Welcome to the Pumped-Up World of Pre-Algebra.With all those Xs and Ys, pre-algebra can be very intimidating for students, and it can seem like a whole new language. Building on math fundamentals, this program eliminates the intimidation factor by presenting the material in an easy-to-understand manner using plenty of examples and computer graphics. With this program and the right preparation, pre-algebra is as easy as 1-2-3!Topics include: Tree diagrams, prime factorization, greatest common factor, least common multiple, absolute value, square roots, radical signs, negative roots, and perfect square.Grade Level: 8-12. 26
Note: This page contains sample records for the topic graph interpretation skillsGraphs have a broad use in science classrooms, especially in physics. In physics, kinematics is probably the topic for which graphs are most widely used. The participants in this study were from two different grade-12 physics classrooms, advanced placement and calculus-based physics. The main purpose of this study was to search for the relationships between student spatial ability, logical thinking, mathematical achievement, and kinematics graphsinterpretationskills. The Purdue Spatial Visualization Test, the Middle Grades Integrated Process Skills Test (MIPT), and the Test of Understanding Graphs in Kinematics (TUG-K) were used for quantitative data collection. Classroom observations were made to acquire ideas about classroom environment and instructional techniques. Factor analysis, simple linear correlation, multiple linear regression, and descriptive statistics were used to analyze the quantitative data. Each instrument has two principal components. The selection and calculation of the slope and of the area were the two principal components of TUG-K. MIPT was composed of a component based upon processing text and a second component based upon processing symbolic information. The Purdue Spatial Visualization Test was composed of a component based upon one-step processing and a second component based upon two-step processing of information. Student ability to determine the slope in a kinematics graph was significantly correlated with spatial ability, logical thinking, and mathematics aptitude and achievement. However, student ability to determine the area in a kinematics graph was only significantly correlated with student pre-calculus semester 2 grades. Male students performed significantly better than female students on the slope items of TUG-K. Also, male students performed significantly better than female students on the PSAT mathematics assessment and spatial ability. This study found that students have different levels of spatial ability, logical thinking, and mathematics aptitude and achievement levels. These different levels were related to student learning of kinematics and they need to be considered when kinematics is being taught. It might be easier for students to understand the kinematics graphs if curriculum developers include more activities related to spatial ability and logical thinking. This website application provides practice interpreting line plots. The format of the website makes it available to use with individual students on one computer or with an entire class on an interactive white board. Each practice problem is submitted to determine if it is correct, when an incorrect answer is submitted the correct answer and an option for an explanation appears. Each problem set is also timed and the user is provided with a percent correct. This website does have a membership option for a fee which would enable the teacher to track the progress of multiple students over time. \\u000a Most visualization tools fail to provide support for missing data. In this paper, we identify sources of missing data and\\u000a describe three levels of impact missing data can have on the visualization: perceivable, invisible or propagating. We then\\u000a report on a user study with 30 participants that compared three design variants. A between-subject graphinterpretation study\\u000a provides strong evidence for This study examined the relationship between mathematics background and performance on graph-related problems in physics before and after instruction on the graphical analysis of motion and several microcomputer-based laboratory experiences. Students identified as either having or not having a graphing technology enhanced precalculus mathematics background were further categorized into one of four groups according to mathematics placement at the university. The performances of these groups were compared to identity differences. Pre- and Post-test data were collected from 589 students and 312 students during Autumn Quarter 1990 and Winter Quarter 1991 respectively. Background information was collected from each student. Significant differences were found between students with the technology enhanced mathematics background and those without when considering the entire populations both quarters. The students with the technology background were favored Autumn quarter and students without the technology background were favored Winter quarter. However, the entire population included an underrepresentation of students at the highest and lowest placements; hence, these were eliminated from the analyses. No significant differences were found between the technology/no technology groups after the elimination of the underrepresented groups. All categories of students increased their mean scores from pretest to post-test; the average increase was 8.23 points Autumn Quarter and 11.41 points Winter Quarter. Males consistently outperformed females on both the pretest and the post-test Autumn 1990. All students found questions involving the concept of acceleration more difficult than questions involving velocity or distance. Questions requiring students to create graphs were more difficult than questions requiring students to interpretgraphs. Further research involving a qualitative component is recommended to identify the specific skills students use when solving graph-related physics problems. In addition, it is recommended that a similar study be conducted to include a control group not participating in the microcomputer -based laboratory experiments. The interpretation of data and construction and interpretation of graphs are central practices in science, which, according to recent reform documents, science and mathematics teachers are expected to foster in their classrooms. However, are (preservice) science teachers prepared to teach inquiry with the purpose of transforming and analyzing data, and interpreting graphical representations? That is, are preservice science teachers prepared to teach data analysis and graphinterpretation practices that scientists use by default in their everyday work? The present study was designed to answer these and related questions. We investigated the responses of preservice elementary and secondary science teachers to data and graphinterpretation tasks. Our investigation shows that, despite considerable preparation, and for many, despite bachelor of science degrees, preservice teachers do not enact the ("authentic") practices that scientists rountinely do when asked to interpret data or graphs. Detailed analysis are provided of what data and graphinterpretation practices actually were enacted. We conclude that traditional schooling emphasizes particular beliefs in the mathematical nature of the universe that make it difficult for many individuals to deal with data processing the random variation found in measurements of natural phenomena. The results suggest that preservice teachers need more experience in engaging in data and graphinterpretation practices originating in activities that provide the degree of variation in and complexity of data present in realistic investigations. Presents an instructional model based on Neurolinguistic Programming that links counseling student course work in measurement and test interpretation with counseling techniques and theory. A process incorporating Neurolinguistic Programming patterns is outlined for teaching graduate students the counseling skills helpful in test interpretation.… \| Use the graph (for example, by marking specific points) to illustrate the statements in (a)–(d). If possible, label the coordinates of any points... One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end, Tononi et al. [Proc. Natl. Acad. Sci. USA. 91, 5033 (1994)] proposed a measure of neural complexity that purports to capture this property based on mutual information between complementary subsets of a system. Neural complexity, so defined, is one of a family of information theoretic metrics developed to measure the balance between the segregation and integration of a system's dynamics. One key question arising for such measures involves understanding how they are influenced by network topology. Sporns et al. [Cereb. Cortex 10, 127 (2000)] employed numerical models in order to determine the dependence of neural complexity on the topological features of a network. However, a complete picture has yet to be established. While De Lucia et al. [Phys. Rev. E 71, 016114 (2005)] made the first attempts at an analytical account of this relationship, their work utilized a formulation of neural complexity that, we argue, did not reflect the intuitions of the original work. In this paper we start by describing weighted connection matrices formed by applying a random continuous weight distribution to binary adjacency matrices. This allows us to derive an approximation for neural complexity in terms of the moments of the weight distribution and elementary graph motifs. In particular, we explicitly establish a dependency of neural complexity on cyclic graph motifs. PMID:21599200 As part of an investigation of the effectiveness of a microcomputer-based laboratory (MBL) activity in developing students' graphingskills, this study was specifically designed to examine the differences between females and males in both performance on graphing tasks and on their attitudes to graphs and graph-based activities. Results based on a… The objective of this ongoing study is to refine an instrument to evaluate conceptual understanding and graphical interpretation of a function and its derivative. The instrument is based on a modified version of the Test of Understanding Graphs in Kinematics (TUG-K) which consists of 26 items (7 dimensions). In the new instrument, Test of Understanding Graphs in Calculus (TUG-C), the kinematics context has been removed from the items creating a new context-free version. To favor the translation from kinematics to Calculus, the focus is on 5 out of the 7 original dimensions of the test, giving a 16-item test. A total of 526 students from a university level Introductory Physics course participated in the study. Half of the students were administered the kinematics test and the other half took the calculus test. This work will present data showing preliminary results of the instrument and new directions on improving the instrument. This survey, created by Milo Schield of Augsburg College, assesses statistical literacy. The survey focuses on the general use of informal statistics in everyday situations: reading and interpreting tables and graphs involving rates and percentages. The survey itself takes between thirty and forty minutes. The author does apologize for the length, but insists that it is due to how comprehensive the survey is. Sixty-nine questions in length, almost every topic concerning statistics is covered. The survey was funded by the W.M. Keck Statistical Literacy Project. In this activity students use Internet skills to find local and Antarctic weather data. They record the data, assemble it in a logical order, graph it, and interpret the graphed information. Students will: prepare a graph using an x and y axis; show graphing increments; arrange data on a graph; interpretgraphed data; demonstrate conversion of Fahrenheit to Celsius and Celsius to Fahrenheit; and differentiate between below and above zero degrees temperature. This article describes a study in which eighth grade physical science students studied graphing with a microcomputer as their lab partner in a microcomputer based laboratory. Graph templates were used to solve problems based on previous learning. It was concluded that the Computer as Lab Partner curriculum was effective in teaching graphing concepts. \|"Bars, Lines, & Pies" is a dynamic math program designed to build graphingskills in students, while also showing them the relevance of math in their lives. Developed by The Actuarial Foundation along with Scholastic, the graphing lessons and activities involve engaging, real-world examples about the environment and recycling. In these lessons,… The purpose of this study was to examine how people may learn life skills through their involvement in regular competitive sport programmes. Interviews were conducted with 40 young adults (20 males and 20 females) who were participants in competitive youth sport during their adolescence. Data were transcribed verbatim and subjected to an interpretive analysis. We present three main interpretations of Sign language is a visual language in which main articulators are hands, torso, head, and face. For simultaneous interpreters of Japanese sign language (JSL) and spoken Japanese, it is very important to recognize not only the hands movement but also prosody such like head, eye, posture and facial expression. This is because prosody has grammatical rules for representing the case and modification relations in JSL. The goal of this study is to introduce an examination called MPR (Measurement of Prosody Recognition) and to demonstrate that it can be an indicator for the other general skills of interpreters. For this purpose, we conducted two experiments: the first studies the relationship between the interpreter's experience and the performance score on MPR (Experiment-1), and the second investigates the specific skill that can be estimated by MPR (Experiment-2). The data in Experiment-1 came from four interpreters who had more than 1-year experience as interpreters, and more four interpreters who had less than 1-year experience. The mean accuracy of MPR in the more experienced group was higher than that in the less experienced group. The data in Experiment-2 came from three high MPR interpreters and three low MPR interpreters. Two hearing subjects and three deaf subjects evaluated their skill in terms of the speech or sign interpretationskill, the reliability of interpretation, the expeditiousness, and the subjective sense of accomplishment for the ordering pizza task. The two experiments indicated a possibility that MPR could be useful for estimating if the interpreter is sufficiently experienced to interpret from sign language to spoken Japanese, and if they can work on the interpretation expeditiously without making the deaf or the hearing clients anxious. Finally we end this paper with suggestions for conclusions and future work. Background The use and interpretation of electrocardiograms (ECGs) are widely accepted as an essential core skill in Emergency Medicine.\\u000a It is imperative that emergency physicians are expert in ECG interpretation when they exit their training programme.\\u000a \\u000a \\u000a \\u000a \\u000a Aim It is unknown whether South African Emergency Medicine trainees are getting the necessary skills in ECG interpretation during\\u000a the training programme. Currently there are no This article reports on an ongoing research program aiming at the pedagogical exploitation of the science fair as a mechanism for developing investigative skills in elementary school and promoting student inquiry through a sequence of formal and non-formal activities. Specifically, this paper refers to the development of data graphingskills by children aged 10-12 years old. The students, who participated This study investigates the effectiveness of an instructional strategy to teach students with little or no prior knowledge in kinematics how to draw and interpret velocity-time graphs representing the motion of objects. The researchers test how presenting velocity-time graphs at the same time that the student observes the motion of an object effects comprehension. Review material on graphing calculator use from the College Board AP Calculus Course Description. The problems are mostly AB level. The page also contains a brief historical remark about Maria Gaetana Agnesi. This article deals with the interpretation of motion Cartesian graphs by Grade 8 students. Drawing on a sociocultural theoretical\\u000a framework, it pays attention to the discursive and semiotic process through which the students attempt to make sense of graphs.\\u000a The students' interpretative processes are investigated through the theoretical construct of knowledge objectification and\\u000a the configuration of mathematical signs, gestures, and Graphs are one of the primary means of exploration and communication in the practice of science, but students in science laboratories are customarily taught only the low-level mechanics of constructing a single kind of graph when given a table of information. The use of a microcomputer can relieve the drudgery of plotting, allowing students to pursue higher-level issues in the design and interpretation of graphs through repeated thought experiments. We introduced computer-assisted graphical data analysis to inner-city high school students with weak math and science backgrounds, emphasizing the dynamic manipulation of various kinds of graphs to answer specific questions. Drawing on extensive recordings and classroom observations, we describe examples of the performance of these students on open-ended problem-solving tasks in which graphs can be used to arrive at meaningful answers to applied data analysis problems. This paper discusses the development of a graphic tool to assist in the teaching of pre-calculus skills to blind students. More specifically, it reviews previous and on-going efforts to develop an instrument that will facilitate or enable blind students to examine and explore data and abstract graphs, and other mathematic entities haptically. The paper also discusses current research plans to This site contains a lesson plan for teaching students about fluid densities and significant figures. It includes a basic experiment, instructions for the students, and questions for the students that test their interpretation of the results. In this article, the learning progress of one fifth-grade student is examined with regard to the development of her graphinterpretationskills as she participated in the Junior Science Institute (JSI), a two-week, science intensive summer camp in which participants engaged in microbiology research and application. By showcasing the student's development of graphinterpretationskills, the authors hope to make apparent some of the cognitive processes students may go through as they attempt to master this important inquiry skill and thus provide fellow teachers with insight as to how to more effectively develop these skills in their own students. The notions of "abstract" and "concrete" are central to the conceptualization of mathematical knowing and learning. Much of the literature takes a dualist approach, leading to the privileging of the former term at the expense of the latter. In this article, we provide a concrete analysis of a scientist interpreting an unfamiliar graph to show how… task is in either case to extract a description from an input diagram. PMID:22499631 Background: Despite published consensus-based statements on assessment of ECG interpretationskills, studies and curricula regarding the training needed to obtain basic ECG interpretationskills are lacking. These consensus statements have focused on attaining competency in ECG interpretation during postgraduate training; however, recommendations regarding assessment of competency in the undergraduate curriculum are not discussed. Purpose: The purpose is to describe the \|Graphing is a key skill in the study of Physics. Drawing and interpretinggraphs play a key role in the understanding of science, while the lack of these has proved to be a handicap and a limiting factor in the learning of scientific concepts. It has been observed that despite the amount of previous graph-working experience, students of all ages… Geometry is everywhere! Use these links to learn about graphing and test your knowledge! Test your coordinate graphingskills and catch the Graph Mole We will be working with graphs in class. Make your own graph of information you compile with this link. Just for Fun! Have fun with some Tricky Tangrams. See how many shapes you ... Practice your graphingskills with these fun activities! Work on your bar graphs with Bar Graph Bugs Take a survey with Data Picking Use pictures to graph with Pictograph Answer graphing questions Use coordinate graphing with Billy Bug and Graph a mole. Use coordinate graphing to Planet Hop! ... This case study follows a family's dilemma about how to save money on gasoline. Should they keep their SUV and trade in their Corolla for a hybrid sedan? Going from 28 (Corolla) to 48 (Hybrid) miles per gallon (MPG) should really save money on gas. That's a change of 20 MPG! Or, should they keep their Corolla and trade in their SUV for a minivan? The SUV gets about 13 MPG while the Minivan gets 17 MPG. Students learn how to analyze fuel efficiency in terms of "gallons per miles" driven instead of miles per gallon, and gain graphing and data analysis skills. An extension activity also relates fuel efficiency to greenhouse gas emissions. The case was developed for use in a high school general science course. It could be adapted for use in introductory physics, chemistry, algebra, or environmental science courses at the high school or college level. Behaviorist teaching of communication skills can interfere with learning of humanistic nursing. Interpretive inquiry can help students experience the transformative power for relationships and develop confidence and trust in their capacity for relational nursing practice. (Contains 20 references.) (SK) The author is concerned about the methodology and instrumentation used to assess both graphing abilities and the impact of microcomputer-based laboratories (MBL) on students' graphing abilities for four reasons: (1) the ability to construct and interpretgraphs is critical for developing key ideas in science; (2) science educators need to have valid information for making teaching decisions; (3) educators and researchers are heralding the arrival of MBL as a tool for developing graphing abilities; and (4) some of the research which supports using MBL appears to have significant validity problems. In this article, the author will describe the research which challenges the validity of using multiple-choice instruments to assess graphing abilities. The evidence from this research will identify numerous disparities between the results of multiple-choice and free-response instruments. In the first study, 72 subjects in the seventh, ninth, and eleventh grades were administered individual clinical interviews to assess their ability to construct and interpretgraphs. A wide variety of graphs and situations were assessed. In three instances during the interview, students drew a graph that would best represent a situation and then explained their drawings. The results of these clinical graphing interviews were very different from similar questions assessed through multiple-choice formats in other research studies. In addition, insights into students' thinking about graphing reveal that some multiple-choice graphing questions from prior research studies and standardized tests do not discriminate between right answers/right reasons, right answers/wrong reasons, and answers scored wrong but correct for valid reasons. These results indicate that in some instances multiple-choice questions are not a valid measure of graphing abilities. In a second study, the researcher continued to pursue the questions raised about the validity of multiple-choice tests to assess graphing, researching the following questions: What can be learned about subjects' graphing abilities when students draw their own graphs compared to assessing by means of a multiple-choice instrument? Does the methodology used to assess graphing abilities: (1) affect the percentage of subjects who answer correctly; (2) alter the percentage of subjects affected by the picture of the event phenomenon? Instruments were constructed consisting of three graphing questions that asked students: (a) multiple-choice-choose a graph that best represents the situation; (b) free-response-draw a graph that best represents the situation. The sample of 1416 subjects from an urbadsuburban area in cluded 50% boys/50% girls from grades 8 through 12; subjects from high, medium, and low ability groups; and subjects from both public and private schools. The subjects completed either the multiple-choice or the free draw instrument. The free draw instrument was scored by comparing the subject's response to categories of possible answers that had been identified from the first study. The results show as much as 19% difference in correct responses, three times as many picture of the events from multiple-choice instruments, and significant differences in how multiple-choice and free-response affect various ability levels and grade levels. As such, some of the research studies that used multiple-choice instruments to examine giaphing and the impact of MBL on student's graphing abilities may be invalid. The aim of this study was to examine how dance teachers work with psychological skills with their students in class. Semi-structured interviews were conducted with six female professional teachers in jazz, ballet and contemporary dance. The interview transcripts were analyzed using interpretative phenomenological analysis (Smith 1996). Results revealed that all teachers used psychological skills training techniques such as goal setting With the help of a new theory using the notion of path in a graph, a physical interpretation and meaning can be given to electroanalytical\\u000a measurements, without recourse to mathematical treatments. The frequency dependence of impedances measured by ac techniques,\\u000a or the scan rate dependence of current vs. potential characterizations in large signal techniques (cyclic voltammetry), can\\u000a be interpreted through Research findings show the difficulties younger students have in working with graphs. Higher mental operations are necessary for a skilledinterpretation of abstract representations. We suggest connecting a concrete representation of the modeled problem with the related graph. The idea is to illustrate essential mental operations externally. This… This activity has students graph the number of sunspots over a long period of time. They then look for a pattern and discover the sunspot cycle. This activity helps to illustrate the need to accumulate data over time and graph that data to discern patterns. Students will also learn about sunspots, Galileo, and instruments for data collection, along with improving their graphingskills. \|Bar Graphs and Pie Charts Students will practice graphing data on bar graphs and pie charts using quizzes and games. Students will also practice interpreting data given information. Watch this video to refresh your memory. Video Today In this activity, learners "dance" (move back and forth at varying speeds) by reading a graph. This is a kinesthetic way to help learners interpret and understand how motion is graphed. This resource includes instructions for three different graph "dances" and an optional extension activity. This article argues that the teaching of behavioral communication skills may interfere with the learning of humanistic nursing practice. By inviting readers to consider moving beyond a method approach, the author discusses the pedagogical value of interpretive inquiry for the teaching-learning of relational practice. The author asserts that, as a "nonmethod," a pedagogy of interpretive inquiry can create opportunities for nursing students to learn and experience the transformative power of relationship, gain confidence in their capacity for relational being and a sense of trust in their ability to be with people in ways that are authentic and meaningful, and develop their overall ability to enact humanistic, relational nursing. PMID:12238897 \|People with Parkinson's disease, essential tremor, or other movement disorders involving tremor have changes in fine motor skills that are among the hallmarks of these diseases. Numerous measurement tools have been created and other methods devised to measure such changes in fine motor skills. Measurement tools may focus on specific features – e.g., motor skills or dexterity, slowness in movement execution associated with parkinsonian bradykinesia, or magnitude of tremor. Less obviously, some tools may be better suited than others for specific goals such as detecting subtle dysfunction early in disease, revealing aspects of brain function affected by disease, or tracking changes expected from treatment or disease progression. The purpose of this review is to describe and appraise selected measurement tools of fine motor skills appropriate for people with tremor disorders. In this context, we consider the tools' content – i.e., what movement features they focus on. In addition, we consider how measurement tools of fine motor skills relate to measures of a person's disease state or a person's function. These considerations affect how one should select and interpret the results of these tools in laboratory and clinical contexts. This paper describes a laboratory-based program in physics designed to help students build effective links between the mathematical\\u000a equations used to solve problems in mechanics and the real world of moving objects. Through the analysis of straight line\\u000a graphs derived from their own data students have been able to achieve a considerable development towards a concept of slope,\\u000a or gradient, \|One essential skill that students who learn physics should possess is the ability to create and interpret kinematic graphs. However, it is well documented in the literature that students show lack of competence in these abilities. They have problems in connecting graphs and physics concepts, as well as graphs and the real world. The present paper… This manual contains 56 teacher-developed activities which can be used in social studies courses to improve students' basic skills. The activities teach location and map skills, writing and study skills, time skills, and thinking skills. Students also learn how to use reference books and how to read and interpret charts and graphs. Each activity… Signature verification is one of the most widely researched areas in document analysis and signature biometric. Various methodologies have been proposed in this area for accurate signature verification and forgery detection. In this paper we propose a unique two stage model of detecting skilled forgery in the signature by combining two feature types namely Sum graph and HMM model for signature generation and classify them with knowledge based classifier and probability neural network. We proposed a unique technique of using HMM as feature rather than a classifier as being widely proposed by most of the authors in signature recognition. Results show a higher false rejection than false acceptance rate. The system detects forgeries with an accuracy of 80% and can detect the signatures with 91% accuracy. The two stage model can be used in realistic signature biometric applications like the banking applications where there is a need to detect the authenticity of the signature before processing documents like checks. Rosemary Richardson and Jenny Laveglia created this course at Bellevue Community College in order to supply students with the graphingskills needed for biology. The creators provide a graphing project specifically tied to biological subjects. The projects provide practice with data collection, analysis, and graphing practice. This is a good resource for educators that want to introduce graphing to their biology students. This article describes a laboratory-based program in physics designed to help students build effective links between the mathematical equations used to solve problems in mechanics and the real world of moving objects. The program is based on a study conducted among senior college students, which illustrated out the value of laboratory work in science education for development of thinking skills and positive attitudes (Contains 14 references). answered the TOGS in one of three ways: as if they were mathematics word problems, science data to be analyzed, or they were confused and had to guess. A second set of findings corroborated how science background knowledge affected graphinterpretationinterpretation, highlighted the importance of heuristics and mathematics procedural knowledge, and documented the importance of perception attentions, motivation, and students' self-generated questions. Recommendations were made for future research in line graphinterpretation in mathematics and science education and for improving instruction in this area. Do any of your students struggle with the scientific and mathematical concepts underlying a lab investigation or to articulate conclusions based on their data? If so, try enhancing their higher-order thinking skills by explicitly linking science and math together. Before students collect and graph their actual data, ask them to predict what they think their data will look like and to sketch a graph of their prediction. Asking students to graph their prediction before they begin a lab investigation helps them construct a theoretical context for the investigation. \|A key challenge in university geoscience teaching is to give students the skills to cope with uncertainty. Professional geoscientists can rarely be certain of the "right answer" to problems posed by most geological datasets, and reasoning through this uncertainty, being intelligently flexible in interpreting data which are limited in resolution… This study examines organizations that emphasize differing types of marketing skills. It is based on a national survey of\\u000a Health Maintenance Organizations. The organizations are first classified into groups based on their distinctive marketing\\u000a skill configurations. Six groups were identified. Next, differences between these organization types are examined with respect\\u000a to organization strategy, characteristics of the chief marketing executive, organizational This study presents an investigation of (n=31) physics students' analysis of videodisc-recorded images with treatments over an extended time. Researchers found no significant learning difference between using simultaneous-time and delayed-time analysis for student understanding of kinematics graphs. This supplement is intended to help schools get the maximum amount of useful information from test results; information that will be helpful in program monitoring, grouping, planning instructional activities, and reporting results to parents and community. Contents include an introduction to test interpretation and interpreting of test scores;… Massachusetts State Dept. of Education, Boston. Bureau of Research and Assessment. Rationale and ObjectivesThe authors evaluated the effect of training in the American College of Radiology (ACR) Breast Imaging Reporting and Data System (BI-RADS) lexicon on the interpretiveskills of radiologists evaluating screening mammograms in Ukraine. Interpretive guidelines and survey procedures for applying conditions of participation in the Medicaid and Medicare programs to skilled medical facilities are outlined to aid the State survey agency, the State Medicaid agency, and providers. Standards are... Focuses on the development of graphingskills through a data collection activity that answers the question of the relationship between rubber band width and flight distance. Includes definitions of terms and instructions for helping students construct line and bar graphs. (DDR) This PowerPoint presentation features an explanation of different types of graphs. Students will learn how to make and interpret a time-series graph, a cross-section graph, and a scatter diagram. Illustrations and text are used to define and calculate the slope of a line and distinguish between linear and nonlinear relationships and between relationships that have a maximum and a minimum. Students visit second- and fourth-grade classes to measure the heights of older students using large building blocks as a non-standard unit of measure. They also measure adults in the school community. Results are displayed in age-appropriate bar graphs (paper cut-outs of miniature building blocks glued on paper to form bar graphs) enabling a comparison of the heights of different age groups. The activities that comprise this activity help students develop the concepts and vocabulary to describe, in a non-ambiguous way, how heights change as children age. This introduction to graphing provides an important foundation for creating and interpretinggraphs in future years. Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k > 2. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth-death (BD), death-birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs. Graph theory is widely used in computer science, engineering and of course, mathematics. Wikipedia offers this definition and overview of Graph Theory (1). This next website from Mega-Math (2) reviews some of the Vocabulary of Graphs and highlights some applications for graph theory, such as the design of computer systems and games. Some additional applications for Graph Theory are discussed in this more technical book called Graph Theory with Applications (3). This website from Georgia Tech (4) discusses a proof that allows a user to create a map of the U.S. using just four colors. For a more involved explanation of Graph Theory, see this Graph Theory book by Reinhard Diestel (5). On this next website (6), Christopher P. Mawata of the University of Tennessee at Chattanooga offers a collection of Graph Theory Lessons for educators. The final website provides a short biography of a key figure in Graph Theory who recently passed away, Frank Harary (7). Making graphs can be a challenging process for some students to understand. Using graphs and student collected data, the class will learn how to construct and interpretgraphs. They will develop simple experiments; designate x and y axis, scale, label and plot points on a graph; determine blood pressure and extrapolate heart rate using pulse, sphygmomanometer, and stethoscope; collect, organize, display, and analyze experimental data; and discover factors affecting heart rate and pressure. Upon completion of this activity, students will be able to designate x and y axis, scale, label and plot points on a graph. In this investigation, three classes of ninth-grade general science students participated in a collaborative report-writing intervention. The purpose of this portion of the study was to evaluate students' collaboratively written laboratory reports for evidence of the use of scientific reasoning skills and to document qualitative changes in reasoning skill use over time. The participants in the study were 6 ninth-grade students, representing three collaborative writing pairs. During the intervention, students wrote 10 laboratory reports over a 4.5-month period. The author and classroom teacher designed report guideline prompts to scaffold students in the use of relevant scientific reasoning skills. The results indicated that students used reasoning skills to assess their current models of scientific understanding, make observations, interpret the meaning of results, and generate new models based on their data and relevant information. Participants showed the most improvement in writing that reflected the reasoning skills of (a) selecting and processing textbook passages, (b) drawing conclusions and formulating models, and (c) comparing/contrasting. Over time, participants improved their ability to compose explanations that represented a synthesis of prior knowledge, activity observations, and other sources of information. Collaborative writing encouraged students to construct their own understandings of science concepts by creating an environment in which thinking, reasoning, and discussion were valued. It has been recently proposed that the robustness of complex networks can be efficiently characterized through the natural connectivity, a spectral property of the graph which corresponds to the average Estrada index. The natural connectivity corresponds to an average eigenvalue calculated from the graph spectrum and can also be interpreted as the Helmholtz free energy of the network. In this article, we explore the use of this index to characterize the robustness of Erdo?s-Rényi (ER) random graphs, random regular graphs, and regular ring lattices. We show both analytically and numerically that the natural connectivity of ER random graphs increases linearly with the average degree. It is also shown that ER random graphs are more robust than the corresponding random regular graphs with the same number of vertices and edges. However, the relative robustness of ER random graphs and regular ring lattices depends on the average degree and graph size: there is a critical graph size above which regular ring lattices are more robust than random graphs. We use our analytical results to derive this critical graph size as a function of the average degree. In this paper we present a novel method for creating realistic, controllable motion. Given a corpus of motion capture data, we automatically construct a directed graph called a motion graph that encapsulates connections among the database. The motion graph consists both of pieces of original motion and automatically generated transitions. Motion can be generated simply by building walks on the \\u000a The contents of the book have focused so far on the mining of data where the underlying structure is characterized by special\\u000a types of graphs where cycles are not allowed, i.e. acyclic graphs or trees. The focus of this chapter is on the frequent pattern\\u000a mining problem where the underlying structure of the data can be of general graph type The lesson begins with graphs of the Dow Jones Industrial Average and water levels of Lake Huron where points on the graph are interpreted. Intervals of increase and maxima are introduced before the graph of F(x) = sqrt (x+4) is completed by first generating a table of data. This is followed by the vertical line test and using graphs to solve equations and inequalities. This report describes the development of a quality assurance-oriented integrated software system designed for an anesthesiology-based intraoperative transesophageal echocardiography service. Entry data include patient and operation demographics, two-dimensional echocardiographic, saline-contrast, and color flow/pulsed Doppler assessments of the heart and great vessels, presented in a defined sequence. A statistical analysis component (kappa coefficient analysis) allows for comparison of intraoperative real-time interpretations with laboratory interpretations made by experienced full-time echocardiographers on a field-by-field basis. This provides a means of quantifying expertise in each individual aspect of the patient examination sequence. We believe that such self-appraisal data are essential for delineating the status and tracking the progress of service being provided. PMID:8222390 This descriptive study investigated two groups of low-income, urban children who had whole-language instruction during their kindergarten and first-grade years. These 17 children were studied previously for those 2 years in their separate schools. The current investigation focused on the general academic success of the two groups and on eight, focal learners' interpretations. In one school, a group of children Student will conduct a coin tossing experiment for 30 trials. Their results will be graphed, showing a line graph that progresses toward the theoretical probability. Students will observe that as the number of trials increases they begin to see a graphical representation of the Law of Large Numbers. Instructions, handouts, and a lesson extension are all included here. Prior empirical work on layout aesthetics for graph drawing algorithms has concentrated on the interpretation of existing graph drawings. We report on experiments which focus on the creation and layout of graph drawings: participants were asked to draw graphs based on adjacency lists, and to lay them out \\ Graph theory is a branch of discrete combinatorial mathematics that studies the properties of graphs. The theory was pioneered by the Swiss mathematician Leonhard Euler in the 18th century, commenced its formal development during the second half of the 19th century, and has witnessed substantial growth during the last seventy years, with applications in areas as diverse as engineering, computer science, physics, sociology, chemistry and biology. Graph theory has also had a strong impact in computational linguistics by providing the foundations for the theory of features structures that has emerged as one of the most widely used frameworks for the representation of grammar formalisms. The purposes of this research study were to determine (a) in-service elementary teachers' familiarity, interest, conceptual knowledge of , and performance on science process skills and (b) how in-service elementary teachers' familiarity with, interest in conceptual knowledge of and performance on science process skills relate to each other. The science process skills include the basic skills [observation, classification, measuring, predicting, inferring, and communication,] and the integrated skills [hypothesizing, experimenting, identifying and controlling variables, formulating models, interpreting data, and graphing]. Twenty-four in-service elementary teachers enrolled in a master of math and science education degree program participated in this study. Participants completed questionnaires on their familiarity and interest in the science process skills, a science processes conceptual knowledge test, and a performance test on science process skills. Results indicate that these teachers were highly familiar with the science process skills, but moderately interested in these skills. Results also indicate that teachers were more interested in learning more about integrated process skills than basic process skills. Teachers possessed very low conceptual knowledge of the science process skills. However, teachers performed well on science process skills performance test. Significant correlations among the four constructs (familiarity, interest, conceptual knowledge and performance) were only significant between familiarity and interest. The implications, discussion and recommendations for future research and instruction on science process skills in teacher education programs have been presented. A framework for skill acquisition is proposed that includes two major stages in the development of a cognitive skill: a declarative stage in which facts about the skill domain are interpreted and a procedural stage in which the domain knowl- edge is directly embodied in procedures for performing the skill. This general framework has been instantiated in the ACT system In this activity, learners track their movements with jumping and leaping graphs. In part A, learners jump as high as they can and press their inked fingers or hands against a large true-to-life chart with vertical distance marked along the vertical edge. Learners compare the results. In part B, learners jump as far as they can and use masking tape to mark their spot on a true-to-life bar graph. Again, learners compare the results. Let's learn how to use the lines on graphs (the x & y axis) to plot information. Choose any of the activities below to test your knowledge of identifying the coordinates correctly. Meteoroid Coordinates Soccer Coordinates Donut Coordinates Graphing Points Save the Zogs!-Using Linear Equations Using your coordinate plane knowledge and linear equations help to rescue the Zogs! Can you find the axis for these problems too? What have you noticed about linear equations? What do the lines in linear equations look ... This dissertation examined the processes generated by eighth-grade students to interpret and represent the functions embedded in dynamic physical models and the instructional decisions that facilitated the processes. Using the teaching experiment method, students were paired to interactively explore a slack rope board. The slack rope board consisted of a string that had been attached to a corkboard and that datasets but also the advantages and strengths of our signature-guided approach presented in the paper. data sets, but also the advantages and strengths of our signature-guided approach presented in the paper. PMID:17073364 Student graphing of high and low tide from locations showing the three tide types (diurnal, semi-diurnal, and mixed) and the Bay of Fundy (tidal amplitude increased by resonance). Students recognize that not all tides are the same and that location is an important control on tides. In this activity, learners use a straight line to learn about circles. Learners measure and record the diameter and circumference of different sized cylindrical objects on a chart. Learners then plot the diameters and circumferences on a graph and calculate the slope to discover the linear relationship between the two proprieties. You are going to put on your math-cap and think about points and graphs in order to solve problems. First you will help help Billy Bug s Grub get into his belly. Then you will find the Mean, Median, Mode of building heights. Finally you will find out: What s the point? ... Students use graph theory to create social graphs for their own social networks and apply what learn to create a graph representing the social dynamics found in a dramatic text. Students then derive meaning based on what they know about the text from the graphs they created. Students learn graph theory vocabulary, as well as engineering applications of graph theory. In theories of closed oriented superstrings, the one-loop amplitude is given by a single diagram, with the topology of a torus. Its interpretation had remained obscure, because it was formally real, converged only for purely imaginary values of the Mandelstam variables, and had to account for the singularities of both the box graph and the one-particle reducible graphs in field A framework for skill acquisition is proposed in which there are two major stages in the development of a cognitive skill--a declarative stage in which facts about the skill domain are interpreted and a procedural stage in which the domain knowledge is em... Geodesic active contours and graph cuts are two stan- dard image segmentation techniques. We introduce a new segmentation method combining some of their benefits. Our main intuition is that any cut on a graph embedded in some continuous space can be interpreted as a contour (in 2D) or a surface (in 3D). We show how to build a grid graph Using a variation of the interpretability concept we show that all graph properties definable in monadic second order logic (MS properties) with quantification over vertex and edge sets can be decided in linear time for classes of graphs of fixed bounded tree-width, giving an alternative proof of a recent result by Courcelle. We allow graphs with directed and\\/or undirected edges, The paper addresses problems in conceptual graph implementation: subsumption and classification in a taxonomy. Conceptual graphs are typically stored using a directed acyclic graph data structure based on the partial order over conceptual graphs. We give an improved algorithm for classifying conceptual graphs into this hierarchy. It prunes the search space in the database using the information gathered while searching. The Resource Description Framework (RDF) describes graphs ofstatements about resources. This paper explores the equality of twoRDF graphs in light of the graph isomorphism literature. Weconsider anonymous resources as unlabelled vertices in a graph,and show that the standard graph isomorphism algorithms,developed in the 1970's, can be used effectively for comparing RDFgraphs. A clique is a maximal complete subgraph of a graph. The maximum number of cliques possible in a graph withn nodes is determined. Also, bounds are obtained for the number of different sizes of cliques possible in such a graph. This Flash applet allows students to create a variety of graphs: line graph, pie chart, bar graph, area graph and x-y plot. Each type provides a variety of layout and design options. Users enter data and labels and choose data parameters. Completed graphs may be printed, saved, and/or emailed. The accompanying tutorial provides general information about graphs and explains how to use the applet. A graph language can be described by a graph grammar in a manner similar to a string grammar known from the theory of formal\\u000a languages. Unfortunately, graph parsing is known to be computationally expensive in general. There are quite simple graph\\u000a languages that crush most general-purpose graph parsers.\\u000a \\u000a In this paper we present graph parser combinators, a new approach to These games show what a bar graph is and how to develop one. Learn how to create your own graph here! Make sure to click "Okay" on the game to start it. This game will show you how to develop a bar graph using data. This game is showing how the bugs make up the bar graph. They are the data being entered into the graph. Create a graph using bugs! Use this game to ... The notion of a random graph is formally defined. It deals with both the probabilistic and the structural aspects of relational data. By interpreting an ensemble of attributed graphs as the outcomes of a random graph, we can use its lower order distribution to characterize the ensemble. To reflect the variability of a random graph, Shannon's entropy measure is used. The size and density of graphs interact powerfully and subtly with other graph-level indices (GLIs), thereby complicating their interpretation. Here we examine these interactions by plotting changes in the distributions of several popular graph measures across graphs of varying sizes and densities. We provide a generalized framework for hypothesis testing as a means of controlling for size and density effects, This article describes the current training and certification procedures in place for linguistic interpreters, the continuum of interpreter roles, and how interpreters' perspectives may influence the interpretive interaction. The specific skills needed for interpreting in either health care or educational settings are identified. A table compares… In many areas of science huge networks (graphs) are central objects of study: the internet, the brain, various social networks,\\u000a VLSI, statistical physics. To study these graphs, new paradigms are needed: What are meaningful questions to ask? When are\\u000a two huge graphs "similar"? How to "scale down" these graphs without changing their fundamental structure and algorithmic properties?\\u000a How to generateStudents This paper presents a novel methodology for viewing large graphs. The basic concept is to allow the user to interactively navigate through large graphs learning about them in appropriately small and concise pieces. An architecture is present to support graph exploration. It contains methods for building custom layout algorithms hierarchically, interactively decomposing large graphs, and creating interactive parameterized layout algorithms. In this paper we present an information retrieval model base d on con- ceptual graphs named ELEN (1). In ELEN a conceptual graph is a representative of the information inherent in the document and query. Graph operators can be used to determine whether a graph is a generalisation of another g raph, in which case the information carried by the . An elementary probabilistic argument is presented which shows that for everyforest F other than a matching, and every graph G containing a cycle, there exists an infinitenumber of graphs J such that J#(F, G)butifwedeletefromJ any edge e the graph J-eobtained in this way does not have this property.Introduction. All graphs in this note are undirected graphs, without loops and \|… The Media Ready Program was designed as a middle school, media literacy education, preventive intervention program to improve adolescents' media literacy skills and reduce their intention to use alcohol or tobacco products. In a short-term efficacy trial, schools in North Carolina were randomly assigned to conditions (Media Ready: n = 214; control: n = 198). Boys in the Media Ready group reported significantly less \|Tested whether 7-month-olds' means-end behaviors were genuine or the repetition of trained behaviors under conditions of greater arousal. Found that infants' learned button-pushing to light a set of distant lights differed from button-pushing to retrieve toys. Infants demonstrated means-end skills with behaviors that they had not been trained to… Because eighth-grade curriculum standards focus in part on systems analysis and graphing, a lesson was created to enhance students' analytical skills with the introduction of a type of graph, the node graph, which can be used to represent the interconnectedness of system components. This lesson is rooted in understanding real-world concepts regarding the transmission of infectious agents throughout a populationDrawing on the knowledge of the people, Wikipedia presents this site on graph theory. Here, the history, problems, and applications of graph theory are explained, and there are links to other print and online resources for more information. Students learn about complex networks and how to represent them using graphs. They also learn that graph theory is a useful mathematical tool for studying complex networks in diverse applications of science and engineering, such as neural networks in the brain, biochemical reaction networks in cells, communication networks, such as the internet, and social networks. Topics covered include set theory, defining a graph, as well as defining the degree of a node and the degree distribution of a graph. We address the problem of generating a minimal state graph from a program, without buildingthe whole state graph. Minimality is considered here with respect to bisimulation. Ageneration algorithm is derived and illustrated. Applications concern program verificationand control synthesis in reactive program compilation.1 IntroductionThis paper concerns the problem of explicitly building a state graph from a program, a formulaor any implicit \|Most current graph layout technology does not lend itself to interactive applications such as animation or advanced user interfaces. We introduce the constrained graph layout model which is better suited for interactive applications. In this model, input to the layout module includes suggested positions for nodes and constraints over the node positions in the graph to be laid out. We From the Graduate Texts in Mathematics series comes this textbook on graph theory by Reinhard Diestel from the University of Hamburg. Topics covered include flows, planar graphs, infinite graphs, and Hamilton cycles. Visitors can read the full text (by clicking on "electronic edition") or summaries of each section, as well as reviews from different scholarly journals. This report describes the Fourth Annual Graph Drawing Contest, held inconjunction with the 1997 Graph Drawing Symposium in Rome, Italy. Thepurpose of the contest is to monitor and challenge the current state of the artin graph-drawing technology [2, 3, 4].This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission tocopy in whole Assuming Pgraph cannot be done in polynomial time. However, it is possible to define a large class of canonicalizable RDF graphs, such that digital signatures for graphs in this cla ss can be created and verified in O( nlog( n)). Without changing its meaning, an Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large number of mutual connections. Such groups of vertices, or communities, can be considered as independent compartments of a graph. Detecting This multimedia mathematics resource deals with graphing data. A video illustrates how math plays a role in the way merchandise is displayed in retail stores. An interactive component allows students to explore and compare line graphs, bar graphs, and circle graphs to determine if the graphs represent the same data. A print activity about data, display, and graphs is included. \|This article discusses the importance of acquiring skills in college to prepare students for the work force. The author describes how college students lack the skills and character needed to succeed. They might take statistics in college and score A's on tests of abstract problem-solving, but they cannot set up a bar graph to display real-world… \\u000a An outerplanar graph is a planar graph that can be embedded in the plane in such a way that all vertices lie on the outer\\u000a boundary. Outerplanar graphs express many chemical compounds. An externally extensible outerplanar graph pattern (eeo-graph pattern for short) represents a graph pattern common to a finite set of outerplanar graphs, like a dataset of chemical compounds. Describe some situations where naive interpretation of Maple's output may be misleading;Show an appropriate viewing rectangle for the graph of a given function;Plot a function using Maple;Compare local and global properties of a given function;Find the solutions of a given equation using Maple. We explore this question by comparing the degree to which an upcoming sentential theme is anticipated by combining information from a prior agent and action. 48 children, aged of 3 to 10, and 48 college-aged adults' eye-movements were recorded as they heard a sentence (e.g., The pirate hides the treasure) in which the object referred to one of four images that included an agent-related, action-related and unrelated distractor image. Pictures were rotated so that, across all versions of the study, each picture appeared in all conditions, yielding a completely balanced within-subjects design. Adults and children quickly made use of combinatory information available at the action to generate anticipatory looks to the target object. Speed of anticipatory fixations did not vary with age. When controlling for age, individuals with higher vocabularies were faster to look to the target than those with lower vocabulary scores. Together, these results support and extend current views of incremental processing in which adults and children make use of linguistic information to continuously update their mental representation of ongoing language. PMID:22632758 \|We have concluded that teaching undergraduate students to use spreadsheet software to analyze, interpret, and communicate spreadsheet data through a graph is an information technology exercise in whole brain thinking. In investigating why our students have difficulty constructing proper graphs, we have discovered that graphing requires two… The purpose of this project is to provide resources for practicing graphing a line in slope-intercept form. Work through each step and make sure you do the assessment at the end. [Utah State Algebra 1 Core Curriculum - Standard II, Objectives 1-3.] Step 1: Click on the link to practice graphing lines. Try at least 10 different equations. Do more if you want to. Graphing Lines Practice Step 2: More Practice Here are some other activity that will help you better understand how to graph a line. Try them out! Graphing from slope intercept form Bug Zap Lines Butterfly slope game Slope Basketball Slope Quiz Interactive Graphing Tutorial (Make up your own equation. Move the ... Students analyze their social networks using graph theory. They gather data on their own social relationships, either from Facebook interactions or the interactions they have throughout the course of a day, recording it in Microsoft Excel and using Cytoscape (a free, downloadable application) to generate social network graphs that visually illustrate the key persons (nodes) and connections between them (edges). The nodes in the Cytoscape graphs are color-coded and sized according to the importance of the node (in this activity, nodes are people in students' social networks). After the analysis, the graphs are further examined to see what can be learned from the visual representation. Students gain practice with graph theory vocabulary, including node, edge, betweeness centrality and degree on interaction, and learn about a range of engineering applications of graph theory. Let G denote a graph class. An undirected graph G is called a probe G graph if one can make G a graph in G by adding edges between vertices in some independent set of G. By definition graph class G is a subclass of probe G graphs. Ptolemaic graphs are chordal and induced gem free. They form a subclass of both chordal graphs and distance-hereditary graphs. Many problems NP-hard on chordal graphs can be solved in polynomial time on ptolemaic graphs. We proposed an O(nm)-time algorithm to recognize probe ptolemaic graphs where n and m are the numbers of vertices and edges of the input graph respectively. We announce an algebraic approach to the problem of assigning canonical forms to graphs. We compute canonical forms and the associated canonical labelings (or renumberings) in polynomial time for graphs of bounded valence, in moderately exponential, exp(n˝ + &ogr;(1)),time for general graphs, in subexponential, nlog n, time for tournaments and for 2-(&ngr;,&kgr;,?) block designs with &kgr;,? bounded and nlog log Abstract A graph G is hamiltonian-connected if any two of its vertices are connected by a Hamilton path (a path including every vertex of G); and G is s-hamiltonian-connected if the deletion of any vertex subset with at most s vertices results in a hamiltonian-connected graph. In this paper, we prove that the line graph of a (t + 4)-edge-connected This tutorial from West Texas A&M University's Virtual Math Lab introduces bar graphs, line graphs, double line graphs and Venn diagrams to beginning algebra students. The unit explains each type of graph and includes examples. Students will use provided sample graphs to answer a series of questions about each example. A periodic graph models various natural and artificial periodic patterns with repetitions of a given static graph, and have vast applications in crystallography, scheduling, VLSI circuits and systems of uniform recurrence equations. This paper considers a graph Voronoi diagram for a given subset of vertices on a periodic graph. The simplest two-dimensional periodic graph is a square lattice, and the Graphing points, lines, and writing equations from tables or graphs. Functions. Read carefully about plotting points at coolmath4kids. Coolmath Plotting Points Play the game twice or more if you aren't getting most of them right. A score of over 7000 would be good. Coordinate plane quadrants and ordered pairs. Read about Time/distance Time and distance graphs and then Time/speed. Time and speed graphs Read about and practice functions. Intro to functions Function crunchersDomain and range. Domain and Range Then vertical line test. Vertical Line Test ... We present preliminary results from a student survey designed to test whether the all-important life skill of numeracy/quantitative literacy can be fostered and improved upon in college students through the vehicle of non-major introductory courses in Astronomy. Many instructors of introductory science courses for non-majors would state that a major goal of our classes is to teach our students to distinguish between science and pseudoscience, truth and fiction, in their everyday lives. It is difficult to believe that such a skill can truly be mastered without a fair amount of mathematical sophistication in the form of arithmetic, statistical and graph reading skills that many American college students unfortunately lack when they enter our classrooms. In teaching what is frequently their "terminal science course in life" can we instill in our students the numerical skills that they need to be savvy consumers, educated citizens and discerning interpreters of the ever-present polls, studies and surveys in which our society is awash? In what may well be their final opportunity to see applied mathematics in the classroom, can we impress upon them the importance of mathematical sophistication in interpreting the statistics that they are bombarded with by the media? Our study is in its second semester, and is designed to investigate to what extent it is possible to improve important quantitative skills in college students through a single semester introductory Astronomy course. Acquired memory skills best account for differences in memory performance. According to Chase and Ericsson's theory of skilled memory, improved memory or memory skills are due to the acquisition of more efficient storage and retrieval processes using long-term memory (LTM). Their theory specifies three principles which characterize the structure of memory skills. First, information rapidly stored in LTM is encoded\|Collecting data and analyzing the results of experiments is difficult for children. The authors found a surprising way to help their third graders make graphs and draw conclusions from their data: digital photographs. The pictures bridged the gap between an abstract graph and the plants it represented. With the support of the photos, students… We present the topic of graph connectivity along with a famous theorem of Menger in the real-world setting of the national computer network infrastructure of "National LambdaRail". We include a set of exercises where students reinforce their understanding of graph connectivity by analysing the "National LambdaRail" network. Finally, we give… The lesson begins with an exploration of the family of graphs of y = ax^2, with an emphasis on tracking the changes in the y-values for differing values of the parameter a. The vertical shifts of y = ax^2 + c follow, leading into the graphs of y = ax^2 + bx and the derivation of the formula for the vertex. Designers of graph drawing algorithms and systems claim to illuminate application data by producing layouts that optimize measurable aesthetic qualities. Examples of these aesthetics include symmetry (where possible, a symmetrical view of the graph should be displayed), minimize edge crossings (the number of edge crossings in the display should be minimized), and minimize bends (the total number of bends in This paper describes novel methods we developed to lay out graphs using Sugiyama's scheme (16) in a tool named GLEE. The main contributions are: a heuristic for creating a graph layout with a given aspect ratio, an efficient method of edge-crossings counting while performing adjacent vertex swaps, and a simple and fast spline routing algorithm. This site includes: Introduction to Graph Theory, Euler Circuits and Paths, Coloring Problems, and Adjacency Matrices (under construction). Each section consists of an interactive tutorial discussing the basic concepts of graph theory. This site is useful for high school and college students. In this activity, students enter in data to be represented in a double bar graph. Multi bar graphs allow the student toThe Graphs and Tracks Model allows instructors to create custom models of a ball rolling on a track with a variable shape. This EJS model was inspired by the Graphs and Tracks program by David Trowbridge. Instructors set the heights of the track segments and the model displays the motion of the ball. Optional displays, including position and velocity graphs, energy graphs, and data tables, can be added depending on the learning goals for the activity. Documents can aslo be added to the model to provide student instructions or activities. The customized simulation is then saved as a new jar file that can be redistributed. The Graphs and Tracks Model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the jar file will run the program if Java is installed. Wireless Sensor Networks (WSNs) is one of the famous researching fields. There are many applications like Smart Grid, Automation Systems, etc. Especially, the ISA100.11a standard that is adapted to the wireless industrial monitoring and control system is most famous sensor network application. In this standard they are suggest a simple and reliable routing mechanism called by graph routing. However the The Graph Structure (GRPHSTRUC) Model is a software system tool specifically developed to be used by a computer security analyst to study the security and analyze the design of computer networks. However, any system that can be characterized and represented by a graph structure could employ GRPHSTRUC with some minor system modifications. The GRPHSTRUC model is a knowledge-based expert system using icons and object-oriented programming methodologies. GRPHSTRUC has been designed and developed to use classical graph theory and allow the display of components and links of a graph structure. A graph G = (V,E) is a structure that consists of a finite set of vertices V and a finite set of edges E. A computer network is a graph structure; the vertices are the components of the network and the edges are the links between components. The GRPHSTRUC model provides a user interface that is designed to give a user the ability to rapidly and efficiently represent graph components, connections, and relationships. 9 refs., 1 fig. This paper will describe a project designed to enhance the numeracy skills of students at two educational levels - elementary and undergraduate. Under the guidance of the university students, students in grades four through six will formulate a research question, gather the appropriate data and summarize the data using graphs. The graphs along with a written summary of the project This article discusses a study which assessed the effect of a brief kinematics unit on: (1) students' ability to translate between a physical event and the graphic representation of it, and; (2) the effect of real-time on graphingskills. Reports the success of the use of a microcomputer-based laboratory with graphing velocity and distance. Positive definite kernels between labeled graphs have recently been proposed. They enable the application of kernel methods, such as support vector machines, to the analysis and classification of graphs, for example, chemical compounds. These graph kernels are obtained by marginalizing a kernel between paths with respect to a random walk model on the graph vertices along the edges. We propose A gain graph is a graph whose oriented edges are labelled invertibly from a group G, the gain group. A gain graph determines a biased graph and therefore has three natural matroids (as shown in Parts I-II): the bias matroid G has connected circuits; the complete lift matroid L0 and its restriction to the edge set, the lift matroid L, presents applications of entropic spanning graphs to imaging and feature clustering applications. Entropic spanning graphs span a set of feature vectors in such a way that the normalized spanning length of the graph converges to the entropy of the feature distribution as the number of random feature vectors increases. This property makes these graphs naturally suited to applications We investigate properties of a certain countably infl- nite graph called the inflnite locally random graph, written RN: The graph RN arises in the study of models for massive, self- organizing networks like the web graph. We characterize the iso- morphism type of RN as a limit of a random process, and via a domination elimination ordering. We prove that Interpretation in medicine is both old and new: old in traditional medical practice and new in conceptual theory. Physicians in every culture have built reputations on skillful readings of signs and symptoms in their fellow humans, but only recently has there arisen shared scholarly reflection on the nature of interpretation as practiced by clinicians. It remains to be seen whether Written by J.A. Bondy and U.S.R. Murty of the Pierre and Marie Curie University in Paris, this online 270-page textbook presents graph theory and its applications. The topics covered here include connectivity, independent sets and cliques, and planar and directed graphs. Each chapter has a list of references for further information, and most have exercises. Visitors can find the solution to those exercises in the Appendices here. . Mallows and Riordan showed in 1968 that labeled trees with a small number of inversions are related to labeled graphs that\\u000a are connected and sparse. Wright enumerated sparse connected graphs in 1977, and Kreweras related the inversions of trees\\u000a to the so-called ``parking problem'' in 1980. A combination of these three results leads to a surprisingly simple analysis Statistics play a vital role in the scientific enterprise. This activity provides background information and tutorials on basic statistics (mean, median, standard deviation, etc.) used in science. Topics include descriptive statistics (measures of central tendency and dispersion) and presenting data (tables, figures, and graphs). Sample datasets from actual scientific experiments are used to illustrate points. Links to an online statisitical tool and an online graphing application are also provided. \|With competition to attract quality students into career and technical education programs and many entrants to the workforce inadequately prepared with employability skills, some community colleges have found a way to answer industry's call--they are launching SkillsUSA chapters on campus. In this article, the author features SkillsUSA, a… Direct reciprocity is a mechanism for the evolution of cooperation based on the idea of repeated encounters between the same two individuals. Here we examine direct reciprocity in structured populations, where individuals occupy the vertices of a graph. The edges denote who interacts with whom. The graph represents spatial structure or a social network. For birth-death or pairwise comparison updating, we find that evolutionary stability of direct reciprocity is more restrictive on a graph than in a well-mixed population, but the condition for reciprocators to be advantageous is less restrictive on a graph. For death-birth and imitation updating, in contrast, both conditions are easier to fulfill on a graph. Moreover, for all four update mechanisms, reciprocators can dominate defectors on a graph, which is never possible in a well-mixed population. We also study the effect of an error rate, which increases with the number of links per individual; interacting with more people simultaneously enhances the probability of making mistakes. We provide analytic derivations for all results. Background Australian epidemiologists have recognised that lay readers have difficulty understanding statistical graphs in reports on population health. This study aimed to provide evidence for graph design improvements that increase comprehension by non-experts. Methods This was a double-blind, randomised, controlled trial of graph-design interventions, conducted as a postal survey. Control and intervention participants were randomly selected from telephone directories of health system employees. Eligible participants were on duty at the listed location during the study period. Controls received a booklet of 12 graphs from original publications, and intervention participants received a booklet of the same graphs with design modifications. A questionnaire with 39 interpretation tasks was included with the booklet. Interventions were assessed using the ratio of the prevalence of correct responses given by the intervention group to those given by the control group for each task. Results The response rate from 543 eligible participants (261 intervention and 282 control) was 67%. The prevalence of correct answers in the control group ranged from 13% for a task requiring knowledge of an acronym to 97% for a task identifying the largest category in a pie chart. Interventions producing the greatest improvement in comprehension were: changing a pie chart to a bar graph (3.6-fold increase in correct point reading), changing the y axis of a graph so that the upward direction represented an increase (2.9-fold increase in correct judgement of trend direction), a footnote to explain an acronym (2.5-fold increase in knowledge of the acronym), and matching the y axis range of two adjacent graphs (two-fold increase in correct comparison of the relative difference in prevalence between two population subgroups). Conclusion Profound population health messages can be lost through use of overly technical language and unfamiliar statistical measures. In our study, most participants did not understand age standardisation and confidence intervals. Inventive approaches are required to address this problem. Chris Caldwell of the University of Tennessee at Martin provides the Graph Theory Tutorials Website. Sections included at the site are Introduction to Graph Theory, Euler Circuits and Paths, Coloring Problems, and Adjacency Matrices (under construction). Each section consists of an interactive tutorial discussing the basic concepts of graph theory. Registration (press the REGISTER button at the bottom of first page of each tutorial) is required for each tutorial. The user must either pass a quiz in the tutorial section or write a comment before continuing to the next page. Links to related resources are also provided at the site. This site is useful for high school students and is definitely worth a visit. We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic expression in terms of a variant of the supersymmetric nonlinear ? model. Our estimate is based on a saddle-point analysis of this expression and leads to a criterion for when equidistribution emerges asymptotically in the limit of large graphs. Our theory predicts a rate of convergence that is a significant refinement of previous estimates, long assumed to be valid for quantum chaotic systems, agreeing with them in some situations but not all. We discuss specific examples for which the theory is tested numerically. Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs. Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w\\colon E(G)\\to {R}^+ can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k \\geq 2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles. Shop Skills is a lesson plan which provides instruction in the safety procedures and work processes for hand and machine tools used in a metal machine shop. Specific skills include sawing, drilling, boring, grinding, lathing, and milling. After completing this module, students should be able to demonstrate proficiency in these skills through a variety of shop projects and in a final exercise that uses a combination of these skills. Note: This module is part of a modularized manufacturing technology curriculum created by the PSCME, found at This lesson uses NASA images of Antarctic ozone (from the Total Ozone Mapping Spectrometer, or TOMS) to motivate a how-to graphing lesson followed by more sophisticated examples of graphing using images from the Neumayer Antarctic Station. Links are provided for investigating current knowledge of the ozone layer, and the impact of human activity on this vital part of the Earth system. We propose a new type of probabilistic graphical model, based on directed information, to represent the causal dynamics between processes in a stochastic system. We show the practical significance of such graphs by proving their equivalence to generative model graphs which succinctly summarize interde- pendencies for causal dynamical systems under mild assumptions. This equivalence means that directed information graphs may \|The teacher's guide and collection of transparency masters are designed for use in teaching adult basic education (ABE) students how to read and interpretgraphs and charts. Covered in the individual lessons of the instructional unit are the reading and interpretation of charts as well as picture, line, bar, and circle graphs. Each unit contains… This inquiry activity should be used before students learn about velocity and distance versus time graphs. Students will discover how the slope of a distance versus time graph is related to the speed of the object. We present a survey of confluence properties of (acyclic) term graph rewriting. Results and counterexamples are given for different kinds of term graph rewriting - besides plain applications of rewrite rules, extensions with the operations of collapsing a... \\u000a AGG is a general development environment for algebraic graph transformation systems which follows the interpretative approach.\\u000a Its special power comes from a very flexible attribution concept. AGG graphs are allowed to be attributed by any kind of Java\\u000a objects. Graph transformations can be equipped with arbitrary computations on these Java objects described by a Java expression.\\u000a The AGG environment consists of a graphical user The need for working with and understanding different types of graphs is a common occurrence in everyday life. Examples include anything having to do investments, being an educated juror in a case that involves evidence presented graphically, and understanding many aspect of our current political discourse. Within a science class graphs play a crucial role in presenting and interpreting data. In astronomy, where the range of graphed values is many orders of magnitude, log-axes must be used and understood. Experience shows that students do not understand how to read and interpret log-axes or how they differ from linear. Alters (1996), in a study of college students in an algebra-based physics class, found little understanding of log plotting. The purpose of this poster is to show the method and progression I have developed for use in my "ASTRO 101" class, with the goal being to help students better understand the H-R diagram, mass-luminosity relationship, and digital spectra. A discrete-time quantum walk on a graph ? is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup. The toughness of a graph G is defined as the largest real number t such that deletion of any s points from G results in a graph which is either connected or else has at most s\\/t components. Clearly, every hamiltonian graph is 1-tough. Conversely, we conjecture that for some t0, every t0-tough graph is hamiltonian. Since a square of A gain graph is a graph whose oriented edges are labelled invertibly from a group G, the gain group. A gain graph determines a biased graph and therefore has three natural matroids (as shown in Parts I and II): the bias matroidG has connected circuits; the complete lift matroidL0 and its restriction to the edge set, the lift matroidL, have Given a graph G and a positive integer k, denote by G(k) the graph obtained from G by replacing each vertex of G with an independent set of size k. A graph G is called pseudo-k Hamiltonian-connected if G(k) is Hamiltonian-connected, i.e., every two distinct vertices of G(k) are connected by a Hamiltonian path. A graph G is called pseudo Abstract Given a graph G and a positive integer k, denote by G[k] the graph obtained from G by replacing each vertex of G with an independent set of size k. A graph G is called pseudo-k Hamiltonian-connected if G[k] is Hamiltonian-connected, i.e., every two distinct vertices of G[k] are connected by a Hamiltonian path. A graph G is called \|In this article, the author shares one effective lesson idea on straight line graphs that he applied in his lower ability Y9 class. The author wanted something interesting for his class to do, something that was fun and engaging with direct feedback, and something that worked because someone else had tried it before. In a word, the author admits… In the past few years, the subject of graph theory (or network analysis) has come very much to the fore, not only as an important mathematical discipline in its own right, but also as a useful mathematical tool in a wide variety of subjects, ranging from organic chemistry and probability, through operational research and geography, to sociology and linguistics. InFrom Elizabeth Stapel at Purplemath, this module helps students understand how to graph linear equations by making a neat T-chart, finding plot points, plotting points, and drawing the line. There are four pages in this module with clear, systematically presented, step-by-step instructions and plenty of examples and illustrations to help students along. We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C. The purpose of this paper is to introduce a form of update based on the minimization of the geodesic distance on a graph. We provide a characterization of this class using set- theoretic operators and show that such operators bijectively correspond to geodesic metrics. As distance is generated by distinguishability, our framework is appropriate in contexts where distance is generated \|Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…This work deals with bounds on the cost of layout problems for lattice graphs and random lattice graphs. Our main result in this paper is a convergence theorem for the optimal cost of the Minim um Linear Arrangement problem and the Minimum Sum Cut problem, for the case where the underlying graph is obtained through a subcritical site percolation process. A large class of diagrams can be informally characterized as node-link diagrams. Typically nodes represent entities, and links represent relationships between them. The discipline of graph drawing is concerned with methods for drawing abstract versions of such diagrams. At the foundation of the disci- pline are a set of graph aesthetics (rules for graph layout) that, it is assumed, will This report describes the Fifth Annual Graph Drawing Con- test, held in conjunction with the 1998 Graph Drawing Symposium in Montreal, Canada. The purpose of the contest is to monitor and chal- lenge the current state of the art in graph-drawing technology (4, 5, 6, 7). Arrangement graphs have been proposed as an attractive interconnection topology for large multiprocessor systems. The authors study these graphs by proving the existence of Hamiltonian cycles in any arrangement graph. They also prove that an arrangement graph contains cycles of all lengths ranging between 3 and the size of the graph. They show that an arrangement graph can be decomposed The risk graph is one of the most popular methods used to determine the safety integrity level for safety instrumented functions. However, conventional risk graph as described in the IEC 61508 standard is subjective and suffers from an interpretation problem of risk parameters. Thus, it can lead to inconsistent outcomes that may result in conservative SILs. To overcome this difficulty, a modified risk graph using fuzzy rule-based system is proposed. This novel version of risk graph uses fuzzy scales to assess risk parameters and calibration may be made by varying risk parameter values. Furthermore, the outcomes which are numerical values of risk reduction factor (the inverse of the probability of failure on demand) can be compared directly with those given by quantitative and semi-quantitative methods such as fault tree analysis (FTA), quantitative risk assessment (QRA) and layers of protection analysis (LOPA). PMID:18835093 \|This study gives an insight into the differences between student understanding of line graph slope in the context of physics (kinematics) and mathematics. Two pairs of parallel physics and mathematics questions that involved estimation and interpretation of line graph slope were constructed and administered to 114 Croatian second year high school… Solving Equations 2. Begin working on ... The basic principle of graph-based approaches for image segmentation is to interpret an image as a graph, where the nodes of the graph represent 2D pixels or 3D voxels of the image. The weighted edges of the graph are obtained by intensity differences in the image. Once the graph is constructed, the minimal cost closed set on the graph can be computed via a polynomial time s-t cut, dividing the graph into two parts: the object and the background. However, no segmentation method provides perfect results, so additional manual editing is required, especially in the sensitive field of medical image processing. In this study, we present a manual refinement method that takes advantage of the basic design of graph-based image segmentation algorithms. Our approach restricts a graph-cut by using additional user-defined seed points to set up fixed nodes in the graph. The advantage is that manual edits can be integrated intuitively and quickly into the segmentation result of a graph-based approach. The method can be applied to both 2D and 3D objects that have to be segmented. Experimental results for synthetic and real images are presented to demonstrate the feasibility of our approach. The purpose of the basic visual observation skills course is to help safeguards inspectors evaluate and improve their skills in making observations during inspections and in evaluating and interpreting this information. The first 12 hours of the course pr... Mapping the detailed connectivity patterns (connectomes) of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron) varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome. In order to exploit the growing amount of RDF data in decision-making, there is an increasing demand for analytics-style processing of such data. RDF data is modeled as a labeled graph that represents a collection of binary relations (triples). In this context, analytical queries can be interpreted as consisting of three main constructs namely pattern matching, grouping and aggregation, and The effect of graph size on segmentation performance and speed is investigated, where segmentation is based on the graph cuts algorithm. The study is performed on lung extraction in 50 complete multi detector computed tomography (MDCT) datasets, and a fully automatic procedure. The experiments were performed on different graph sizes for both 2-D (4 and 8 neighbours) and 3-D (6 and 26 neighbours) graphs. Five slices from each segmented dataset were compared to the reference delineation provided by a radiologist. Our evaluations highlight the fact that when medical image segmentation is performed using graph cuts, increasing graph and neighbourhood connection size does not necessarily improve the segmentation performance, but also increase the running time dramatically. NLP applications for Sanskrit so far work within computational paradigm of string grammars. However, to compute 'meanings', as in traditional ?? bdabodha prakriy?-s, there is a need to develop suitable graph grammars. Ontological structures are fundamentally graphs. We work within the formal framework of Neo-Vai?e?ika Formal Ontology (NVFO) to propose a generative graph grammar. The proposed formal grammar only produces well-formed graphs that can be readily interpreted in accordance with Vai?e? ika Ontology. We show that graphs not permitted by Vai?e? ika ontology are not generated by the proposed grammar. Further, we write Interpreter of these graphical structures. This creates computational environment which can be deployed for writing computational applications of Vai?e? ika ontology. We illustrate how this environment can be used to create applications like computing ?? bdabodha of sentences. The purpose of this study was to assess the electrocardiogram (ECG) interpretationskills of pediatric residents in a controlled environment and determine if the level of residency training (intern vs senior) improves accuracy. A list of ECG diagnoses was provided to four pediatric residency educators with instructions to categorize each diagnosis as follows: I, all residents; II, the majority of \|This teaching plan is designed to assist nursing instructors assigned to advanced medical surgical nursing courses in acquainting students with the basic skills needed to perform electrocardiographic (ECG or EKG) interpretations. The first part of the teaching plan contains a statement of purpose; audience recommendations; a flow chart detailing…Let G be a non-abelian group and let Z(G) be the center of G. Associate a graph ?G (called non-commuting graph of G) with G as follows: Take G\\\\Z(G) as the vertices of ?G and join two distinct vertices x and y, whenever xy?yx. We want to explore how the graph theoretical properties of ?G can effect on the group In the ICCS 2000 proceedings we introduced negation to simple concept graphs without generic markers by adding cuts to their definition. The aim of this paper is to extend this approach of cuts to simple concept graphs with generic markers. For these graphs, a set-theoretical semantics is presented. After this a modification of Peirce's beta-calculus\\u000a is provided, and definitions for We present a user-controllable, general-purpose,pseudorandom task graph generator called TaskGraphs For Free (TGFF). TGFF creates probleminstances for use in allocation and scheduling research.It has the ability to generate independenttasks as well as task sets which are composed of partiallyordered task graphs. A complete description ofa scheduling problem instance is created, includingattributes for processors, communication resources,tasks, and inter-task communication. The user... . This report describes the Sixth Annual Graph Drawing Contest,held in conjunction with the 1999 Graph Drawing Symposiumin Prague, Czech Republic. The purpose of the contest is to monitorand challenge the current state of the art in graph-drawing technology[2, 3, 5, 6, 4].1 IntroductionText descriptions of the four categories for the 1999 contest are available via theWorld Wide Web (WWW) A random $n$-lift of a base graph $G$ is its cover graph $H$ on the vertices $[n]\\\\times V(G)$, where for each edge $u v$ in $G$ there is an independent uniform bijection $\\\\pi$, and $H$ has all edges of the form $(i,u),(\\\\pi(i),v)$. A main motivation for studying lifts is understanding Ramanujan graphs, and namely whether typical covers of such a Conceptual graphs allow for powerful and computationally affordable representation of the semantic contents of natural language\\u000a texts. We propose a method of comparison (approximate matching) of conceptual graphs. The method takes into account synonymy\\u000a and subtype\\/supertype relationships between the concepts and relations used in the conceptual graphs, thus allowing for greater\\u000a flexibility of approximate matching. The method also allows the \|Describes an interpretative experiment involving the application of symmetry and temperature-dependent proton and fluorine nmr spectroscopy to the solution of structural and kinetic problems in coordination chemistry. (MLH)\| The problem of graph classification has drawn much attention in the last decade. Conventional approaches on graph classification focus on mining discriminative sub graph features under supervised settings. The feature selection strategies strictly follow the assumption that both positive and negative graphs exist. However, in many real-world applications, the negative graph examples are not available. In this paper we study Graphs as conceptual data models are accepted and used in a wide range of different problem areas. Giving some examples we outline common aspects for modeling complex structures by graphs. We present a formal frame-work based on graph grammars to specify graph classes and the corresponding graph manipulations. We show that such a specification can be written in a systematic, This data with the use of a chart and a table and model linear equations to describe relationships between independent and dependent variables. Background Genome-wide association studies (GWAS) using single nucleotide polymorphism (SNP) markers generate large quantities of tests results. Global and local graphical viewing of the test results is an effective approach to digest and interpret GWAS results. Results SNPEVG is a set of graphical tools for instant global and local viewing and graphing of GWAS results for all chromosomes and for each trait. The current version includes three programs, SNPEVG1, SNPEVG2 and SNPEVG3. SNPEVG1 is a graphical tool for SNP effect viewing of P-values allowing multiple traits. The total number of graphs that can be generated by one 'Run' is n(c + 2), where n is number of 'traits' with 0 < n ? 100, and c is the number of chromosomes. SNP effect viewing and graphing is accomplished through a user friendly graphical user interface (GUI) that provides a wide-range of options for the user to choose. The GUI can produce the Manhattan plot, the Q-Q plot of all SNP effects, and graphs for SNP effects by chromosome by clicking one command. Any or all the graphs can be saved with publication quality by clicking one command. SNPEVG2 is for the viewing and graphing of multiple traits on the same graph with options to graph any or all of the traits, customizable colors and user specified Y1 or Y2 axis for each traits. The SNPEVG3 program uses the output file of single-locus test results from the epiSNP computer package as the input file. Each chromosome figure can display three genetic effects (genotypic, additive and dominance effects), and the number of observations. Conclusions The SNPEVG package is a versatile, flexible and efficient graphical tool for rapid digestion of large quantities of GWAS results with mouse clicks. Software which simulates, infers, or analyzes ancestral recombination graphs (ARGs) faces the problem of communicating them. Existing formats omit information either about the location of recombinations along the chromosome or the position of recombinations relative to the branching topology. We present a specialization of GraphML, an XML-based standard for mathematical graphs, for communication of ARGs. The GraphML type is specialized to contain the node type, time, recombination location, and name. The GraphML type is specialized to contain the ancestral material passed along that edge. This approach, which we call ArgML, retains all information in the original ARG. Due to its use of established formats ArgML can be parsed, checked and displayed by existing software. ) \|)\| \|The services of the Living Skills Center for the Visually Handicapped, a habilitative service for blind young adults, are described. It is explained that the Center houses its participants in their own apartments in a large complex and has served over 70 young people in 4 years. The evaluation section describes such assessment instruments as an… A high school program is described that uses an informal survey to help teachers identify potential academic, social, and career oriented problems facing mainstreamed handicapped students. These problems and suggested intervention procedures are listed for study/coping skills of time management, memory systems, listening ability, compensatory… \|This annotated bibliography lists approximately 150 braille books and 300 audiocassettes of books which address coping skills for people in a variety of situations. All items listed are available in the network library collections provided by the National Library Service for the Blind and Physically Handicapped of the Library of Congress.… Library of Congress, Washington, DC. National Library Service for the Blind and Physically Handicapped. Pedigree graphs, or family trees, are typically constructed by an expensive process of examining genealogical records to determine which pairs of individuals are parent and child. New methods to automate this process take as input genetic data from a set of extant individuals and reconstruct ancestral individuals. There is a great need to evaluate the quality of these methods by comparing the estimated pedigree to the true pedigree. In this article, we consider two main pedigree comparison problems. The first is the pedigree isomorphism problem, for which we present a linear-time algorithm for leaf-labeled pedigrees. The second is the pedigree edit distance problem, for which we present (1) several algorithms that are fast and exact in various special cases, and (2) a general, randomized heuristic algorithm. In the negative direction, we first prove that the pedigree isomorphism problem is as hard as the general graph isomorphism problem, and that the sub-pedigree isomorphism problem is NP-hard. We then show that the pedigree edit distance problem is APX-hard in general and NP-hard on leaf-labeled pedigrees. We use simulated pedigrees to compare our edit-distance algorithms to each other as well as to a branch-and-bound algorithm that always finds an optimal solution. PMID:22897201 A unified framework for grey value and texture segmentation has been developed. It makes use of a special graph structure (feature similarity graph - FSG) which is based on a feature similarity criterion and a feature smoothing procedure applied in each layer of the network. The feature similarity criterion reflects the fact that not the features themselves but their differences We propose a new algorithm that simultaneously estimates the intrinsic dimension and intrinsic entropy of random data sets lying on smooth manifolds. The method is based on asymptotic properties of entropic graph constructions. In particular, we compute the Euclidean -nearest neighbors ( - NN) graph over the sample points and use its overall total edge length to estimate intrinsic dimension A new kernel function between two labeled graphs is presented. Feature vectors are de- fined as the counts of label paths produced by random walks on graphs. The kernel com- putation finally boils down to obtaining the stationary state of a discrete-time linear sys- tem, thus is eciently performed by solv- ing simultaneous linear equations. Our ker- nel is based We present a graph-based iterative algorithm for clustering task. The existing literatures in this domain often use the distance measure between the testing data point individual which is proved not enough in the real applications. In this paper, we think about the core concept in semi-supervised learning method, and use a graph to reflect the original distance measure, and combine In the Walking Out Graphs Lesson described here, students experience several types of representations used to describe motion, including words, sentences, equations, graphs, data tables, and actions. The most important theme of this lesson is that students have to understand the consistency among these representations and form the habit of transforming among these representation (Shen and Confrey 2007). In a recent paper L. Lovasz has settled in the affirmative a conjecture due to Berge that had been outstanding in graph theory for over a decade, the perfect graph conjecture. In an earlier paper the author had obtained a closely related result, the plupe... Statistical graphs both illustrate a set of data and provide an analytical perspective. The distinction between these two functions is one of emphasis. Where the purpose of a graph is to dramatize or highlight a set of data, its primary function is illustration. Where the purpose of a graph is to explore, measure, calculate, and derive relationships, the primary function of the graph is analytical. In general practice, these two functions can be so interdependent as to be indistinguishable. The following guidelines are intended to aid in resolving problems common to the presentation of data in statistical graphs. The variety and complexity of data to be presented call for a flexible approach; therefore, the following examples are intended not as inflexible specifications but rather as guides to the design of graphs that are attractive and easily understood. All the types of graphs discussed here have appeared in EIA publications. A list of references that provides further examples is included. Also included is a glossary of statistical terms used in discussing the statistical properties of different types of graphs. 11 refs., 24 figs. A new algorithm for automated fingerprint encoding and matching is presented. The algorithm is intended to be insensitive to imperfections introduced during fingerprint registration, such as noise. distortion and displacement. A fingerprint is represented in the form of a graph whose nodes correspond to ridges in the print. Edges of the graph connect nodes that represent neighboring or intersecting ridges. Let G = (V,E) be a graph. A set S V is a restrained dominating set if every vertex in V S is adjacent to a vertex in S and to a vertex in V S. The restrained domination number of G, denoted by r(G), is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is The cluster structure of many real-world graphs is of great interest, as the clusters may correspond e.g. to communities in social networks or to cohesive modules in software systems. Layouts can naturally represent the cluster structure of graphs by grouping densely connected nodes and separating sparsely connected nodes. This article introduces two energy models whose minimum energy layouts represent theThis Web unit introduces the coordinate plane with the help of Sam the Chameleon, who illustrates how to find points on a number line and graph points in the coordinate plane. A link to a Java applet for graphing with Sam is included. An Overview A major consideration we had in writing this survey was to make it accessible to mathematicians as well as to computer scientists, since expander graphs ,t he protagonists of our story, come up in numerous and often surprising contexts in both fields. But, perhaps, we should start with a few words about graphs in general. They are, of Graph logic (GL) is a spatial logic for querying graphs intro- duced by Cardelli et al. It has been observed that in terms of expressive power, this logic is a fragment of Monadic Second Order Logic (MSO), with quantication over sets of edges. We show that the containment is proper by exhibiting a property that is not GL denable but A method for conceptual clustering of a collection of texts represented with conceptual graphs is presented. It uses an incremental strategy to construct the cluster hierarchy and incorporates some characteristics attractive for text mining purposes. For instance, it considers the structural information of the graphs, uses domain knowledge to detect the clusters with generalized descriptions, and uses a user-defined similarity A method for conceptual clustering of a collection of texts represented with conceptual graphs is presented. It uses the incremental strategy to construct the clus- ter hierarchy and incorporates some characteristics attractive for text mining proposes. For instance, it considers the structural information of the graphs, uses domain knowledge to detect the clusters with generalized descriptions, and uses a user-defined \|Identifies points where beliefs are important when making decisions about how graphs are drawn. Describes a simple case of the reaction between 'bicarb soda' and orange or lemon juice and discusses how drawing a graph becomes a statement of belief. (KHR)\| We study the Schrödinger equation on an infinite metric graph where the Hamiltonian is given by a suitable one-dimensional Dirichlet Laplacian. The metric structure is defined by assigning an interval In = (0,ln), n 2 N, to each edge of the graph with ln = n. The spectrum of this system is purely discrete with the eigenvalues given by n This lesson is designed to introduce students to graphing coordinates and lines in the Cartesian coordinate plane. This lesson provides links to discussions and activities related to graphing as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one. This step by step lesson from Math Ops demonstrates graphing slope-intercept equations. Students can read the text on each slide or follow along as it is read out loud. Four examples are given along with detailed instructions on how to graph this type of equation. It is established that if G is a reducible flow graph, then edge (n, m) is backward (a back latch) if and only if either n = m or m dominates n in G. Thus, the backward edges of a reducible flow graph are unique.Further characterizations of reducibility are presented. In particular, the following are equivalent: (a) G = (N, The coupled graph c(G) of a plane graph G is the graph de.ned on the vertex set V (G)?F(G) so that two vertices in c(G) are joined byan edge if and onlyif theyare adjacent or incident in G. We prove that the coupled graph of a 2-connected plane graph is edge-pancyclic. However, there exists a 2-edge-connected plane graph G such In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs. interpreterskillsDifficulties and discomfort with the interpretation of quantum mechanics are due to differences in language between it and classical physics. Analogies to The Special Theory of Relativity, which also required changes in the basic worldview and language of non-relativistic classical mechanics, may help in absorbing the changes called for by quantum physics. There is no need to invoke extravagances such A project (1972-1973) designed to study methods of evaluating the skills of interpreters for deaf people and to establish criteria for classifying such interpreters according to their levels of skill distributed a survey questionnaire to 300 of the partic... Graph data mining algorithms are increasingly applied to biological graph dataset. However, while existing graph mining algorithms can identify frequently occurring sub-graphs, these do not necessarily represent useful patterns. In this paper, we propose a novel graph mining algorithm, MIGDAC (Mining Graph DAta for Classification), that applies graph theory and an interestingness measure to discover interesting sub-graphs which can be These are short exercises that allow students practice with concepts in Structural Geology, Tectonics, or Geophysics. (Many of them were designed with Eric Horsman.) The basic idea is to give students opportunities for frequent practice with difficult concepts, many of which require spatial visualization skills. These activities nearly always fit on a half-sheet of paper, and include a visual and verbal component. Instructors may use them for formative assessment or as group activities in class. GRAPH is an interactive program that allows the user to perform two functions. The first is to plot two dimensional graphs and the second is to digitize graphs or plots to create data files of points. The program is designed to allow the user to get results quickly and easily. It is written in RATIV (a FORTRAN preprocessor) and is currently in use at Sandia under VMS on a VAX computer and CTSS on a Cray supercomputer. The program provides graphical output through all of the Sandia Virtual Device Interface (VDI) graphics devices. 2 refs., 3 figs., 3 tabs. GraphGrep is an application-independent method for querying graphs, finding all the occurrences of a sub- graph in a database of graphs. The interface to Graph- Grep is a regular expression graph query language Glide that combines features from XPath and Smart. Glide in- corporates both single node and variable-length wildcards. Our algorithm uses hash-based fingerprinting to represent the graphs in This case study characterizes the inscriptional practices demonstrated by seventh graders, particularly their use of data tables and graphs, in an inquiry-based learning environment. Using a naturalistic approach, we collected multiple sources of data during an 8-month instructional unit that emphasized water quality and relevant concepts. The analyses show that constructing and interpretinggraphs and tables provided students with opportunities Current reform documents in science and mathematics call for teachers to include inquiry and data analysis in their teaching. This interpretive quasi-ethnographic case study examined two middle school science teachers as they planned and implemented inquiry and graphing in their science curricula. The focus question for this research was: What are middle school science teachers' experiences as they include graphing Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets. Difficulties and discomfort with the interpretation of quantum mechanics are\\u000adue to differences in language between it and classical physics. Analogies to\\u000aThe Special Theory of Relativity, which also required changes in the basic\\u000aworldview and language of non-relativistic classical mechanics, may help in\\u000aabsorbing the changes called for by quantum physics. There is no need to invoke\\u000aextravagances such Interpreting Rankings Data A natural reaction of some readers when looking at charts that rank their state's cancer rates is to seek explanations as to why their state has higher incidence rates for some cancers than other states or than the national average. Some may be alarmed that exposure to environmental carcinogens may be responsible when in fact there are several other more likely explanations. \|Presents an activity incorporating basic terminology, concepts, and solution methods of graph theory in the context of solving problems related to air travel. Discusses prerequisite knowledge and resources and includes a teacher's guide with a student worksheet. (KHR)\| We explore the effectiveness of visualizing dense directed graphs by replacing individual edges with edges connected to 'modules'-or groups of nodes-such that the new edges imply aggregate connectivity. We only consider techniques that offer a lossless compression: that is, where the entire graph can still be read from the compressed version. The techniques considered are: a simple grouping of nodes with identical neighbor sets; Modular Decomposition which permits internal structure in modules and allows them to be nested; and Power Graph Analysis which further allows edges to cross module boundaries. These techniques all have the same goal-to compress the set of edges that need to be rendered to fully convey connectivity-but each successive relaxation of the module definition permits fewer edges to be drawn in the rendered graph. Each successive technique also, we hypothesize, requires a higher degree of mental effort to interpret. We test this hypothetical trade-off with two studies involving human participants. For Power Graph Analysis we propose a novel optimal technique based on constraint programming. This enables us to explore the parameter space for the technique more precisely than could be achieved with a heuristic. Although applicable to many domains, we are motivated by-and discuss in particular-the application to software dependency analysis. PMID:24051826 We study the problem how to draw a planar graph crossing-free such that every vertex is incident to an angle greater than ?. In general a plane straight-line drawing cannot guarantee this property. We present algorithms which construct such drawings with either tangent-continuous biarcs or quadratic Bézier curves (parabolic arcs), even if the positions of the vertices are predefined by a given plane straight-line drawing of the graph. Moreover, the graph can be drawn with circular arcs if the vertices can be placed arbitrarily. The topic is related to non-crossing drawings of multigraphs and vertex labeling.In this activity, students will learn about seismic data and the basics of how to use it. Using a single-channel seismomgraph, they will establish a survey line, set up the instrument, and make readings (time, in milliseconds) at measured intervals. They will graph their data, attempt to locate the water table (indicated by a break in slope in the graph), and calculate its depth. Sample data for constructing practice graphs, instructions for using the seismograph, and the formula for calculating depth are provided. Instructions for obtaining a video that outlines the procedure are also included. There are surprisingly few good software tools available for presenting time series data on the internet. The most common practice is to use a desktop program such as Excel or Matlab to save a graph as an image which can be included in a web page like any other image. This disconnects the graph from the data in a way that makes updating a graph with new data a cumbersome manual process, and it limits the user to one particular view of the data. The Multigraph project defines an XML format for describing interactive data graphs, and software tools for creating and rendering those graphs in web pages and other internet connected applications. Viewing a Multigraph graph is extremely simple and intuitive, and requires no instructions; the user can pan and zoom by clicking and dragging, in a familiar "Google Maps" kind of way. Creating a new graph for inclusion in a web page involves writing a simple XML configuration file. Multigraph can read data in a variety of formats, and can display data from a web service, allowing users to "surf" through large data sets, downloading only those the parts of the data that are needed for display. The Multigraph XML format, or "MUGL" for short, provides a concise description of the visual properties of a graph, such as axes, plot styles, data sources, labels, etc, as well as interactivity properties such as how and whether the user can pan or zoom along each axis. Multigraph reads a file in this format, draws the described graph, and allows the user to interact with it. Multigraph software currently includes a Flash application for embedding graphs in web pages, a Flex component for embedding graphs in larger Flex/Flash applications, and a plugin for creating graphs in the WordPress content management system. Plans for the future include a Java version for desktop viewing and editing, a command line version for batch and server side rendering, and possibly Android and iPhone versions. Multigraph is currently in use on several web sites including the US Drought Portal ( the NOAA Climate Services Portal ( the Climate Reference Network ( NCDC's State of the Climate Report ( and the US Forest Service's Forest Change Assessment Viewer (ews.forestthreats.org/NPDE/NPDE.html). More information about Multigraph is available from the web site Interactive Multigraph Display of Real Time Weather Data \|OBJECTIVE Oral presentation skills are central to physician-physician communication; however, little is known about how these skills are learned. Rhetoric is a social science which studies communication in terms of context and explores the action of language on knowledge, attitudes, and values. It has not previously been applied to medical discourse. We used rhetorical principles to qualitatively study how students learn oral presentation skills and what professional values are communicated in this process. DESIGN Descriptive study. SETTING Inpatient general medicine service in a university-affiliated public hospital. PARTICIPANTS Twelve third-year medical students during their internal medicine clerkship and 14 teachers. MEASUREMENTS One-hundred sixty hours of ethnographic observation. including 73 oral presentations on rounds. Discoursed-based interviews of 8 students and 10 teachers. Data were qualitatively analyzed to uncover recurrent patterns of communication. MAIN RESULTS Students and teachers had different perceptions of the purpose of oral presentation, and this was reflected in performance. Students described and conducted the presentation as a rule-based, data-storage activity governed by "order" and "structure." Teachers approached the presentation as a flexible means of "communication" and a method for "constructing" the details of a case into a diagnostic or therapeutic plan. Although most teachers viewed oral presentations rhetorically (sensitive to context), most feedback that students received was implicit and acontextual, with little guidance provided for determining relevant content. This led to dysfunctional generalizations by students, sometimes resulting in worse communication skills (e.g., comment "be brief" resulted in reading faster rather than editing) and unintended value acquisition (e.g., request for less social history interpreted as social history never relevant). CONCLUSIONS Students learn oral presentation by trial and error rather than through teaching of an explicit rhetorical model. This may delay development of effective communication skills and result in acquisition of unintended professional values. Teaching and learning of oral presentation skills may be improved by emphasizing that context determines content and by making explicit the tacit rules of presentation. Graphs are useful data structures capable of efficiently repre- senting a variety of technological and social networks. They are therefore utilized in simulation-based studies of new algorithms and protocols. In- spired by the popular tgff (Task Graphs For Free) toolkit, which creates task graphs for embedded systems, we present the ngce ,a n easy to use graph generator that produces Graph data such as chemical compounds and XML documents are getting more common in many application domains. A main di-culty of graph data processing lies in the intrinsic high dimensionality of graphs, namely, when a graph is represented as a binary feature vector of indicators of all possible subgraph patterns, the dimensionality gets too large for usual statistical methods. We The present paper is an introduction to a combinatorial theory arising as a natural generalisation of classical and virtual knot theory. There is a way to encode links by a class of `realisable' graphs. When passing to generic graphs with the same equivalence relations we get `graph-links'. On one hand graph-links generalise the notion of virtual link, on the other We propose constructing provable collision resistant hash functions from expander graphs in which finding cycles is hard. As examples, we investigate two spe- cific families of optimal expander graphs for provable collision resistant hash function constructions: the families of Ramanujan graphs constructed by Lubotzky-Phillips- Sarnak and Pizer respectively. When the hash function is constructed from one of Pizer's Ramanujan graphs, We propose constructing provable collision resistant hash functions from expander graphs. As examples, we investigate two spe- cific families of optimal expander graphs for provable hash function con- structions: the families of Ramanujan graphs constructed by Lubotzky- Phillips-Sarnak and Pizer respectively. When the hash function is con- structed from one of Pizer's Ramanujan graphs, (the set of supersingular elliptic curves Systems such as proteins, chemical compounds, and the Internet are being modeled as complex networks to identify local and global characteristics of the system. In many instances, these graphs are very large in size presenting challenges in their analysis. Hence, graph indexing techniques are developed to enhance various graph mining algorithms. In this paper, we propose a new Structural Graph We describe an algorithm and experiments for inference of edge replacement graph grammars. This method generates candidate recursive graph grammar productions based on isomorphic subgraphs which overlap by two nodes. If there is no edge between the two overlapping nodes, the method generates a recursive graph grammar production with a virtual edge. We guide the search for the graph grammar A linear graph is a graph whose vertices are linearly ordered. This linear ordering allows pairs of disjoint edges to be either preceding (<), nesting (?) or crossing (?). Given a family of linear graphs, and a non-empty subset R?{,?,?}, we are interested in the Maximum Common Structured Pattern (MCSP) problem: find a maximum size edge-disjoint graph, with edge pairs This animation shows the El Nino-La Nina Sea Surface Temperature Anomaly from January 1997 through July 1999. A graph inset shows the global average sea surface temperature fluctuation during this time period. This inquiry activity should be performed before students have learned about acceleration but after they have learned about speed. Students should have already completed distance versus time graphs for objects traveling at constant speed (see Lab 1). Some Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail. Scene graphs have become an established tool for developing interactive 3D applications, but with the focus lying on support for multi-processor and multi-pipeline systems, for distributed applications and for advanced rendering effects. Contrary to these developments, this work focusses on the expressiveness of the scene graph structure as a central tool for developing 3D user interfaces. We present the idea ionCommon visualization techniques like windowing, zooming, fish-eye view or graphfolding are not suitable to render graphs larger than a few thousand vertices and edges[7, 8, 9, 11]. Beyond this threshold either the required drawing area gets too large orthe size of the graph elements approaches the size of a pixel. In any case the amount ofthe displayed information easily overloads In this paper we propose a class of prior distributions on decomposable graphs, allowing\\u000afor improved modeling flexibility. While existing methods solely penalize the number of edges,\\u000athe proposed work empowers practitioners to control clustering, level of separation, and other\\u000afeatures of the graph. Emphasis is placed on a particular prior distribution which derives its\\u000amotivation from the class of We consider a compromise model in one dimension in which pairs of agents interact through first-order dynamics that involve both attraction and repulsion. In the case of all-to-all coupling of agents, this system has a lowest energy state in which half of the agents agree upon one value and the other half agree upon a different value. The purpose of this paper is to study the behavior of this compromise model when the interaction between the N agents occurs according to an Erd?s-Rényi random graph {G}(N,p). We study the effect of changing p on the stability of the compromised state, and derive both rigorous and asymptotic results suggesting that the stability is preserved for probabilities greater than pc=O(log N/N). In other words, relatively few interactions are needed to preserve stability of the state. The results rely on basic probability arguments and the theory of eigenvalues of random matrices. Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock Scissors Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games. We study evolutionary games on graphs. Each player is represented by a vertex of the graph. The edges denote who meets whom. A player can use any one of n strategies. Players obtain a payoff from interaction with all their immediate neighbors. We consider three different update rules, called 'birth-death', 'death-birth' and 'imitation'. A fourth update rule, 'pairwise comparison', is shown to be equivalent to birth-death updating in our model. We use pair-approximation to describe the evolutionary game dynamics on regular graphs of degree k. In the limit of weak selection, we can derive a differential equation which describes how the average frequency of each strategy on the graph changes over time. Remarkably, this equation is a replicator equation with a transformed payoff matrix. Therefore, moving a game from a well-mixed population (the complete graph) onto a regular graph simply results in a transformation of the payoff matrix. The new payoff matrix is the sum of the original payoff matrix plus another matrix, which describes the local competition of strategies. We discuss the application of our theory to four particular examples, the Prisoner's Dilemma, the Snow-Drift game, a coordination game and the Rock-Scissors-Paper game. This work presents a brief review of some selected knowledge-based approaches to electrocardiographic (ECG) pattern interpretation for diagnosing various malfunctions of the human heart. The knowledge-based approaches discussed here include modeling an ECG pattern through an AND\\/OR graph, a rule-based approach and a procedural semantic network (PSN) based approach for ECG interpretation. However, certain syntactic approaches to ECG interpretation are Teachers were taught "Translation Activities" (TA) to teach science process skills in three special education schools in South Africa. In TA, information and data are provided as text, diagrams, tables, or graphs, and cooperative learning takes place. Teachers indicated the use of TA enabled them to deliver Outcomes Based Education. (Contains… This quick YouTube video from high school statistics teacher Roger W. Davis explains how to find one variable statistics using the TI-84 graphing calculator. The demonstration goes through three steps: entering the data, finding one variable statistics using the STAT menu, and interpreting the results. The data created includes mean, sum, median and more. Flash player is required to view this video, and the running time for the clip is 3:12. The ability to interpret graphical information is a prime concern in physics as graphs are widely used to give quick summaries of data sets, for pattern recognition, and for analysis of information. While visual graphs have been developed so that their content can be readily and concisely discerned, there is great difficulty when someone is unable, because of their environment or due to physical handicaps, to view graphs. An alternative to the visual graph is the auditory graph. An auditory graph uses sound rather than pictures to transmit information. This study shows that useful auditory graphs of single valued x-y data were constructed by mapping the y axis to pitch, the x axis to time, and by including drum beats to mark first and second derivative information. Further audio enhancement was used to indicate negative data values. The study used a World Wide Web based test consisting of a series of math and physics questions. Each question was based on a graph and had multiple-choice answers. The test instrument was refined through a series of pilot tests. The main study compared the results of over 200 introductory physics students at Oregon State University, as well as other selected subjects. A computer program randomly assigned subjects to one of three groups. Each group was presented with the same test but had a different graph presentation method. The presentation methods were: only visual graphs, only auditory graphs, or both auditory and visual graphs. This study shows that students with very little training can use auditory graphs to answer analytical and identification type questions. Student performance for the group using only auditory graphs is 70% of the level attained by subjects using visually presented graphs. In addition, five blind subjects from remote locations participated in this test. Their performance level exceeded that of the first-year physics students. This work also displays the results from a pilot study of various auditory preference choices. Elements of this test may be useful for future auditory graph research and development. The RDF Graph Modeling Language (RGML) is a W3C RDF vocabulary to describe graph structures, including semantic information associated with a graph. Viewing general graphs as Web resources, RGML defines graph, node, and edge as RDF classes and attributes of graphs (such as label and weight) as RDF properties. Some of these RDF properties establish relationships between graph, node, and In this paper, I develop a model to analyze how skill premia differ over time and across countries, and use this model to study the impact of international trade on wage inequality. Skill premia are determined by technology and the relative supply of skills. An increase in the relative supply of skills, holding technology constant, reduces the skill premium. Among Skeptics may view DSM as a convenient cover for using ratepayer funds (in the form of rebates and other financial inducements) to keep customers on the grid, thus providing electric utilities with an unfair competitive advantage. Actually, the most powerful advantages may result from the marketing skills DSM fosters. Put simply, DSM teaches utilities to understand and meet customer needs more effectively. Managing customers use of electricity has taught utilities unprecedented amounts about specific end-use technologies, about customers fuel and equipment selection practices and preferences, and about what it costs to serve their customers. As DSM programs have become more market-driven, utilities have become better communicators and salesmen in order to win customer participation. The result: DSM departments play an increasingly central role in managing customer relationships overall and in developing and implementing competitive strategies. Let [Gamma] be a connected G-symmetric graph of valency r, whose vertex set V admits a non-trivial G-partition [script B], with blocks B[set membership][script B] of size v and with k[less-than-or-eq, slant]v independent edges joining each pair of adjacent blocks. In a previous paper we introduced a framework for analysing such graphs [Gamma] in terms of (a) the natural quotient graph [Gamma][script B] of valency b=vr/k, and (b) the 1-design [script D](B) induced on each block. Here we examine the case where k=v and [Gamma][script B]=Kb+1 is a complete graph. The 1-design [script D](B) is then degenerate, so gives no information: we therefore make the additional assumption that the stabilizer G(B) of the block B acts 2-transitively on B. We prove that there is then a unique exceptional graph for which [mid R:]B[mid R:]=v>b+1. We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric {sigma} model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder. Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security. We show how to prepare any graph state of up to 12 qubits with (a) the minimum number of controlled-Z gates and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any graph state belongs to an equivalence class under local Clifford operations. We extend up to 12 qubits the classification of graph states according to their entanglement properties, and identify each class using only a reduced set of invariants. For any state, we provide a circuit with both properties (a) and (b), if it does exist, or, if it does not, one circuit with property (a) and one with property (b), including the explicit one-qubit gates needed. Complex diffusion was introduced in image processing literature as a means to achieve simultaneous denoising and enhancement of scalar valued images. In this paper, we present a novel geometric framework for achieving complex diffusion on color images expressed as image graphs. In this framework, we develop a new variational formulation for achieving complex diffusion. This formulation involves a modified harmonic map functional and is quite distinct from the Polyakov action described in earlier work by Sochen et al. Our formulation provides a framework for simultaneous (feature preserving) denoising and enhancement. We present results of comparison between the complex diffusion, and Beltrami flow all in the image graph framework. In this dissertation, the dynamics of socially or biologically interacting populations are investigated. The individual members of the population are treated as particles that interact via links on a social or biological network represented as a graph. The effect of the structure of the graph on the properties of the interacting particle system is studied using statistical physics techniques. In the first chapter, the central concepts of graph theory and social and biological networks are presented. Next, interacting particle systems that are drawn from physics, mathematics and biology are discussed in the second chapter. In the third chapter, the random walk on a graph is studied. The mean time for a random walk to traverse between two arbitrary sites of a random graph is evaluated. Using an effective medium approximation it is found that the mean first-passage time between pairs of sites, as well as all moments of this first-passage time, are insensitive to the density of links in the graph. The inverse of the mean-first passage time varies non-monotonically with the density of links near the percolation transition of the random graph. Much of the behavior can be understood by simple heuristic arguments. Evolutionary dynamics, by which mutants overspread an otherwise uniform population on heterogeneous graphs, are studied in the fourth chapter. Such a process underlies' epidemic propagation, emergence of fads, social cooperation or invasion of an ecological niche by a new species. The first part of this chapter is devoted to neutral dynamics, in which the mutant genotype does not have a selective advantage over the resident genotype. The time to extinction of one of the two genotypes is derived. In the second part of this chapter, selective advantage or fitness is introduced such that the mutant genotype has a higher birth rate or a lower death rate. This selective advantage leads to a dynamical competition in which selection dominates for large populations, while for small populations the dynamics are similar to the neutral case. The likelihood for the fitter mutants to drive the resident genotype to extinction is calculated. Graph-based learning provides a useful approach for modeling data in classification problems. In this modeling scenario, the relationship between labeled and unlabeled data impacts the construction and performance of classifiers, and therefore a semi-supervised learning framework is adopted. We propose a graph classifier based on kernel smoothing. A regularization framework is also introduced, and it is shown that the proposed classifier optimizes certain loss functions. Its performance is assessed on several synthetic and real benchmark data sets with good results, especially in settings where only a small fraction of the data are labeled. PMID:18000333 In the context of the EU project Mobius on Proof Carrying Code for Java programs (midlets) on mobile devices, we present a way to express midlet navigation graphs in JML. Such navigation graphs express certain security policies for a midlet. The resulting JML specifications can be automatically checked with the static checker ESC/Java2. Our work was guided by a realistically sized case study developed as demonstrator in the project. We discuss practical difficulties with creating efficient and meaningful JML specifications for automatic verification with a lightweight verification tool such as ESC/Java2, and the potential use of these specifications for PCC. The Web is a typical example of a social network. One of the most intriguing features of the Web is its self-organization behavior, which is usually faced through the existence of communities. The dis- covery of the communities in a Web-graph can be used to improve the eectiv eness of search engines, for purposes of prefetching, bibliographic citation ranking, spam This collection of one-minute videos depicts scenarios with measurements that can be graphed over a time scale of zero to 15 seconds. Eight different types of graphs are represented. A pdf file of grids is provided. A graph theoretic version of Steiner's problem in plane geometry is described. An approach for solving the problem, related to Melzak's solution to Steiner's problem, is presented. The problems of finding shortest route and minimal spanning tree in graphs... As an alternative to loading graphs, a graph of mean influent phosphorus concentration versus phosphorus retention capacity is proposed to express the relationship between phosphorus supply and hydraulic flow to, and resultant trophic state of, lakes. Lin... This collection of maps and graphs provides information on the locations of breeding colonies, distributions of biomass, seasonal species density, and deposition graphs for seabird and shorebird species of the central California coast. Visual graph representations are increasingly used to represent, display, and explore scenarios and the structure of organizations. The graph representations of scenarios are readily understood, and commercial software is available to create and manage th... \|Standard distributions are ubiquitous but not unique. With suitable scaling, the graph of a standard distribution serves as the graph for every distribution in the family. The standard exponential can easily be taught in elementary statistics courses.\| The medial axis being an homotopic transformation, the skeleton of a 2D shape corresponds to a planar graph having one face for each hole of the shape and one node for each junction or extremity of the branches. This graph is non simple since it can be composed of loops and multiple-edges. Within the shape comparison framework, such a graph is usually transformed into a simpler structure such as a tree or a simple graph hereby loosing major information about the shape. In this paper, we propose a graph kernel combining a kernel between bags of trails and a kernel between faces. The trails are defined within the original complex graph and the kernel between trails is enforced by an edition process. The kernel between bags of faces allows to put an emphasis on the holes of the shapes and hence on their genre. The resulting graph kernel is positive semi-definite on the graph domain. Given a graphG, a subgraphG' is at-spanner ofG if, for everyu,v ?V, the distance fromu tov inG' is at mostt times longer than the distance inG. In this paper we give a simple algorithm for constructing sparse spanners for arbitrary weighted graphs. We then apply this algorithm to obtain specific results for planar graphs and Euclidean graphs. We discuss the Conceptual graphs are similar to entity-relationship diagrams. They are however a visual, advanced knowledge-based representation formalism based upon much richer philosophical, psychological, linguistic, and object-oriented principles. Although there is much interesting and ongoing work in the conceptual graphs arena, there is little of an introductory nature for newcomers to conceptual graphs. Given the beauty of conceptual graphs is that their The number of vertex-colourings of a simple graphG in not more than? colours is a polynomial in?. This polynomial, denoted byP(G, ?), is called the chromatic polynomial ofG. A graphG is said to be chromatically unique, in short?-unique, ifH ? G for any graphH withP(H, ?) = P(G, ?). Since the appearance of the first paper on?-unique graphs by Chao In this paper, we describe PeGaSus, an open source Peta Graph Mining library which performs typical graph mining tasks such as computing the diameter of the\\u000a graph, computing the radius of each node, finding the connected components, and computing the importance score of nodes. As\\u000a the size of graphs reaches several Giga-, Tera- or Peta-bytes, the necessity for such a In an increasing number of domains such as bioinformatics, combi- natorial graph problems arise. We propose a novel way to solve these problems, mainly those that can be translated to constrained subgraph nding. Our approach extends constraint programming by introducing CP(Graph), a new computation domain focused on graphs including a new type of variable: graph domain vari- ables as well Abstract. We have been developing a theory for the generic representation of 2-D shape, where structural descriptionsWe have been developing a theory for the generic representation of 2-D shape, where structural de- scriptionsThis paper presents an algorithm for finding a minimum cost partition of the nodes of a graph into subsets of a given size, subject to the constraint that the sequence of the nodes may not be changed, that is, that the nodes in a subset must have consecutive numbers. The running time of the procedure is proportional to the number Traditionally, using only pencil and paper the graphing of parametric functions was a time-consuming task. Microsoft Excel is a convenient tool that can be used in the classroom to facilitate and enhance this procedure. A simple, but effective, spreadsheet is described. Increased availability of large repositories of chemical compounds is creating new challenges and opportunities for the application of machine learning methods to problems in computational chemistry and chemical informatics. Because chemical compounds are often represented by the graph of their covalent bonds, machine learning methods in this domain must be capable of processing graphical structures with variable size. Here we The Matching Game is a two person game, which is played on a (possibly infinite) bipartite graph (X,Y). The analysis of this game leads to some interesting results in the theory of matchings. It turns out that the first player has a winning strategy if an... A partition of V (G), all of whose classes are dominating sets in G, is called a domatic partition of G. The maximum number of classes of a domatic partition of G is called the domatic number of G. The concept of a domatic number was introduced in (1). More interesting results on domatically full graphs, domatically critical, domatically cocritical Several versions of the closed graph theorem are presented. That is, various conditions on pairs (E,F) of locally convex linear topological spaces are given which ensure that every closed linear map T of E into F is continuous. Additional restraints (such... \|General strategies used to help discover, prove, and generalize identities for Fibonacci numbers are described along with some properties about the determinants of square matrices. A matrix proof for identity (2) that has received immense attention from many branches of mathematics, like linear algebra, dynamical systems, graph theory and others… \|Description of a technique in Maple programming language that automatically prints all paths of any desired length along with the name of each vertex, proceeding in order from the beginning vertex to the ending vertex for a given graph. (Author/MM) Graphical models such as factor graphs allow a unified approach to a number of key topics in coding and signal processing such as the iterative decoding of turbo codes, LDPC codes and similar codes, joint decoding, equalization, parameter estimation, hidden-Markov models, Kalman filtering, and recursive least squares. Graphical models can represent complex real-world systems, and such representations help to derive We introduce cryptographic hash functions that are in correspondence with directed Cayley graphs, and for which finding collisions is essentially equivalent to finding short factorisations in groups. We show why having a large girth and a small diameter are properties that are relevant to hashing, and illustrate those ideas by proposing actual easily computable hash functions that meet those requirements. Let G be a graph and dv the degree (=number of first neighbors) of its vertex v. The connectivity index of G is ?=?(dudv)?1\\/2, with the summation ranging over all pairs of adjacent vertices of G. In a previous paper (Comput. Chem. 23 (1999) 469), by applying a heuristic combinatorial optimization algorithm, the structure of chemical trees possessing extremal (maximum This paper shows how to rapidly determine the path relationships between k different elements of a graph (of the type primarily resulting from programs) in time proportional to k log k. Given the path relations between elements u,v, and w, it is easy to answer questions like \\ In previous work, we have introduced a "linear framework" for time-scale separation in biochemical systems, which is based on a labelled, directed graph, G, and an associated linear differential equation, [Formula: see text], where [Formula: see text] is the Laplacian matrix of G. Biochemical nonlinearity is encoded in the graph labels. Many central results in molecular biology can be systematically derived within this framework, including those for enzyme kinetics, allosteric proteins, G-protein coupled receptors, ion channels, gene regulation at thermodynamic equilibrium, and protein post-translational modification. In the present paper, in response to new applications, which accommodate nonequilibrium mechanisms in eukaryotic gene regulation, we lay out the mathematical foundations of the framework. We show that, for any graph and any initial condition, the dynamics always reaches a steady state, which can be algorithmically calculated. If the graph is not strongly connected, which may occur in gene regulation, we show that the dynamics can exhibit flexible behavior that resembles multistability. We further reveal an unexpected equivalence between deterministic Laplacian dynamics and the master equations of continuous-time Markov processes, which allows rigorous treatment within the framework of stochastic, single-molecule mechanisms. PMID:24018536 A criterion is given for an immersed horizontal 1-injective surface in a graph mani- fold to be separable. Examples are constructed of such surfaces, which are not separable and do not satisfy the k-plane property, for any k. It is shown that the simple loop conjecture holds in graph manifolds and that any graph manifold with boundary has an immersed A facilities design algorithm is developed based upon such graph theory concepts as maximal spanning trees and planar graphs. The upper bound to the demands made by closeness ratings is developed from graph theory. The algorithm lends itself to computer solution minimizing the costs of flow between activities. An alternative approach using strings and the list processing capabilities of computers In this article we provide a combinatorial description of an arbitrary minor of the Laplacian matrix (L) of a mixed graph (a graph with some oriented and some unoriented edges). This is a generalized Matrix Tree Theorem. We also characterize the non-singular substructures of a mixed graph. The sign attached to a nonsingular substructure is described in terms of labeling We introduce a new tool for approximation and testing algorithms called partitioning oracles. We develop methods for constructing them for any class of bounded-degree graphs with an excluded minor, and in general, for any hyperfinite class o f bounded-degree graphs. These oracles utilize only local compu- tation to consistently answer queries about a global partition that breaks the graph into Attributed graphs are increasingly more common in many appli- cation \|As a college biology instructor, I often see graphs in lab reports that do not meet my expectations. I also observe that many college students do not always adequately differentiate between good and poor (or misleading) graphs. The activity described in this paper is the result of my work with students to improve their graphing literacy. The… The aim of this paper is to give a coherent account of the problem of constructing cubic graphs with large girth. There is a well-dened integer 0(g), the smallest number of vertices for which a cubic graph with girth at leastg exists, and furthermore, the minimum value 0(g) is attained by a graph whose girth is exactly g .T he Graphs are a vital way of organizing data with complex correlations. A good visualization of a graph can fundamentally change human understanding of the data. Consequently, there is a rich body of work on graph visualization. Although there are many techn... . We present algorithms for computing similarityrelations of labeled graphs. Similarity relations haveapplications for the refinement and verification of reactivesystems. For finite graphs, we present an O(mn) algorithmfor computing the similarity relation of a graphwith n vertices and m edges (assuming m n). For effectivelypresented infinite graphs, we present a symbolicsimilarity-checking procedure that terminates if a finitesimilarity relation exists. We We treat the stationary (cubic) nonlinear Schrödinger equation (NLSE) on simplest graphs. The solutions are obtained for primary star graph with the boundary conditions providing vertex matching and flux conservation. Both, repulsive and attractive nonlinearities are considered. It is shown that the method can be extended to the case of arbitrary number of bonds in star graphs and for other simplest topologies. mo- tivation is to obtain a succinct output The paradigm of simulated annealing is applied to the problem of drawing graphs "nicely." Our algorithm deals with general undirected graphs with straight-line edges, and employs several simple criteria for the aesthetic quality of the result. The algorithm is flexible, in that the relative weights of the criteria can be changed. For graphs of modest size it produces good results, Online graph coloring, in which the vertices are presented one at a time, is considered. Each vertex must be assigned a color, different from the colors of its neighbors, before the next vertex is given. The class of d-inductive graphs is treated. A graph G is said to be d-inductive if the vertices of G can be numbered so that We propose a new algorithmic framework for database concurrency control using multiple versions of data items and a serialization graph of the transactions as a synchronization technique, which generalizes all concurrency control methods known so far. This class of algorithms, called MVSGA for Multi Version Serialization Graph set of Algorithms, works by monitoring the acyclicity of the serialization graph which We present an analytic and geometric view of the sample mean of graphs. The theoretical framework yields efficient subgradient methods for approximating a structural mean and a simple plug-in mechanism to extend existing central clustering algorithms to graphs. Experiments in clustering protein structures show the benefits of the proposed theory. I. INTRODUCTION Graphs often occur as \\ Attack graphs are a valuable tool to network defenders, illustrating paths an attacker can use to gain access to a targeted network. Defenders can then focus their efforts on patching the vulnerabilities and configuration errors that allow the attackers the greatest amount of access. We have created a new type of attack graph, themultiple-prerequisite graph, that scales nearly linearly as We define a locally grid graph as a graph in which the structure around each vertex is a 3×3 grid ?, the canonical examples being the toroidal grids Cp×Cq. The paper contains two main results. First, we give a complete classification of locally grid graphs, showing that each of them has a natural embedding in the torus or in the A conceptual graph (CG) is a graph representation for logic based on the semantic networks of artificial intelligence and the existential graphs of Charles Sanders Peirce. CG design principles emphasize the requirements for a cognitive representation: a smooth mapping to and from natural languages; an \\ With the rapid development of advanced data acquisition techniques such as high-throughput biological experiments and wireless sensor networks, large amount of graph-structured data, graph data for short, have been collected in a wide range of applications. Discovering knowledge from graph data has witnessed a number of applications and received a lot of research attentions. Recently, it is observed that uncertainties Abstract. It is well known,that the maximum,chromatic number,of a graph on the orientable surface Sg is (g,=7). For specic surfaces we prove that every graph on the double torus and of girth at least six is 3-colorable and we characterize completely those triangle-free projective graphs that are not 3-colorable. We present a taxonomy of fuzzy graphs that treats fuzziness in vertex existence, edge existence, edge connectivity, and edge weight. Within that framework, we formulate some standard graph-theoretic problems (shortest paths and minimum cut) for fuzzy graphs using a uni\\ The Physics Education Group at the University of Washington is examining the extent to which students are able to use graphs of potential energy vs. position to infer kinematic and dynamic quantities for a system. The findings indicate that many students have difficulty in relating the graphs to real-world systems. Some problems seem to be graphical in nature (e.g., interpretinggraphs of potential energy vs. position as graphs of position vs. time). Others involve relating the graphs to total, kinetic, and potential energies, especially when the potential energy is negative. The results have implications beyond the introductory level since graphs of potential energy are used in advanced courses on classical and quantum mechanics. At the core of the seminal Graph Minor Theory of Robertson and Seymour is a powerful structural theorem capturing the structure of graphs excluding a fixed minor. This result is used throughout graph theory and graph al- gorithms, but is existential. We develop a polynomial- time algorithm using topological graph theory to decom- pose a graph into the structure guaranteed An outerplanar graph is a planar graph which can be embedded in the plane in such a way that all of vertices lie on the outer boundary. Many chemical compounds are known to be expressed by outerplanar graphs. In this paper, firstly, we introduce an externally extensible outerplanar graph pattern (eeo-graph pattern for short) as a graph pattern common to Graph has become increasingly important in modelling complicated structures and schemaless data such as proteins, chemical compounds, and XML documents. Given a graph query, it is desirable to retrieve graphs quickly from a large database via graph-based indices. In this paper, we investigate the issues of indexing graphs and propose a novel solution by applying a graph mining technique. Different The performance of codes defined from graphs depends on the expansion property of the underlying graph in a crucial way. Graph products, such as the zig-zag product (13) and replacement product provide new infinite families of constant degree expander graphs. The paper investigates the use of zig-zag and replacement product graphs for the construction of codes on graphs (16). A The purpose of the basic visual observation skills course is to help safeguards inspectors evaluate and improve their skills in making observations during inspections and in evaluating and interpreting this information. The first 12 hours of the course provide training in five skill areas: perception and recognition; attention to detail; memory; mental imaging, mapping, and modeling skills; and judgment and decision making. Following this training is an integrating exercise involving a simulated safeguards inspection. This report contains the in-class exercises in the five skill areas; pre- and post-course exercises in closure, hidden figures, map memory, and mental rotations; the final examination; a training evaluation form; and the integrating exercise. When geology students are confronted with their first rock exposure, they are often bewildered by the volume of information available and the need to filter out the irrelevant and unnecessary while recording the remainder in a format that lends itself to later analysis. In spite of the problems, the first experience of fieldwork provides many students with the inspiration to devote themselves to this branch of science. The critical factor appears to be the realisation that many of the vaguely interesting topics that have previously been studied in isolation all contribute to an understanding of the rocks in front of the observer. Even with only basic facts and limited understanding, the willing student rapidly gains a deeper appreciation of the ways in which the disparate fields of geoscience are inter-related. However, the initial enthusiasm this generates can be lost if the student is unable to record the information systematically and analyse it logically. The current project seeks to develop in students the intellectual skills necessary to analyse an exposure. In many ways finding the answers to any exposure's history is easy; the difficult part is formulating the right questions. By creating a series of 'Outcrop Exercises', I am seeking to imbue students with an appreciation of the way a structured series of questions can lead to understanding. If they go into the field knowing the sort of questions that they will have to ask themselves, they are more likely to understand the nature and purpose of the data they will have to collect. The earliest exercises were designed to enhance a stratigraphy course, and were intended for use by students who already had field experience. Rather than providing them with accepted facies models for the geological past, the data and questions with which they were provided allowed them to generate their own environmental interpretations. The success of these suggested that they had wider applicability: they could be used to develop essential reasoning skills before going into the field; they could form the basis of follow-up work after a field day, or could be used as a substitute for field work if severe weather prevented an excursion. Each Outcrop Exercise consists of an A3 data sheet, a question sheet, specimen cards and, if appropriate, topographic and geologic maps. The most important dimension of each exercise is the nature and structure of the questions, which begin by requiring the student to make simple observations and lead to a comprehensive interpretation of the exposure. The materials are intended to be used in a variety of ways: for example, if the resources are available it is preferable to replace the specimen cards with real specimens; if time is short, data processing can be omitted by supplying students with prepared graphs. With future developments, it will be possible to link exercises together to generate a geological history for a whole area from primary data. These exercises must not be seen as a substitute for real fieldwork, but it is hoped that they will enhance students' appreciation of the data that they must collect in the field. Residential segregation is a multidimensional phenomenon that encompasses several conceptually distinct aspects of geographical separation between populations. While various indices have been developed as a response to different definitions of segregation, the reliance on such single-figure indices could oversimplify the complex, multidimensional phenomena. In this regard, this paper suggests an alternative graph-based approach that provides more detailed information than simple indices: The concentration profile graphically conveys information about how evenly a population group is distributed over the study region, and the spatial proximity profile depicts the degree of clustering across different threshold levels. These graphs can also be summarized into single numbers for comparative purposes, but the interpretation can be more accurate by inspecting the additional information. To demonstrate the use of these methods, the residential patterns of three major ethnic groups in Auckland, namely M?ori, Pacific peoples, and Asians, are examined using the 2006 census data. In this paper the authors show how the Turaev-Viro invariant, which is closely related to the partition function of three-dimensional gravity, can be understood within the framework of SU(2) Chern-Simons theory. The authors also show that, for S{sub 3} and RP{sub 3}, this invariant is equal to the absolute value square of their respective partition functions in SU(2) Chern-Simons theory and give a method of evaluating the latter in a closed form for a class of 3D manifolds, thus in effect obtaining the partition function of three-dimensional gravity for these manifolds. By interpreting the triangulation of a manifold as a graph consisting of crossings and vertices with three lines we also describe a new invariant for certain class of graphs. Diagrams of trajectories of two-dimensional motions were shown to five students in introductory physics and five physics faculty. Analysis of how the two groups interpreted the diagrams enabled the investigators to identify the underlying knowledge and skills required. \|The interpretation of single-case data requires systematic visual analysis across and within conditions. Graphs are a vital component for analyzing and communicating single-case design data and a necessary tool for applied researchers and practitioners. Several articles have been published with task analyses for graphing data with the new… In this paper we ask the question, "What must be added tofirst-order logic plus least-fixed point to obtain exactly the polynomial-timeproperties of unordered graphs?" We consider the languages Lk consistingof first-order logic restricted to k variables and Ck consisting of Lk plus"counting quantifiers". We give efficient canonization algorithms for graphscharacterized by Ck or Lk . It follows from known results Students in a general education science course made significant gains in scientific reasoning skills when they were taught using carefully designed hands-on activities and writing assignments. The activities required students to make use of scientific skills such as graphing, predicting outcomes under changing conditions, or designing experiments,… The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications. In some contexts, a photograph may be worth a thousand words. Previous research revealed a dialectical character of photo- graphs: they simultaneously lack determinacy and exhibit an excess of meaning. The purpose of this study was to understand how, under this condition, high school students interpret photographs that were accom- panied by different amounts and types of co-text (caption, main Students analyze dramatic works using graph theory. They gather data, record it in Microsoft Excel and use Cytoscape (a free, downloadable application) to generate graphs that visually illustrate the key characters (nodes) and connections between them (edges). The nodes in the Cytoscape graphs are color-coded and sized according to the importance of the node (in this activity nodes represent characters in the work and their relative importance to the story). After the analysis, the graphs are further examined to see what the visual depiction of the story in the form of a graph tells readers about the inner workings of the dramatic work. Students gain practice with graph theory vocabulary, including node, edge, betweeness centrality and degree on interaction, and learn about a range of engineering applications of graph theory. Short circuit studies are undertaken to determine if equipment selections have adequate electrical and mechanical ratings. In addition to the ratings check, the devices` performance in the time periods required to minimize damage during a system component failure is examined. The results are shown as computer listings of voltages and currents at each node of the network. While full of useful information, they are hard to visualize. Graphs developed from the computer printouts make interpretation of the numbers easier. The following explains how the graphs are created and each device`s meaning. The data presented are from a real installation: a pumping station with four 1,000-hp pumps and a small 125-hp pump. Each portion of a coordination curve will be discussed and, at the end of the article, the composite curves will be shown. It was demonstrated recently that the line graphs are clustered and assortative. These topological features are known to characterize some social networks [M.E.J. Newman, Y. Park, Why social networks are different from other types of networks, Phys. Rev. E 68 (2003) 036122]; it was argued that this similarity reveals their cliquey character. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8×106 people PMID:19773605 In this activity, learners help a poor cartographer color in the countries on a map, making sure each country is colored a different color than any of its neighbors. Through this exercise, learners discover the "has-to-be" rule and the value of place-holders. This activity reveals the complexity of graph coloring algorithms in computer science. Variations, extensions, background information, and solutions are included in the PDF. When considering a graphical Gaussian model ${\\\\mathcal{N}}_G$ Markov with respect to a decomposable graph $G$, the parameter space of interest for the precision parameter is the cone $P_G$ of positive definite matrices with fixed zeros corresponding to the missing edges of $G$. The parameter space for the scale parameter of ${\\\\mathcal{N}}_G$ is the cone $Q_G$, dual to $P_G$, of incomplete A directed graph is set-homogeneous if, whenever U and V are isomorphic finite subdigraphs, there is an automorphism g of the digraph with U^gA directed graph is set-homogeneous if, whenever U and V are isomorphic finite subdigraphs, there is an automorphism g of the digraph with UgThe objective of this research was to identify Facione's six critical thinking skills using graduate students blogs as a reflection tool in the context of leadership using structured and unstructured blogs. The skills researched were (a) Interpretation, (b) Analysis, (c) Evaluation, (d) Inference, (e) Explanation, and (f) Self-Regulation (Facione,… \|Participants' performances of outdoor skills and leadership are interpreted for environmental learning using Ingold's (2000) notion of an "education of attention": the fine-tuning of their perception. The actual tasks and activities of adventure travel have until recently gone largely unquestioned; but the relationship between skills and… We report on the results from an empirical study deal-ing with the semantic interpretation of prepositional phrases in medical free texts. We use a small number of semantic interpretation schemata only, which operate on well-defined configurations in dependency graphs. We provide a quantitative analysis of the performance of the semantic interpreter in terms of recall/precision data, and consider, in qualitative terms, the impact semantic interpretation patterns have on the construction of the underlying medical ontology. We develop a generalized optimization framework for graph-based semi-supervised learning. The framework gives as particular cases the Standard Laplacian, Normalized Laplacian and PageRank based methods. We have also provided new probabilistic interpretation based on random walks and characterized the limiting behaviour of the methods. The random walk based interpretation allows us to explain di erences between the performances of methods We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers—that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 103 and 104. A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed. Drugs are devised to enter into the metabolism of an organism in order to produce a desired effect. From the chemical point of view, cellular metabolism is constituted by a complex network of reactions transforming metabolites one in each other. Knowledge on the structure of this network could help to develop novel methods for drug design, and to comprehend the root of known unexpected side effects. Many large-scale studies on the structure of metabolic networks have been developed following models based on different kinds of graphs as the fundamental image of the reaction network. Graphs models, however, comport wrong assumptions regarding the structure of reaction networks that may lead into wrong conclusions if they are not taken into account. In this article we critically review some graph-theoretical approaches to the analysis of centrality, vulnerability and modularity of metabolic networks, analyzing their limitations in estimating these key network properties, consider some proposals explicit or implicitly based on directed hypergraphs regarding their ability to overcome these issues, and review some recent implementation improvements that make the application of these models in increasingly large networks a viable option. PMID:21539508 This paper examines the relation between bodily actions, artifact-mediated activities, and semiotic processes that students experience while producing and interpretinggraphs of two-dimensional motion in the plane. We designed a technology-based setting that enabled students to engage in embodied semiotic activities and experience two modes of… Crime activities are geospatial phenomena and as such are geospatially, thematically and temporally correlated. Thus, crime datasets must be interpreted and analyzed in conjunction with various factors that can contribute to the formulation of crime. Discovering these correlations allows a deeper insight into the complex nature of criminal behavior. We introduce a graph based dataset representation that allows us to This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems involving the construction and interpretation of graphs and… Described by their proponents as an alternative to positivistic perspectives on media effects that ignore audience activity, interpretive approaches center on the interpretive processes employed by audience members in their decoding of media content. Meaning is viewed as a product of the interaction between media texts and the varied, at times contradictory, interpretive strategies employed by audience members. This article In this paper we motivate the use of qualitative spatial actions as the fundamental unit in processing user route instructions. The spatial action model has been motivated by an analysis of empirical studies in human-robot interaction on the navigation task, and can be interpreted as a conceptual representation of the spatial action to be performed by the agent in their navigation space. Furthermore, we sketch out two distinct models of interpretation for these actions in cognitive robotics. In the first, the actions are related to a formalized conceptual user modeling of navigation space, while in the second the actions are interpreted as fuzzy operations on a voronoi graph. Moreover, we show how this action model allows us to better capture the points at which user route instructions become out of alignment with a robot's knowledge of the environment through a number of examples. \|\|This instructor guide, which was developed for use in a manufacturing firm's advanced technical preparation program, contains the materials required to present a learning module that is designed to prepare trainees for the program's statistical process control module by improving their basic math skills in working with line graphs and teaching… In this paper, we study a problem of inferring blood relationships which satisfy a given matrix of genetic distances between all pairs of n nodes. Blood relationships are represented by our proposed graph class, which is called a pedigree graph. A pedigree graph is a directed acyclic graph in which the maximum indegree is at most two. We show that the number of pedigree graphs which satisfy the condition of given genetic distances may be exponential, but they can be represented by one directed acyclic graph with n nodes. Moreover, an O(n3) time algorithm which solves the problem is also given. Although phylogenetic trees and phylogenetic networks are similar data structures to pedigree graphs, it seems that inferring methods for phylogenetic trees and networks cannot be applied to infer pedigree graphs since nodes of phylogenetic trees and networks represent species whereas nodes of pedigree graphs represent individuals. We also show an O(n2) time algorithm which detects a contradiction between a given pedigreee graph and distance matrix of genetic distances. Information value has been implicitly utilized and mostly non-subjectively computed in information retrieval (IR) systems. We explicitly define and compute the value of an information piece as a function of two parameters, the first is the potential semantic impact the target information can subjectively have on its recipient's world-knowledge, and the second parameter is trust in the information source. We model these two parameters as properties of RDF graphs. Two graphs are constructed, a target graph representing the semantics of the target body of information and a context graph representing the context of the consumer of that information. We compute information value subjectively as a function of both potential change to the context graph (impact) and the overlap between the two graphs (trust). Graph change is computed as a graph edit distance measuring the dissimilarity between the context graph before and after the learning of the target graph. A particular application of this subjective information valuation is in the construction of a personalized ranking component in Web search engines. Based on our method, we construct a Web re-ranking system that personalizes the information experience for the information-consumer. \\u000a The term "social skills" encompasses an array of learned behaviors that share the common goal of maintaining or increasing\\u000a reinforcement within a social context. Deficits in social skills can occur at any developmental period and are not likely\\u000a to improve spontaneously because impaired social skills impede interactions with other people. In turn, unsatisfying or disruptive\\u000a interactions exacerbate social skill deficits Undergraduate igneous and metamorphic petrology is often one of the few courses in which students use field, thin section, hand sample and geochemical observations to interpret a suite of related rocks. Many students may not have encountered the idea of separating observation from interpretation prior to petrology; yet being able to distinguish these is an important skill for any budding petrologist to learn. Labs that require students to integrate abstract concepts from the lecture portion of the course to present a coherent story based on observations are essential to producing students that are well versed in petrology. A capstone-type lab allows students use many of their recently acquired skills to solve real problems in petrology. These integrated labs can take a number of forms from a short lab looking at a few related thin sections, to a multi-week lab with specified tasks, to a semester-long project culminating in a paper or a presentation. For the past few years, I have used a suite of rocks from the Sierra Nevada batholith to give petrology students a capstone experience for the igneous portion of the course. Students are given thin sections with hand samples, a map and a table of geochemical analyses and asked to record hand-sample and thin section observations with the idea that these will be used to understand processes that were active during batholith generation. Because students are given geochemical analyses, they are also expected to experiment with the use of graphs (e.g., Harker and spider diagrams) to better understand tables of geochemical analyses. The students use observations about rocks and geochemistry to build a coherent story around these rocks; the final product is a short paper in which they use petrographic observations and geochemical diagrams to back up their interpretations. Although the lab presented is specifically designed around a set of thin sections housed at the University of Wisconsin Oshkosh for an upper level course, the lab is highly adaptable. I present some options for adapting this lab to any set of thin sections and hand samples with associated geochemical analyses. This lab can also be tailored to a variety of skill levels - from 2nd year introductory petrology to a graduate course. In this article, Bates, the Inmate Programs Manager of the Hillsborough County Sheriff's Office in Tampa, Florida, describes her office's Life Skills Project, a comprehensive program that has significantly enhanced three existing programs by adding extensive life skills components. The added life skills modules reinforce the importance of… Describes methods used in the nursing curriculum at the University of Iowa College of Nursing to evaluate inclusion of physical assessment skills and to test students' use of cognitive, perceptual, and psychomotor assessment skills in nursing diagnosis. Includes an example of motor and perceptual skill objectives for examining thorax and lungs.… \|\|Issues pertaining to thinking skills are discussed in an attempt to clarify what thinking skills are and their components, how they function and how they can be developed in the teaching-learning environment. Chapter 1 reviews the definitions of thinking skills. These definitions are selected from the current literature on education and… Most educators are familiar with instances of authentic assessment of "content" within the disciplines or of authentic assessment of "discipline-specific skills." In such authentic assessments, students apply the knowledge and skills of the discipline to situations or tasks that replicate real world challenges. The measurement of skills is… Graph Languages 1 emerged during the seventies from the necessity to process data structures with complex interrelations. Nowadays, various variants of these languages can be found for querying (1)(2), in-place transforming (3)(4), and trans- lating graph structures (5)(6). Still, new graph languages supporting dierent paradigms and usage scenarios are proposed regularly. In fact, languages tai- lored for a dedicated application The automata arising from the well known conversion of regular expression to\\u000anon deterministic automata have rather particular transition graphs. We refer\\u000ato them as the Glushkov graphs, to honour his nice expression-to-automaton\\u000aalgorithmic short cut (On a synthesis algorithm for abstract automata, Ukr.\\u000aMatem. Zhurnal, 12(2):147-156, 1960, In Russian). The Glushkov graphs have been\\u000acharacterized (P. Caron and D. Mining chemical compounds in silico has drawn increasing attention from both academia and pharmaceutical industry due to its effectiveness in aiding the drug\\u000a discovery process. Since graphs are the natural representation for chemical compounds, most of the mining algorithms focus\\u000a on mining chemical graphs. Chemical graph mining approaches have many applications in the drug discovery process that include\\u000a structure-activity-relationship (SAR)We introduce a new method to optimize the required area, minimum angle, and number of bends of planar graph drawings on a grid. The main tool is a new type of ordering on the vertices and faces of triconnected planar graphs. Using this method linear-time-and-space algorithms can be designed for many graph-drawing problems. Our main results are as follows:Every triconnected The present paper is an introduction to a combinatorial theory arising as a\\u000anatural generalisation of classical and virtual knot theory. There is a way to\\u000aencode links by a class of `realisable' graphs. When passing to generic graphs\\u000awith the same equivalence relations we get `graph-links'. On one hand\\u000agraph-links generalise the notion of virtual link, on the other In this paper we shed new light on the fundamental gap between graph-based models used by protocol designers and fading channel models used by communication theo- rists in wireless networks. We experimentally demonstrate that graph-based models capture real-world phenomena in- adequately. Consequentially, we advocate studying models beyond graphs even for protocol-design. In the main part of the paper we present We present an efficient and scalable technique for spatiotem In (E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Alge- bra Appl. 373 (2003), 241-272) we gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph. In particular, the usual adjacency matrix and the Laplacian matrix were addressed. Furthermore, we formulated In this lesson plan students learn to create bar graphs using unifix cubes, translate this representation to graph paper, and then compare the data that has been collected and displayed. Students are encouraged to make up their own questions about the data (favorite juice) and to practice with multiple sets of data. Sample questions for students and extension ideas are included. The lesson contains links to a PDF of graph paper and the Bar Grapher tool which is cataloged separately in this database. The 'classical' random graph models, in particular G(n,p' random graph In this paper, we aim at showing the advantages of Conceptual Graph formalism for the Semantic Web through several real-world applications in the framework of Corporate Semantic Webs. We describe the RDF(S)-dedicated semantic search engine, CORESE, based on a correspondence between RDF(S) and Conceptual Graphs, and we illustrate the interest of Conceptual Graphs through the analysis of several real-world applications Interplanetary communication networks comprise orbiters, deep-space relays, and stations on planetary surfaces. These networks must overcome node mobility, constrained resources, and significant propagation delays. Opportunities for wireless contact rely on calculating transmit and receive opportunities, but the Euclidean-distance diameter of these networks (measured in light-seconds and light-minutes) precludes node discovery and contact negotiation. Propagation delay may be larger than the line-of-sight contact between nodes. For example, Mars and Earth orbiters may be separated by up to 20.8 min of signal propagation time. Such spacecraft may never share line-of-sight, but may uni-directionally communicate if one orbiter knows the other's future position. The Contact Graph Routing (CGR) approach is a family of algorithms presented to solve the messaging problem of interplanetary communications. These algorithms exploit networks where nodes exhibit deterministic mobility. For CGR, mobility and bandwidth information is pre-configured throughout the network allowing nodes to construct transmit opportunities. Once constructed, routing algorithms operate on this contact graph to build an efficient path through the network. The interpretation of the contact graph, and the construction of a bounded approximate path, is critically important for adoption in operational systems. Brute force approaches, while effective in small networks, are computationally expensive and will not scale. Methods of inferring cycles or other librations within the graph are difficult to detect and will guide the practical implementation of any routing algorithm. This paper presents a mathematical analysis of a multi-destination contact graph algorithm (MD-CGR), demonstrates that it is NP-complete, and proposes realistic constraints that make the problem solvable in polynomial time, as is the case with the originally proposed CGR algorithm. An analysis of path construction to complement hop-by-hop forwarding is presented as the CGR-EB algorithm. Future work is proposed to handle the presence of dynamic changes to the network, as produced by congestion, link disruption, and errors in the contact graph. We conclude that pre-computation, and thus CGR style algorithms, is the only efficient method of routing in a multi-node, multi-path interplanetary network and that algorithmic analysis is the key to its implementation in operational systems. In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in com- puter vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet because these graph constructions are complex and highly specific to a particular en- ergy function, graph The end result of graph visualization is that people read the graph and understand the data. To make this effective, it is essential to construct visualizations based on how people read graphs. Despite the popularity and importance of graph usage in a variety of application domains, little is known about how people read graphs. The lack of this knowledge has As a graph with attributes assigned to its nodes is very well suited for the specification of semi-structured application domains, attributed graphs and adequate graph rewriting systems are also useful tools for the specification and representation of user interfaces based on end user tasks. A rewriting system for attributed graphs, which is based on the controlled rewriting of graphs using In this paper we consider the problem of testing bipartitene ss of gen- eral , where is Abstract: In this paper we consider the problem of testing bipartiteness of general ~ where n is Graph matching and graph edit distance have become important tools in structural pattern recognition. The graph edit distance concept allows us to measure the structural similarity of attributed graphs in an error-tolerant way. The key idea is to model graph variations by structural distortion operations. As one of its main constraints, however, the edit distance requires the adequate definition of The Journal of Graph Algorithms and Applications found at this Web site is the electronic version of the scientific journal with the same name. It is a collection of research papers dealing with the "analysis, design, implementation, and applications of graph algorithms." The current volume consists of select papers presented at the 1999 Symposium on Graph Drawing, which have since been revised. Previous volumes are archived on this site as well, and they can be freely accessed. Almost any discipline requires some sort of graphical representation, and specific uses of graph algorithms in various fields are addressed in this journal. The Reeb graph provides a structure that encodes the topology of a shape, and it has been gaining in popularity in shape analysis and understanding. We introduce a spectral clustering method to compute the Reeb graph. Given a 3-D model embedded in the Euclidean space, we define the Morse function according to the connected components of the 3-D model in a spectral space. The spectral clustering formulation gives rise to a consistent Reeb graph over pose changes of the same object with meaningful subparts and yields a hierarchical computation of the Reeb graph. We prove that this method is theoretically reasonable, and experimental results show its efficiency. Most of the relations are represented by a graph structure, e.g., chemical bonding, Web browsing record, DNA sequence, Inference\\u000a pattern (program trace), to name a few. Thus, efficiently finding characteristic substructures in a graph will be a useful\\u000a technique in many important KDD\\/ML applications. However, graph pattern matching is a hard problem. We propose a machine learning\\u000a technique called Graph- \\u000a Graph kernels have been successfully applied on chemical graphs on small to medium sized machine learning problems. However,\\u000a graph kernels often require a graph transformation before the computation can be applied. Furthermore, the kernel calculation\\u000a can have a polynomial complexity of degree three and higher. Therefore, they cannot be applied in large instance-based machine\\u000a learning problems. By using kernel principal Incorporating skills in reinforcement learning methods results in accelerate agents learning performance. The key problem of automatic skill discovery is to find subgoal states and create skills to reach them. Among the proposed algorithms, those based on graph centrality measures have achieved precise results. In this paper we propose a new graph centrality measure for identifying subgoal states that is crucial to develop useful skills. The main advantage of the proposed centrality measure is that this measure considers both local and global information of the agent states to score them that result in identifying real subgoal states. We will show through simulations for three benchmark tasks, namely, "four-room grid world", "taxi driver grid world" and "soccer simulation grid world" that a procedure based on the proposed centrality measure performs better than the procedure based on the other centrality measures. We address how the structure of a social communication system affects language coordination. The naming game is an abstraction of lexical acquisition dynamics, in which N agents try to find an agreement on the names to give to objects. Most results on naming games are specific to certain communication network topologies. We present two important results that are general to any graph topology: the first proves that under certain topologies the system always converges to a name-object agreement; the second proves that if these conditions are not met the system may end up in a state in which sub-networks with different competing object-name associations coexist. Let \\u000a$${\\\\mathcal{C}}$$\\u000aG(X) be the set of all (equivalence classes of) regular covering projections of a given connected graph X along which a given group G = Aut X of automorphisms lifts. There is a natural lattice structure on \\u000a$${\\\\mathcal{C}}$$\\u000aG(X), where P1 = P2 whenever P2 factors through P1. The sublattice \\u000a$${\\\\mathcal{C}}$$\\u000aG(P) of coverings which are below a For a positive integer k, a k-subdominating function of a graph G=(V,E) is a function f:V?{?1,1} such that ?u?NG[v]f(u)?1 for at least k vertices v of G. The k-subdomination number of G, denoted by ?ks(G), is the minimum of ?v?Vf(v) taken over all k-subdominating functions f of G. In this article, we prove a conjecture for k-subdomination on trees proposed The inverse problem for the magnetic Schrödinger operator on the lasso graph with different matching conditions at the vertex is investigated. It is proven that the Titchmarsh-Weyl function known for different values of the magnetic flux through the cycle determines the unique potential on the loop, provided the entries of the vertex scattering matrix S parametrizing matching conditions satisfy s12s23s31 ? s13s21s32. This is in contrast to numerous examples showing that the potential on the loop cannot be reconstructed from the boundary measurements. This paper, presented at the 2002 Physics Education Research Conference, presents the results of a study intended to investigate students' cognitive processes when reading line graphs. The researchers developed a computer program to determine the order readers glance the components of a line graph, and then analyzed the glancing order of each component. The results help identify secondary students' cognitive processes for line graphs. Background Biomedical and chemical databases are large and rapidly growing in size. Graphs naturally model such kinds of data. To fully exploit the wealth of information in these graph databases, a key role is played by systems that search for all exact or approximate occurrences of a query graph. To deal efficiently with graph searching, advanced methods for indexing, representation and matching of graphs have been proposed. Results This paper presents GraphFind. The system implements efficient graph searching algorithms together with advanced filtering techniques that allow approximate search. It allows users to select candidate subgraphs rather than entire graphs. It implements an effective data storage based also on low-support data mining. Conclusions GraphFind is compared with Frowns, GraphGrep and gIndex. Experiments show that GraphFind outperforms the compared systems on a very large collection of small graphs. The proposed low-support mining technique which applies to any searching system also allows a significant index space reduction. \|An achievement test score can be viewed as a joint function of skill and will, of knowledge and motivation. However, when interpreting and using test scores, the "will" part is not always acknowledged and scores are mostly interpreted and used as pure measures of student knowledge. This paper argues that students' motivation to do their best on… What is interpretation? One can imagine a range of answers to this question. One answer might begin with the observation that the English word "interpretation" is used to refer to a variety of human activities. Translators at the United Nations interpret remarks made in French when they offer an English translation. Literary critics interpret novels when they investigate the deep Background: Teaching electrocardiogram (ECG) interpretation is a recommended component of the family practice residency curriculum.\\u000a Published information concerning the ECG interpretation ability of residents is sparse. This study sought to ascertain the\\u000a base line knowledge of family practice residents' ECG interpretationskills and extent of improvement after one year of training.\\u000a \\u000a Methods: A 15 ECG examination was administered to 38In this paper we study path integral for a single spinless particle on a star graph with N edges, whose vertex is known to be described by U(N) family of boundary conditions. After carefully studying the freeThis research study focused on the development and administration of a laboratory investigation task involving ninth grade students currently studying Earth Science. Students were required to Plan and Perform the investigation based on concepts of Chemical Weathering. Science inquiry skills associated with Planning, Data Collection, Graphing, and Reasoning were evaluated using an analytical scoring rubric. Students completed a Survey Instrument, which provided contextual information about their prior laboratory experiences, and preferences about working individually versus pairs while completing science experiments. The sample was composed of 446 students from five schools in Western New York. Students completed the laboratory investigation individually and in pairs. One hundred and fifty students completed the task individually, and 296 students assigned to 148 pairs completed the task. T-tests and ANOVA's were used to evaluate achievement differences between individuals and pairs; by gender and individual ability for the individual sub-sample; and by the gender and ability composition for the pairs' sub-sample respectively. Mean scores for the Likert type Survey instrument provided contextual data about students' prior laboratory experiences. Factor analysis generally supported the theoretical model used to design the investigation. The results indicated there were significant differences in achievement between individuals and pairs in Graphing and Reasoning skills. Females outperformed males on the Total task, Data Collection, Graphing and Reasoning categories of skills. High ability students outperformed medium and low ability students on the Total Task, Planning, Graphing and Reasoning categories of skills. The composition of pairs by ability indicated significant differences in achievement on the Total Task, Planning and Reasoning skills. There were significant differences in achievement by female/female versus male/male and male/female pairs on the Total Task, Data Collection, Graphing and Reasoning skills. This paper considers an agent-based labor market simulation to examine the influence of skills on wages and unemployment rates. Therefore less and highly skilled workers as well as less and highly productive vacancies are implemented. The skill distribution is exogenous whereas the distribution of the less and highly productive vacancies is endogenous. The different opportunities of the skill groups on the labor market are established by skill requirements. This means that a highly productive vacancy can only be filled by a highly skilled unemployed. Different skill distributions, which can also be interpreted as skill-biased technological change, are simulated by incrementing the skill level of highly skilled persons exogenously. This simulation also provides a microeconomic foundation of the matching function often used in theoretical approaches. In this paper, we deal with both the complexity and the approximability of the labeled perfect matching problem in bipartite graphs. Given a simple graph G = (V,E) with \|V \| =2 n vertices such that E contains a perfect matching (of size n), together with a color (or label) function L : E ?{ c1,...,cq}, the labeled perfect matching The representation depicts a position-time graph showing the motion of an object as it is moved by the user. The user can also move the object to match the motion represented on 8 different types of position-time graphs. Discovery of knowledge from geometric graph databases is of particular importance in chemistry and biology, be- cause chemical compounds and proteins are represented as graphs with 3D geometric coordinates. In such applica- tions, scientists are not interested in the statistics of the whole database. Instead they need information about a novel drug candidate or protein at hand, represented as a Even well administered networks are vulnerable to attack. Recent work in network security has focused on the fact that combinations of exploits are the typical means by which an attacker breaks into a network. Researchers have proposed a variety of graph-based algorithms to generate attack trees (or graphs). Either structure represents all possible sequences of exploits, where any given exploit In this work a general multibody system theory is implemented within a bond graph modeling framework. In classical mechanics several procedures exist by which differential equations can be derived of a system of rigid bodies. In the case of large systems these procedures are labor-intensive and consequently error-prone, unless they are computerized. The bond graphs formalism allows for a unified We propose two new spectral measures for graphs and networks which characterize the ratios between the width of the "bulk" part of the spectrum and the spectral gap, as well as the ratio between spectral spread and the width of the "bulk" part of the spectrum. Using these definitions we introduce the concept of golden spectral graphs (GSG), which are Our recent work has described a framework for matching solid of mechanical artifacts models based on scale-space feature decomposition. In this work we adopt a method of comparing solid models based on Multiresolutional Reeb Graphs (MRG) similarity computations. This method was originally proposed by Hilaga et al. in (1). Reeb Graph technique applies MRG struc- ture to comparisons of approximate \|Describes a laboratory exercise that introduces physics students to graphing. Presents the program format and sample output of a computer simulation of an experiment which tests the effects of sound intensity on the crawling speed of a snail. Provides students with practice in making exponential or logarithmic graphs. (ML)\| In this paper we describe the graph grammar approach to modeling self-assembly. The approach is used to describe how the topol- ogy of an assembling aggregate changes as it grows. The main purpose of the paper is to demonstrate the utility of the approach by giving detailed examples. We also describe the beginnings of our approach to physically embedding graph Two natural generalizations of knot theory are the study of spatial graphs and virtual knots. Our goal is to unify these two approaches into the study of virtual spatial graphs. This paper is a survey, and does not contain any new results. We state the definitions, provide some examples, and survey the known results. We hope that this paper will Mining frequent substructures has gained importance in the recent past. Number of algorithms has been presented for mining undirected graphs. Focus of this paper is on mining frequent substructures in directed labeled graphs since it has variety of applications in the area of biology, web mining etc. A novel approach of using equivalence class principle has been proposed for reducing We continue our study of online prediction of the labelling of a graph. We show a fundamental limitation of Laplacian-based algorithms: if the graph has a large di- ameter then the number of mistakes made by such algorithms may be proportional to the square root of the number of vertices, even when tackling simple problems. We overcome this drawback by The representation depicts an animated distance time graph for a vehicle that moves at a constant velocity, stops and then changes direction to move at a different constant velocity. A speedometer is also shown. Resource is first graph on this page Several graph related formalisms such as Petri nets, abstract state machines, automata, membrane systems, mobile ambients, etc., are already used as modeling tools for nat- ural processes. On the other hand, in human-designed computing inspired by nature, graph theoretical formulations and problems are often used as benchmarks,for the in- vestigation of the potential of the proposed computational paradigms. The program We consider the spectral structure for differential equations on graphs. In particular, we show that self-adjointness does not necessarily imply regularity, we also show that the algebraic and geometric eigenvalue multiplicities of formally self-adjoint differential operators on graphs are equal. Asymptotic bounds for the eigenvalues are then found. Over 800 million people around the world share their social interactions with friends on Facebook, providing a rich body of information referred to as the social graph. In this talk, I describe how we model and serve this graph. Our model uses typed nodes (fbobjects) and edges (associations) to express the relationships and actions that happen on Facebook. We access Measures of central tendency for graphs are important for protoype construction, frequent substructure mining, and multiple alignment of protein structures. This contribution proposes subgradient-based methods for determining a sample mean of graphs. We assess the performance of the proposed algorithms in a comparative empirical study. Various aspects of the theory of random walks on graphs are surveyed. In particular, estimates on the important parameters of access time, commute time, cover time and mixing time are discussed. Connections with the eigenvalues of graphs and with electrical networks, and the use of these connections in the study of random walks is described. We also sketch recent algorithmic The Padmakar–Ivan index of a graph G is the sum over all edges uv of G of number of edges which are not equidistant from u and v. In this work, an exact expression for the PI index of the Cartesian product of bipartite graphs is computed. Using this formula, the PI indices of C4 nanotubes and nanotori are computed. The paper proposes a methodology to assist the designer at the initial stages of the design synthesis process by enabling him\\/her to employ knowledge and algorithms existing in graph network theory. The proposed method comprises three main stages: transforming the synthesis problem into a graph theoretic problem; devising the topology possessing special engineering properties corresponding to the system requirements; finding We call a rational map f graph critical if any critical point either belongs to an invariant nite graph G, or has minimal limit set, or is non- recurrent and has limit set disjoint from G. We prove that, for any conformal measure, either for almost every point of the Julia set J(f) its limit set coin- cides with J(f), Based on the original idea of Sowa on conceptual graph and a recent formalism by Corbett on ontology, this paper presents a rigorous mathematization of basic concepts encountered in the conceptual structure theory, including canon, ontology, conceptual graph, projection, and canonical formation operations, with the aim of deriving their mathematical properties and applying them to future research and development on Let G = (V, E) be an arbitrary undirected source graph to be embedded in a target graph EM, the extended grid with vertices on integer grid points and edges to nearest and next-nearest neighbours. We present an algorithm showing how to embed G into EM in both time and space O(\|V \|2) using the new notions of islands and In a flowchart scheme an atomic action is modelled as a vertex (box), while in a process graph an atomic action is modelled as an edge. We define translations between these two graphical representations. By using these translations, we show that the classical bisimulation equivalence on process graphs coincides with the natural extension of the classical step-bystep flowchart equivalence to Control of vehicle formations has emerged as a topic of signiflcant interest to the controls community. In this paper, we merge tools from graph theory and control theory to derive stability criteria for vehicle formations. The interconnection between vehicles (i.e., which vehicles are sensed by other vehicles) is modeled as a graph, and the eigenvalues of the Laplacian matrix of In the following exercises, the graph drawn is of acceleration versus time. The animation still shows the position of the particle as time progresses. There, a couple of assumptions had to be taken. An acceleration versus time graph does not provide all the information necessary for deducing position. This paper presents a new heuristic algorithm for the graph coloring problem based on a combination of genetic algorithms and sim- ulated annealing. Our algorithm exploits a novel crossover operator for graph coloring. Moreover, we investigate various ways in which simulated annealing can be used to enhance the performance of an evolutionary al- gorithm. Experiments performed on various collections ofThe Artificial Intelligence (AI) literature contains a wide range of suggestions for capturing semantic concepts. One that has received wide attention through two international conferences is Sowa's conceptual graphs. The claim made is that these conceptual graphs are a good knowledge representation language which could be used as an intermediate stage towards a relational database schema. It is this latter In this paper we explore the relationship between multivariate data analysis and techniques for graph drawing or graph layout. Although both classes of techniques were created for quite different purposes, we find many common principles and implemen- tations. We start with a discussion of the data analysis techniques, in particular multiple correspondence analysis, multidimensional scaling, parallel coordinate plotting, and seri- Power pole detection from images is an important problem in the future electric power industry application. A precise detection is essential to inspect the defects of a power pole. In this paper, we propose a novel approach to detect the power pole object from images. Graph cut for image segmentation is a newly developing graph based image segmentation technique. It Abstract Let G be a graph, and ?(G) and ?(G) be the minimum degree and the independence number of G, respectively. For a vertex v ? V (G), d(v) and N(v) represent the degree of v and the neighborhood of v in G, respectively. A number of sufficient conditions for a connected simple graph G of order n to be In this paper we discuss the design of computer-based haptic graphs for blind and visually impaired people with the support of our preliminary experimental results. Since visual impairment makes data visualisation techniques inappropriate for blind people, we are developing a system which can make graphs accessible through haptic and audio media. The disparity between human haptic perception and the sensation Let G = (V,E) be a biconnected graph and let C be a cycle in G. The subgraphs of G identified with the biconnected components of the contraction of C in G are called the bridges of C. Associated with the set of bridges of a cycle C is an auxilliary graphical structure GC called a bridge graph or anWe introduce a novel multi agent patrolling algorithm inspired by the behavior of gas filled balloons. Very low capability ant-like agents are considered with the task of patrolling an unknown area modeled as a graph. While executing the proposed algorithm, the agents dynamically partition the graph between them using simple local interactions, every agent assuming the responsibility for patrolling his subgraph. Balanced graph partition is an emergent behavior due to the local interactions between the agents in the swarm. Extensive simulations on various graphs (environments) showed that the average time to reach a balanced partition is linear with the graph size. The simulations yielded a convincing argument for conjecturing that if the graph being patrolled contains a balanced partition, the agents will find it. However, we could not prove this. Nevertheless, we have proved that if a balanced partition is reached, the maximum time lag between two successive visits to any vertex using the proposed strategy is at most twice the optimal so the patrol quality is at least half the optimal. In case of weighted graphs the patrol quality is at least (1)/(2){lmin}/{lmax} of the optimal where lmax (lmin) is the longest (shortest) edge in the graph. Abstract Several Several bibliogra- Motion Graph, as an effective data structure for captured data, can be adopted to improve the automatism in motion edit, preserving the details of motion. But the traditional method based on Motion Graph always takes lot of time in constructing and searching, especially searching time which makes it not suitable for interactive editing. This paper introduces a novel method about Twenty-eight sign language interpreters participated in a battery of tests to determine if a profile of cognitive, motor, attention, and personality attributes might distinguish them as a group and at different credential levels. Eight interpreters held Level II and nine held Level III Virginia Quality Assurance Screenings (VQAS); the other 11 held Registry of Interpreters for the Deaf (RID) certification. Six formal tests, the Quick Neurological Screening Test-II, the Wonderlic Personnel Test, the Test of Visual-Motor Skills (TVMS), the d2 Test of Attention, the Integrated Visual and Auditory Continuous Performance Test, and the Sixteen Personality Factor Questionnaire (16PF), were administered to the interpreters. Average scores were high on most of the tests; differences across the three groups were not statistically significant. Results from only one test, the d2 Test of Attention, were significantly correlated with interpreter level. Comparisons between educational and community interpreters also revealed no differences. Personality traits were widely distributed, but one trait, abstract reasoning, tested extremely high in 18 interpreters. Discussion of the potential implications of these results, particularly for educational interpreters, is offered. PMID:15304401 We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A10.1103/PhysRevA.79.022317 79, 022317 (2009)] to other tensor-network states such as the tensor tree states (TTS) and projected entangled pair states. We investigate the suitability of the bare TTS to describe ground states, showing that the description of certain graph states and condensed-matter models improves. We investigate graph-enhanced tensor-network states, demonstrating that in some cases (disturbed graph states and for certain quantum circuits) the combination of weighted graph states with TTS can greatly improve the accuracy of the description of ground states and time-evolved states. We comment on delineating the boundary of the classically efficiently simulatable states of quantum many-body systems. Maximizing rewards per unit time is ideal for success and survival in humans and animals. This goal can be approached by speeding up behavior aiming at rewards and this is done most efficiently by acquiring skills. Importantly, reward-directed skills consist of two components: finding a good object (i.e., object skill) and acting on the object (i.e., action skill), which occur sequentially. Recent studies suggest that object skill is based on high-capacity memory for object-value associations. When a learned object is encountered the corresponding memory is quickly expressed as a value-based gaze bias, leading to the automatic acquisition or avoidance of the object. Object skill thus plays a crucial role in increasing rewards per unit time. PMID:23911579 Many methods have been proposed for community detection in networks. Some of the most promising are methods based on statistical inference, which rest on solid mathematical foundations and return excellent results in practice. In this paper we show that two of the most widely used inference methods can be mapped directly onto versions of the standard minimum-cut graph partitioning problem, which allows us to apply any of the many well-understood partitioning algorithms to the solution of community detection problems. We illustrate the approach by adapting the Laplacian spectral partitioning method to perform community inference, testing the resulting algorithm on a range of examples, including computer-generated and real-world networks. Both the quality of the results and the running time rival the best previous methods. The report contains fourteen bibliographies on a variety of topics. These bibliographies are designed as basic references for park interpreters. Each bibliography has two parts: a key list of ten annotated references followed by other less significant wor... The purpose of the Image Interpretation Cell is to generate forward echelon accurate intelligence data in the form of Flash and Immediate Photo Interpretation Reports. The IIC is a completely self-contained, deployable and adaptable image data system. It ... In many applications, the available information is encoded in graph structures. This is a common problem in biological networks, social networks, web communities and document citations. We investigate the problem of classifying nodes' labels on a similarity graph given only a graph structure on the nodes. Conventional machine learning methods usually require data to reside in some Euclidean spaces or to have a kernel representation. Applying these methods to nodes on graphs would require embedding the graphs into these spaces. By embedding and then learning the nodes on graphs, most methods are either flexible with different learning objectives or efficient enough for large scale applications. We propose a method to embed a graph into a feature space for a discriminative purpose. Our idea is to include label information into the embedding process, making the space representation tailored to the task. We design embedding objective functions that the following learning formulations become spectral transforms. We then reformulate these spectral transforms into multiple kernel learning problems. Our method, while being tailored to the discriminative tasks, is efficient and can scale to massive data sets. We show the need of discriminative embedding on some simulations. Applying to biological network problems, our method is shown to outperform baselines. PMID:21788187 Networks play a crucial role in computational biology, yet their analysis and representation is still an open problem. Power Graph Analysis is a lossless transformation of biological networks into a compact, less redundant representation, exploiting the abundance of cliques and bicliques as elementary topological motifs. We demonstrate with five examples the advantages of Power Graph Analysis. Investigating protein-protein interaction networks, we show how the catalytic subunits of the casein kinase II complex are distinguishable from the regulatory subunits, how interaction profiles and sequence phylogeny of SH3 domains correlate, and how false positive interactions among high-throughput interactions are spotted. Additionally, we demonstrate the generality of Power Graph Analysis by applying it to two other types of networks. We show how power graphs induce a clustering of both transcription factors and target genes in bipartite transcription networks, and how the erosion of a phosphatase domain in type 22 non-receptor tyrosine phosphatases is detected. We apply Power Graph Analysis to high-throughput protein interaction networks and show that up to 85% (56% on average) of the information is redundant. Experimental networks are more compressible than rewired ones of same degree distribution, indicating that experimental networks are rich in cliques and bicliques. Power Graphs are a novel representation of networks, which reduces network complexity by explicitly representing re-occurring network motifs. Power Graphs compress up to 85% of the edges in protein interaction networks and are applicable to all types of networks such as protein interactions, regulatory networks, or homology networks.
Algebra Unplugged - 95 edition Summary: A lighthearted, sometimes irreverent introduction to the concepts, vocabulary and strategies of first year algebra. Designed for people who learn best by reading, it includes no exercises. Beginning with some pre algebra concepts, like working with fractions, it explains linear equations, quadratic equations and graphing in easy to understand, non frightening language. Ideal for people who think they hate math to read before they take the class or as a supplement during it. It provides an additi...show moreonal explanation to the confused and comfort for the fearful. For nearly twenty years this book has been helping math-phobes survive their most dreaded class
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
Functional Skills Maths Entry Level 3 - Study and Test Practice for an Amazon Gift Card of up to £0.25, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more Book DescriptionMy daughter was having problems with her Maths and kept failing the several mock examinations. We were not given any examples from her school.. I phone and was told the name and what to buy. So, I did. What I discovered is that this book covers all they need they need to know for they 11 year examinations. My daughter had not even been told, shown, or even taught this level of maths. The book is very easy and yes at first you will have to sit down with your child until it comes back to you as it set out different way then parents are taught. Never the less its still easy and will do the trick just make sure they do the questions. Now my daughter gets high marks in the mocks as its a set of generic books and covers every kind of maths problem and solution. Just as a not we all so bought level 1 and 2 and they were just has helpful. What they were doing in there classroom was concentrating on just one area so that they would at least get a grade an grade so the school would not loose any funding.
10,191We try to put all this together along with a strong algebraic vocabulary that enables a student to have continued success in Algebra II. Proficiency in Algebra I requires a student to be able to simplify basic expressions, solve basic equations, graph basic linear
Product Description The Standard Deviants start you off on the right foot by explaining all the differential equation basics, starting with "What is a differential equation'" Then we'll explain the different types of differential equations you'll encounter.Grade Level: 11
This guide features 180 pages of hands-on, standards-driven study material on how to understand and retain seventh grade math. Full explanations with ...Show synopsisThis guide features 180 pages of hands-on, standards-driven study material on how to understand and retain seventh grade math. Full explanations with step-by-step instructions are provided. Worksheets for each standard are provided along with two, full-length, 100-problem, comprehensive final exams. (Education
Sunday, September 9, 2012 What's the Big Idea with Algebra 2? Lately, I've been following some of the conversation around the big ideas in an advanced algebra/pre-calculus course. The Global Math Department* hosted an interesting panel discussion around this topic a couple of weeks ago. I appreciated the thoughtfulness and complementary ideas of the presenters (John Burk, Dan Goldner, Michael Pershan, and Paul Salomon), and especially the thoughts behind proof and 'the well-crafted solution.' Without entirely reaching a consensus, the focus of the discussions tended to lean towards prediction as the overarching theme for algebra ii. The reasoning was thoughtful and grounded, but this theme did not satisfy me. While I can certainly see it, I also think that prediction is the theme for statistics. Can Algebra 2 and Statistics have the same theme? They can, I suppose, but it is not satisfying enough. Some of the new bloggers from the New Blogger Initiative also tackled this topic last week. gooberspeaks got me thinking about the focus on families of functions and David Price included ideas about varying ways of representing functions and modifying their behavior. Kyle Eck has a strong bent towards applications which resonates with the GMD theme of predictions. And all these ideas muddled around in my brain for a long time before emerging as a single construct that currently satiates my desire for deeper inspection. Algebra 2 is all about: generalizing patterns of behavior in bivariate relationships. But that's my academic's definition. In the UbD-influenced language of a high school classroom, I'd say that Algebra 2 asks these questions: How can we communicate the behavior of a relationship between two ideas? Are there rules of behavior that apply to all relationships? Why is it important to be able to generalize patterns of behavior? Functions certainly play a large role here, because it's easier to generalize patterns when there are overt rules of behavior to follow. But just as importantly, we also look at conic sections and the elusive inverses of even polynomials and periodic functions, because these ideas give us essential insight about the comforting nature of functions that are both one-to-one and onto, and about the obstacles presented by relationships that are not. Graphing also plays a large role, because it is a most excellent tool for alternate representations of bivariate relationships. Seeing patterns emerge in the shape of coordinate graphs can be enlightening long before symbolic manipulation clears a path through the brain... and I thank the math gods for that! I am wary though of too much graphical emphasis, for our well-loved coordinate system has obvious limits as our brains allow us to consider relationships with more variables. And applications clearly play an important role too, especially in the attempt to answer that third question. But I hesitate to put applications at the forefront of an advanced algebra theme. I think that is perhaps better handled by a physics class. In algebra we are attempting to represent scenarios with a generalized pattern of behavior, and manipulate this generalization to highlight useful information. I think I agree with Paul Salomon in that proof and 'well-crafted solutions' may trump (but certainly not replace) applications in the hierarchy of an overarching theme in algebra. To end, I'll just say that my desire to ask (and attempt to answer) the big questions is never entirely satiated, but I do so enjoy the conversations that emerge from them. I welcome your thoughts, criticisms, and further insights. The discourse is what makes being a mathematician so much fun. *Megan Hayes-Golding, where have you been all my life? What a terrific thing the GMD is, and one of these Tuesday nights, I will not have bedtime routines or NBI deadlines to worry about and will be able to attend a session while it is actually happening! Thanks to you and all others who are making this happen. 3 comments: I really enjoyed the thought behind your post and the conclusion(s) you came up with. I particularly like the three everyday-language questions you pose here. I have taught Algebra 1 more than any other subject, and I wonder what the Algebra 1 Big Idea would be. I talk about relationships when discussing this with my students, but I tend to refer to relationships between people. I am interested in thinking further on whether I could expand my discussion to include ideas. I am curious if in your framing of the Big Idea you think it could refer to relationships between two people? (Or other types of relationships perhaps, like relationships between species in Biology or some such thing. I'm just thinking out loud here.) Steve, I like where you are going with these questions. To me, I think that algebra is about logic and communication of patterns. We observe the way quantities relate to each other and use abstraction to communicate patterns of behavior. We quickly discover that some relationships are easier to describe than others. Why is that? Human behavior, for example, while it does follow some predictable patterns, is not in and of itself predictable. Some numerical relationships, on the other hand, are especially easy to describe: like the relationship where two quantities are always the same (y = x). I think it is no mistake that in Algebra I, we mention numerical 'relations' only briefly in order to define the truly utilitarian 'function.' We start our students off with simple, highly-predictable, injective relationships between two quantities... and then take them as far as they will let us. I think statistics shows us a wonderful marriage of the power of algebra combined with the less uniform patterns we observe in other life relationships around us. We observe, gather data, and attempt to fit a uniform pattern of behavior to our model. How close is close enough? Let the statistics decide. Thank you for providing me with more food for thought. It's this kind of stuff that keeps me up at night! Very impressive and knowledgeable blog.Algebra is a major component of math that is used to unify mathematic concepts. Algebra is built on experiences with numbers and operations, along with geometry and data analysis. Some students think that algebra is like learning another language. This is true to a small extent, algebra is a simple language used to solve problems that can not be solved by numbers alone. It models real-world situations by using symbols, such as the letters x, y, and z to represent numbers.
The following released test questions are taken from the Grade 2Mathematics Standards Test. ... the number of items that appear on the exam, and the ... 2MG2.2* Put shapes together and take them apart to form other shapes ... 2014 Exam2 Syllabus Financial MathematicsExam. The purpose of the syllabus for this examination is to develop knowledge of the fundamental concepts of ... The syllabus for this exam is defined in the form of learning objectives that set forth, ... 1. help students appreciate the use of mathematics as a form of communication; 2. help students acquire a range of mathematical techniques and skills and to foster and maintain the awareness of the importance of accuracy; 3. Mathematics Test Book 2 Grade 8 20302 March 6–12, 2008 Name _____ Developed and published ... distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of New York State Upon receipt of this registration form, an exam packet will be mailed to your address listed above. The placement exam consists of a mathematicsexam. This exam is two (2) parts, each 45 minutes in length. Detailed instructions will be included as well. Mathematics Test Book 2 Grade Name _____ 7 21655 May_5–7,_2010_ Developed and published ... Write your answer in exponential form. Show your work. Answer Jerry wants his deck to be more than 6 feet wide. Using your result from above, Mathematics Final Exam Review. ... 2 . 27. Write in standard form: seven and two hundred two ten-thousandths 28. Multiply: 7.9142 x 1000 29. What is 3.278 times 4.6 ? 30. Rainfall for the last three months of the year was 3.42 inches, 6.19 inches, and 4.65 inches. Exam2 Precalculus Mathematics I Directions: Exam2 is due Tuesday, November 1st by 8am. Answer all questions carefully. Do all steps with brief explanations similar to what was done in the examples in the notes. Business Mathematics I: Math 173 Sample Exam 1 - Solutions Name: Print your name neatly. If you forget to write your name, or write so sloppy that I can't read it, you can lose all of the points! Answer all the questions that you can. Assessment For The California Mathematics Standards Grade 2 Introduction: Summary of Goals GRADE TWO By the end of grade two, students understand place value and number ... Which two triangles can be put together to form a rectangle? Measurement and Geometry MG 2.2 15. Introduction - Grade 2Mathematics ... the number of items that appear on the exam, and the number of released test questions that appear in this document. ... 2MG2.2* Put shapes together and take them apart to form other shapes (e.g., two
More About This Textbook Overview This accessible introduction to Calculus is designed to demonstrate how calculus applies to various fields of study. The text is packed with real data and real-life applications to business, economics, social and life sciences. Applications using real data enhances student motivation. Many of these applications include source lines, to show how mathematics is used in the real world. NEW! Conceptual problems ask students to put the concepts and results into their own words. These problems are marked with an icon to make them easier to assign. More opportunities for the use of graphing calculator, including screen shots and instructions, and the use of icons that clearly identify each opportunity for the use of spreadsheets or graphing calculator. Work problems appear throughout the text, giving the student the chance to immediately reinforce the concept or skill they have just learned. Chapter Reviews contain a variety of features to help synthesize the ideas of the chapter, including: Objectives Check, Important Terms and Concepts, True-False Items, Fill in the Blanks and Review Exercises. Product Details Related Subjects Meet the Author Michael Sullivan is Professor Emeritus in the Department of Mathematics and Computer Science at Chicago State University where he taught for 35 years before retiring a few years ago. Dr. Sullivan is a member of the American Mathematical Society, the Mathematical Association of America, and the American Mathematical Society, the Mathematical Association of America, and the American Mathematical Association of Two year Colleges. he is President of the Text and Academic Authors Association and Represents that organization on the Authors Coalition of America. Mike has been writing textbooks in mathematics for over 30 years. He currently has 13 books in print: 3 texts with John Wiley & Sons and 10 with Prentice-Hall. Six of these titles are co-authored with his son, Michael Sullivan III. Mike has four children: Kathleen, who teaches college mathematics; Michael, who teaches college mathematics, Dan, who is a Prentice-Hall sales representative , and Colleen, who teaches middle-School mathematics. Nine grandchildren round out
The book "Single variable Differential and Integral Calculus" is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book is unique in the field of mathematical analysis in content and in style. It aims to define, compare and discuss topics in... more... The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric... more... Aimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequalities for bounded linear operators on complex Hilbert spaces for the case of one and two operators. Students at the graduate level will learn some essentials that may... more... This lucid and balanced introduction for first year engineers and applied mathematicians conveys the clear understanding of the fundamentals and applications of calculus, as a prelude to studying more advanced functions. Short and fundamental diagnostic exercises at the end of each chapter test comprehension before moving to new material. Provides... more... Designed for those seeking help studying calculus in school - also valuable for adults attempting to learn/re-learn calculus. A resource for instructors supplementing their instruction. 501 Calculus Problems helps users prepare for academic exams and build problem-solving skills. Unlike textbooks, full answer explanations are provided for all problems.... more...
It's the gateway to more advanced mathematics and the foundation for many other courses in mathematics and science. I have taught it many times in a community college setting. I was an actuary for about 7 years.
Math Review for Physics Get math review for physics and study guides here. Learn about geometry, trigonometry, and algebra for physics or brush up on your skills. Thorough explanations and practice examples will help you review math concepts require to understand physics. Study Guides Introduction Here are some other coordinate systems that you are likely to encounter in your journeys through the world of physics. Keep in mind that the technical details are simplified for this presentation. As you gain experience using ... Fundamental Rules The fundamental rules of geometry are used widely in physics and engineering. These go all the way back to the time of the ancient Egyptians and Greeks, who used geometry to calculate the diameter of the earth and the ... Introduction If it's been a while since you took a course in plane geometry, perhaps you think of triangles when the subject is brought up. Maybe you recall having to learn all kinds of theoretical proofs concerning triangles using ... Introduction A four-sided geometric figure that lies in a single plane is called a quadrilateral . There are several classifications and various formulas that apply to each. Here are some of the more common formulas that can be useful ... Introduction Let's go from two dimensions to three. Here are some formulas for surface areas and volumes of common geometric solids. The three-space involved is flat ; that is, it obeys the laws of euclidean geometry. These ... Introduction A logarithm (sometimes called a log ) is an exponent to which a constant is raised to obtain a given number. Suppose that the following relationship exists among three real numbers a , and x , ... Introduction There are six basic trigonometric functions . They operate on angles to yield real numbers and are known as sine, cosine, tangent, cosecant, secant , and cotangent . In formulas and equations, they are ... Introduction The following paragraphs depict common trigonometric identities for the circular functions. Unless otherwise specified, these formulas apply to angles θ and ϕ in the standard range as follows:
Department of Math & Technology Contact Math & Technology First Name:* Last Name:* Email Address:* Comments:* Flagler College's Math Program is an integral part of a student's education. The Math Program offers courses to support other departments that have major disciplines. These mathematics courses help to prepare students for courses in their majors or minors, as well as to strengthen mathematical and logical reasoning skills useful in daily life. Programs Major/Minor Clubs and Organizations Math Lab/Help The Flagler College MATH LAB is a service of the college and the mathematics department. The lab is available for all students, full-time or part-time, at all course levels. The MATH LAB helps with the content of any mathematics course offered at Flagler College. MATH LAB assistants are available to provide guidance in understanding mathematical concepts, completing homework assignments, and mastering calculator functions on the TI – 83 series of calculators. The MATH LAB provides Internet-connected computers for tutorial work, and extra texts and worksheets for additional practice.
Mathematics Our objective is to supply students with knowledge of mathematics necessary for success in their chosen field while upholding the Christian purpose of Campbell University. Why Should I Study Mathematics? In "The Jobs Rated Almanac", author Les Krantz ranks 250 jobs based on the following six criteria: income, stress, physical demands, potential growth, job security, and work environment. In the latest list, published in the spring of 2009, Mathematician ranked as the #1 job. Actuary and Statistician, jobs that require an extensive understanding of mathematics, were ranked #2 and #3, respectively. A degree in mathematics is extremely versatile. You will be qualified for a variety of careers in fields ranging from education to cryptography to finance. You will also be qualified for graduate study in mathematics, mathematics education, actuarial science, statistics, operations research, and engineering, among others. Professional graduate programs such as law, medicine, and business also respect applicants with a mathematics degree for their analytical skills. Campbell's size allows mathematics students to interact closely with fellow students and professors in and out of the classroom. The average size of sophomore, junior, and senior level mathematics classes at Campbell is approximately 14 students. Students feel comfortable participating in class and seeking help outside of class. In our department, you are not just a number.
Trigonometry book (98 pages) covers material from GCSE Level (approximately age 16 years) to GCE Advanced Level (approximately age 18 years) - teaching text, worked examples, exercises (with full... More > worked answers)- ideal for examination revision. It is available also from our website at and on iPad from the iBookstore.< Less A comprehensive review of trigonometry, this book covers topics like the inverses, trigonometric identities, trigonometric ratios, the law of sine, and the law of cosine. The book contains 487... More > questions that are convenient to practice. Each chapter has an explanation, practice questions, and answer keys. The content is high quality.< Less Calculus 1 & 2 covers differentiation and integration of functions using a guided and an analytical approach. All the normally difficult to understand topics have been made easy to understand,... More > apply and remember. The topics include continuity, limits of functions; proofs; differentiation of functions; applications of differentiation to minima and maxima problems; rates of change, and related rates problems. Also covered are general simple substitution techniques of integration; integration by parts, trigonometric substitution techniques; application of integration to finding areas and volumes of solids. Guidelines for general approach to integration are presented to help the student save trial-and-error time on examinations. Other topics include L'Hopital's rule, improper integrals; and memory devices to help the student memorize the basic differentiation and integration formulas, as well as trigonometric identities. This book is one of the most user-friendly calculus textbooks ever published.< Less
Book Description: Paperback. Book Condition: New. 141mm x 10mm x 210mm. Paperback. A series of 9 books based on U.S. Government teaching materials. They make math interesting and fun. The series of books begins with basic arithmetic and extends through pre-algebra, algeb.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 160 pages. 0.181. Bookseller Inventory # 9780878912001 Book Description: Paperback. Book Condition: New. Paperback. The Notebook Reference Math Fact Book offers students everything they need for success in math right at their fingertips! This convenient 144 page fact book is filled with illustrations, formulas, definitions, and examples that children can use to review virtually every type of math problem. Plus, essential information can be found at-a-glance with a section of ready reference charts that cover everything from multiplication to precalculus. The 3-hole punched format allows students to carry this book in a 3-ring binder for quick reference at school, home or on the go! Topics covered include: Basic number concepts Operations and computations Decimals, fractions, and percents Ratios, proportions, and probability Pre-algebra Simple and compound interest and other formulas Customary and metric measurements Problem solving Geometry Organizing and graphing data Glossary and mathematical data And more! The Notebook Reference series offers students everything they need for school success in a convenient, 3-hole punched format. Containing essential information, each comprehensive guide offers subject-specific text that is easy to read and easy to use. The 3-hole punched format allows the guides to be inserted into notebooks for quick and easy reference. Our other titles include Science, Student Planner, Dictionary, Spanish Dictionary, Thesaurus, and Writers Guide This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN, Momence,IL, Commerce,GA. book. Bookseller Inventory # 9780769643403 Book Description: Educational Impressions, United States, 2008. Paperback. Book Condition: New. 290 x 240 mm. Brand New Book *** Print on Demand *. Mathematics is much more than numbers, formulas, and theories. It is a vital, fascinating part of our daily lives. Whether we re hitting a grand slam, making chocolate chip cookies, or reading a science-fiction novel, math helps us understand and enjoy the world in which we live. The Tall Tale Math Series is a comprehensive resource that empowers students by helping them understand and utilize the fundamentals of mathematics. Highly creative story problems spark curiosity and help students appreciate math as a powerful tool for solving real-life questions. Grades 4-8.n Part 2 of the series, Pre-Algebra, students will explore the fundamental principles of algebra, including equations, variables, algebraic expressions, and probabilities. Pre-Algebra is divided into three useful sections: Review Sheets contain easy-to-understand definitions and examples that clearly explain particular concepts, such as Equations. In addition to providing valuable practice exercises, the sheets can also serve as handy reference guides. Skill-Builder Sheets present intriguing story problems that use humor, creativity, and mystery to engage students. Each sheet covers a specific concept, which is clearly labeled at the top of the page. Extra-Practice Sheets are designed to add an additional challenge for students who have mastered the previous sheets. In addition to the basic concepts, students must use additional skills, such as measurement conversion, chart analysis, and selection of the most appropriate number form. These sheets give teachers the extra flexibility to tailor lessons based on grade level and ability. Pre-Algebra was designed to help instructors implement the National Council of Teachers of Mathematics Curriculum and Evaluation Standards. Aimed at students in grades 5 through 8, the sheets will help students meet the following specific objectives: solving basic equations;identifying and working with variables;understanding and working with equations containing fractions;understanding and working with equations containing parentheses;understanding and working with equations containing negative and positive integers;writing algebraic expressions; writing equations to solve word problems;writing and solving equations with variables on both sides of the equal sign;using probability to solve equations; connecting math to the world outside the classroom;using investigation and reasoning to solve problemsGrades 5-8. Bookseller Inventory # APC9781566440578 Book Description: Createspace, United States, 2011. Paperback. Book Condition: New. 229 x 152 mm. Brand New Book * Print on Demand *. A14 Createspace, United States, 2011. Paperback. Book Condition: New. 203 x 133 mm. Brand New Book * Print on Demand *. This is no ordinary math book! How to Homeschool Math - Even if you Hate Fractions!! is a humorous and lively parent-to-parent chat about the ups and downs of homeschooling math. This groundbreaking and insightful book outlines a foolproof method, not only to teach your kids math - but to get them to love it too! She calls it Full-Contact Math, and anyone can do it! This book answers many of the questions homeschool parents have about math: Which curriculum should I use? How much math should my child do each day? How much help should I give my child on math? What level should my child be at for his age? What should he take first: Algebra or Geometry? When should I get a tutor? What the heck is Pre-Algebra ? How on earth can we homeschool Calculus?! .and most of all: Why does my kid HATE math? .and how can I change that? In this sometimes serious, sometimes laugh-out-loud funny book you will learn why whatever curriculum you do choose is just one of many things to consider when homeschooling math. It is what you do with the curriculum that counts! A homeschool mom and math tutor herself, Robin draws on her years of experience teaching not only her own kids, but also other homeschoolers as well as school children. Bookseller Inventory # APC9781463673543 success Incentive Publications, United States, 1996. Paperback. Book Condition: New. 280 x 217 mm. Brand New Book. Motivate students to solve multi-step equations; use exponents and decimals; work with integers; simplify, multiply, and divide fractions; and graph equations, slopes, and intercepts with the challenging math riddles in this book. All of the skills are based on NCTM standards and each page is an engaging and humorous puzzle. Bookseller Inventory # UGH978086530338623 Book Description: Paperback. Book Condition: New. 2nd. 137mm x 20mm x 208mm. Paperback. Packed with in-depth, student-friendly topic reviews that fully explain everything about the subject, this title includes coverage of fundamental maths concepts, sets, decimals, fractions.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 284 pages. 0.340. Bookseller Inventory # 9780738611198 Book Description: Createspace, United States, 2011. Paperback. Book Condition: New. 229 x 152 mm. Brand New Book * Print on Demand *.A Goods of the Mind, LLC, United States, 2013. Paperback. Book Condition: New. 279 x 216 mm. Brand New Book * Print on Demand *. About Competitive Mathematics for Gifted Students This series provides practice materials and short theory reminders for students who aim to excel at problem solving. Material is introduced in a structured manner: each new concept is followed by a problem set that explores the content in detail. Each book ends with a problem set that reviews both concepts presented in the current volume and related topics from previous volumes. The series forms a learning continuum that explores strategies specific to competitive mathematics in depth and breadth. Full solutions explain both reasoning and execution. Often, several solutions are contrasted. The problem selection emphasizes comprehension, critical thinking, observation, and avoiding repetitive and mechanical procedures. Ready to participate in a math competition such as AMC-8, AMC-10, Math Kangaroo in USA, Math Leagues, USAMTS, or AIME? This series will open the doors to consistent performance. About Level 3 This level of the series is designed for students who can solve linear equations, are fluent with fractions, and can factor into primes. The problem sets are designed to strengthen specific areas where we know students have difficulty on AMC-8 and AMC-10. The level 2 books are a strong preparation for AMC-8 and a partial preparation for AMC-10 and AIME. Level 2 consists of: Word Problems (volume 9), Arithmetic and Number Theory (volume 10), Operations and Algebra (volume 11), Geometry (volume 12), and Combinatorics (volume 13). On the contest list for this level: MATHCOUNTS, Math Kangaroo levels 5-6 and 7-8, MOEMS-M, Purple Comet, AMC-8, AMC-10. The computational complexity makes these problem sets useful for preparing the AIME in the long run. About Volume 10 - Arithmetic and Number Theory The problem sets reflect the use of the most elementary facts of number theory in challenging ways. Instead of imitating contest problems, we have focused on presenting questions that explore the nuts and bolts used to create problems. This volume is particularly suitable for young students who aim to do well on AIME in later years and have the patience to explore the elementary facts of number theory in depth. We continue in level 4 with more advanced number theory. Fluency with order of operations and the ability to handle simple algebraic expressions are pre-requisites. Bookseller Inventory # APC9780615943855 Learning Express Llc, United States, 2009. Paperback. Book Condition: New. 255 x 183 mm. Brand New Book. You don t have to be a genius to become an algebra ace-you can do it in just 15 minutes a day Packed with short and snappy lessons, Junior Skill Builders: Algebra in 15 Minutes a Day makes learning algebra easy. It s true: making sense of algebra doesn t have to take a long time .and it doesn t have to be difficult! In just one month, students can gain expertise and ease in all the algebra concepts that often stump students. How? Each lesson gives one small part of the bigger algebra problem, so that every day students build upon what was learned the day before. Fun factoids, catchy memory hooks, and valuable shortcuts make sure that each algebra concept becomes ingrained. With Junior Skill Builders: Algebra in 15 Minutes a Day , before you know it, a struggling student becomes an algebra pro-one step at a time. In just 15 minutes a day, students master both pre-algebra and algebra, including: fractions, multiplication, division, and other basic math; translating words into variable expressions; linear equations; real numbers; numerical coefficients; inequalities and absolute values; systems of linear equations; powers, exponents, and polynomials; quadratic equations and factoring; rational numbers and proportions; and, much more! In addition to all the essential practice that kids need to ace classroom tests, pop quizzes, class participation, and standardized exams, Junior Skill Builders: Algebra in 15 Minutes a Day provides parents with an easy and accessible way to help their children excel. Bookseller Inventory # AAC9781576856734 Book Description: Createspace, United States, 2011. Paperback. Book Condition: New. 229 x 152 mm. Brand New Book * Print on Demand ***. This short book is intended to help those struggling with basic pre-algebra and beginning algebra skills. Written by a former high school math teacher, it simplifies topics such as fractions and exponents by using a mechanic s toolbox approach to problem solving. Bookseller Inventory # APC9781463777906 Book Description: Career Press, United States, 2011. Paperback. Book Condition: New. Enhanced, Updated ed. 229 x 153 mm. Brand New Book. Homework Helpers: Basic Math and Pre-Algebra will help build a solid mathematical foundation and enable students to gain the confidence they need to continue their education in mathematics. Particular attention is placed on topics that students traditionally struggle with the most. The topics are explained in everyday language before the examples are worked. The problems are solved clearly and systematically, with step-by-step instructions provided. Problem-solving skills and good habits, such as checking your answers after every problem, are emphasized along with practice problems throughout, and the answers to all of the practice problems are provided. Homework Helpers: Basic Math and Pre-Algebra is a straightforward and easy-to-read review of arithmetic skills. It includes topics that are intended to help prepare students to successfully learn algebra, including: A[a A[ Working with fractions A[a A[ Understanding the decimal system A[a A[ Calculating percentages A[a A[ Solving linear equalities A[a A[ Graphing functions A[a A[ Understanding word problems. Bookseller Inventory # ABZ9781601631688
books.google.com - Students can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example,... geometry from an advanced standpoint
College Algebra College Algebra College Algebra with Smart CD (Windows) Student Solutions Manual College Algebra Summary The Barnett/Ziegler/Byleen/Sobecki College Algebra series is designed to give students a solid grounding in pre-calculus topics in a user-friendly manner. The series emphasizes computational skills, ideas, and problem solving rather than theory. Explore/Discuss boxes integrated throughout each text encourage students to think critically about mathematical concepts. All worked examples are followed by Matched Problems that reinforce the concepts being taught. New to these editions, Technology Connections illustrate how concepts that were previously explained in an algebraic context may also be solved using a graphing calculator. Students are always shown the underlying algebraic methods first so that they do not become calculator-dependent. In addition, each text in the series contains an abundance of exercises - including numerous calculator-based and reasoning and writing exercises - and a wide variety of real-world applications illustrating how math is useful.
Description of Item Alpha Omega Publications makes learning about statistics and graphs easy and fun with the LIFEPAC Pre-Algebra & Pre-Geometry I Unit 9 Worktext. This ninth in a series of ten worktexts covers the gathering and organizing of data, central tendency and dispersion, graphs of statistics, and graphs of points. With the help of this outstanding homeschool math curriculum, your seventh grader will be able explain statistics like a pro! There's more! In addition to text-based instruction, this self-paced math worktext includes colorful illustrations, easy-to-understand examples and models of math concepts, regular self tests, and a teacher-administered unit test—all designed to encourage mastery of important math concepts. And because each LIFEPAC worktext in this Alpha Omega curriculum can be completed in as little as three to four weeks, your student will experience a sense of accomplishment with the completion of each one. What are you waiting for? Order the LIFEPAC Pre-Algebra & Pre-Geometry I Unit 9 Worktext today and help your child become a statistics master Product: Lifepac Math Grade 7 Data, Statistics, & Unit 9 Edition Number: 2014 Media Type: Book Minimum Grade: 7th Grade Maximum Grade: 7th Grade Weight: 0.33 pounds Length: 10.75 inches Width: 8.25 inches Height: 0.125 inches Vendor Part Number: MAT 0709 Subject: Math Learning Style: Visual Teaching Method: Traditional There are currently no reviews for Lifepac Math Grade 7 Data, Statistics, & Unit 9.
447 University Park business tutors Find the best business business and marketing...) and then using this information to label the correct part(s) of the diagram, as needed, 3) linking together the algebraic representations by the correct math operations required by the problem, 4) carrying out the algebraic manipulations to solve for the unknown(s),
Book Description: The Homework Practice Workbook contains two worksheets for every lesson in the Student Edition. This workbook helps students: Practice the skills of the lesson, Use their skills to solve word problems. Geometry, Homework Practice Workbook Book Description: The Homework Practice Workbook contains two worksheets for every lesson in the Student Edition. This workbook helps students: Practice the skills of the lesson, Use their skills to solve word problems
Buy New Textbook Used Textbook We're Sorry Sold Out eTextbook We're Sorry Not Available More New and Used from Private Sellers Starting at $42 exciting approach to the history and mathematics of number theory ". . . the author's style is totally lucid and very easy to read . . .the result is indeed a wonderful story." —Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2+ ny2 details the history behind how Pierre de Fermat's work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2 + ny2, which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including: • A well-motivated introduction to the classical formulation of class field theory • Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations • An elementary treatment of quadratic forms and genus theory • Simultaneous treatment of elementary and advanced aspects of number theory • New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography Primes of the Form p = x2 + ny2, Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduate-level courses in number and Galois theory. Author Biography DAVID A. COX,PhD, is William J. Walker Professor of Mathematics in the Department of Mathematics at Amherst College. Dr. Cox is the author of Galois Theory, Second Edition, also published by Wiley.
By presenting problem solving in purposeful and meaningful contexts, MATHEMATICAL EXCURSIONS, 2/e, provides students in the Liberal Arts course with a glimpse into the nature of mathematics and how it is used to understand our world. Highlights of the book include the proven Aufmann Interactive Method and multi-part Excursion exercises that emphasize collaborative learning. An extensive technology program provides instructors and students with a comprehensive set of support tools. This Enhanced Edition includes instant access to WebAssign®, the most widely-used and reliable homework system. WebAssign® presents over 500 problems, as well as links to relevant textbook sections, that help students grasp the concepts needed to succeed in this course. As an added bonus, the Start Smart Guide has been bound into this text. This guide contains instructions to help students learn the basics of WebAssign quickly210.95 Purchase Options Hardcover $168.49 $168.49 Save $4299 from$41.99 Save up to $168.96! Rent thru 01/06/15 for $41.99 $41.99 Save $168.96! Rent thru 07/05/15 for $47.99 $47.99 Save $162.96! Rent thru 06/29/16 for $51.99 $51.99 Save $158.96! Rent thru 06/19/18 for $58.49 $58.49 Save $152
More About This Textbook Overview An engrossing, how-to book designed to pique students' interest in the process of modelling in order to acquire both critical and creative modelling skills and the confidence to apply them. The author uses exercises, case studies and models, based on scientific literature, that are freely adaptable and presented in a fresh perspective as interlocking fragments of a mosaic. Examples are chosen from population dynamics, heat flow, optimal harvesting, traffic management and other areas that use models. Includes material for model builders. Editorial Reviews Booknews A textbook that teaches both critical and creative modeling skills, primarily for a senior-level course that gives equal weight to deterministic and probabilistic modeling. It emphasizes both the validation of mathematical models and the rationale behind improving them. The approach embodies the belief that the three most fundamental ideas in mathematical modeling are transience, permanence, and optimality. The minimal mathematical prerequisites are the standard calculus sequence and first courses in linear algebra, ordinary differential equations, and probability and statistics. Probability and statistics are reviewed in an appendix. Annotation c. Book News, Inc., Portland, OR (booknews.com) Product Details Related Subjects Meet the Author MIKE MESTERTON-GIBBONS, PhD, is Professor of Mathematics at Florida State University. A British citizen, he was educated at the University of York and Oxford University, from which he received his doctorate in mathematics in 1977
Find a Golf, FL Algebra 2To me, teaching genetics has two components (1) relating genetics to the students using specific examples and (2) some of memorization is required. Genetics is difficult, but understanding the basics will allow most students to reason out problems. Finite math is a catch all term used to describe many mathematics fields outside of calculus.
Computational Geometry : Algorithms and Applications - 3rd edition Summary: This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students...show more this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In this third edition, besides revisions to the second edition, new sections discussing Voronoi diagrams of line segments, farthest-point Voronoi diagrams, and realistic input models have been added. ...show less Used - Very Good Book. Shipped from US within 4 to 14 business days. Established seller since 2000 $42.85 +$3.99 s/h Good TextbookBarn Woodland Hills, CA 3540779791 +$3.99 s/h Good Dominion Bookstore Norfolk, VA 2008 Hardcover Good
ISBN: 0321756452 / ISBN-13: 9780321756459 Prealgebra This clear, accessible treatment of mathematics features a building-block approach toward problem solving and realistic, diverse applications. The ...Show synopsisThis clear, accessible treatment of mathematics features a building-block approach toward problem solving and realistic, diverse applications. The "Putting Your Skills to Work" and new chapter-end feature, "Math in the Media," present readers with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life. The goal of the changes in the 2nd edition is to upgrade the level of algebra in the book--This is accomplished by introducing equations, evaluating expressions, and properties of exponents earlier and revisiting the topics more often. Readers now learn how to solve equations using one principle first (Chapters 1, 3, 4, and 5)--Using both principles together is covered (Ch. 6) after readers have had substantial practice using one principle of equality. Contains 2 chapters dedicated to algebra skills (Ch. 3 and 6). A substantial increase in coverage of evaluating expressions (nearly double) from the first edition. Signed numbers are now covered earlier in Chapter 2 and Whole number operations are covered in one chapter vs. two in the previous edition.Hide synopsis ...Show moreHide Description:Fine. Paperback. Instructor Edition: Same as student edition...Fine. Paperback. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 9780321773517735Paperback. Instructor Edition: Same as student edition with...Paperback. Instructor Edition: Same as student edition with additional notes or answers. New Condition. SKU: 9780321773548Very Good. 0321756452 ANNOTATED INSTRUCTOR'S EDITION contains...Very Good. 0321756452 0321756452 ANNOTATED INSTRUCTOR'S EDITION contains the...New. 0321756452
The most helpful favorable review The most helpful critical review 198 of 205 people found the following review helpful 5.0 out of 5 starsExcellent Book. Belongs on Your Bookshelf. Courant's 500-page text is not entirely suitable for the layman. Its target audience includes those who enjoy reading and studying mathematics and have a good background through precalculus or higher. "What is Mathematics?" is a mathematics book, not a book about mathematics. "What is Mathematics?" is not a new book. It was first published by Oxford University... 1.0 out of 5 starstypos galore, terrible layout The book is littered with mangled formulas, mostly due to the fact the minus sign is missing from most formulas. This is completely unacceptable in any math book, but particularly so in a book aimed at beginners, who will probably feel bewildered by the huge amount of nonsensical formulas. This review is from: What Is Mathematics? An Elementary Approach to Ideas and Methods (Paperback) This book has been around now for a few years to say the least. It is intriguing and captivating in its concise approach to explain and answer the question of just what Mathematics is. If you have a hankering to understand what Mathematics does or perhaps why it even exists, this book is pretty informative and interesting reading. One feature I liked about it is its use of many examples to propel the thought process into that zone of understanding within us. When you are in the zone many basic concepts used in both rudimentary and complex problems become apparent frequently leading one to say "Now I get it." This review is from: What Is Mathematics? An Elementary Approach to Ideas and Methods (Paperback) Whether or not you are a mathematician or if it is just a hobby, this book is fantastic!!! You can open it up to any page and just begin reading...there is no need to start beginning to end. A great work to read as time allows!!! This review is from: What Is Mathematics? An Elementary Approach to Ideas and Methods (Paperback) It's a lucid presentation of the ideas that govern the different domains of Mathematics. Clear but not too easy, it needs commitment by the reader in order to understand its essence to the full. Courant (as his mentor Hilbert) shows how important and useful it is to demystify the cumbersome technicalities that often dominate the subject. 5.0 out of 5 starsYou'll also learn lots of solid mathematics., July 24, 1998 By A Customer This review is from: What Is Mathematics? An Elementary Approach to Ideas and Methods (Paperback) So Einstein thought this book "easily understandable" ? Well, if you are a beginner at calculus you will not find it "easily understandable", for that would mean you didn't learn a single new thing! Calculus is perhaps the most profound and far-reaching discovery of the millenium, and is certainly not trivial. However, this magical book is the best possible introduction. It is written so that your perplexities will always be accompanied by so beautiful results or promises of results, that you will be more than ready to do the necessary efforts. These come, for instance, in the form of exercises and in the details of the demonstrations, which are all there. There is no cheating. Well, the book is not only about calculus. There are many previous chapters on theory of numbers, geometry, algebra, topology. But I think it culminates with calculus, and the preceding chapters serve as steps of a staircase leading to it. The new edition has the collaboratio! n of Ian Stewart, an inspired writer. This review is from: What Is Mathematics? An Elementary Approach to Ideas and Methods (Paperback) I give this book 5 stars because it is a classic. I believe, however, that it is too sketchy to be useful for the beginner as it is advertised. For chapter 1, for example, on number theory, I recommend Hardy's "Introduction to the Theory of Numbers." For the second chapter, on the number systems, I recommend a book like Birkhoff and MacLane's "Modern Algebra." It's difficult to write a survey of mathematics textbook without being sketchy and Courant isn't up to the task. In addition, the bibliography at the end of the book is fairly outdated, although the two books I mentioned above are included there. I also wish Courant would have provided more information on the evolution of mathematical concepts and ideas. This is something Kline does in his "History of Mathematical Thought." I find this information vital in answering the question "what is mathematics?" If you really want to get a good idea of what mathematics is you should start with a general history of mathematics like Kline's book and quickly move on to Greek mathematics. Even a small understanding of Euclid's axiomatic method will help you understand modern day mathematics and why mathemticians do what they do the way they do it. Having said that, I plan on making more use of Courant's book later on in my mathematics career. This review is from: What Is Mathematics? An Elementary Approach to Ideas and Methods (Paperback) I am a college student, majoring in math, but not very far along in my major sequence. I found that this book gave me an understandable perspective on what might lie ahead in my studies. I highly recommend this book for anyone who thinks they might be interested in learning more about Mathematics! It inspired me! This review is from: What Is Mathematics? An Elementary Approach to Ideas and Methods (Paperback) I can't do this book justice, as many reviewers before me have. As an undergrad who's majoring in math, this book helps to illuminate so many fields of mathematics that I had not learned in school. From basic number theory to introductory calculus, this is the perfect companion for anyone who has an understanding of the beauty and power that numbers hold. Five stars, easy. This review is from: What Is Mathematics? An Elementary Approach to Ideas and Methods (Paperback) The purpose of this review is to bring your attention to the second author of this timeless classic. Apparently most reviewers give all the credit to the first author, Richard Courant. Allow me to bring the second author, Herbert Robbins, to your attention. Google his name and you will find that Herbert Robbins is one of the most prolific and creative statisticians ever existed. Robbins studied mathematics at Harvard in the 1930s. At the time he worked with Courant on this book, he was a young rising star in mathematics/statistics. I have every reason to believe that Robbins has done more to this book than we give him credit for. We may never know the exact magnitude of Robbins's contribution to this book, but a complete ignorance of him is certainly unjust. My first attempt to read this book was during my undergraduate studies. Twenty years later, I am now discarding my college textbooks and "What Is Mathematics" has resurfaced. When the student is ready, the master will appear. It's a great book and for certain people worth the journey. Yes, a little dated but I think that adds to the charm.
Calculus was developed in the latter half of the seventeenth century by two mathematicians, Namely Gottfried Leibniz and Isaac Newton. Calculus can be divided into two branches: Differential Calculus and Integral Calculus. Differential calculus is used to find the rate of change of a measures; integral calculus is used to find the measures where the rate of change is known. "Functions" are defined by a formula. Solve Precalculus problems: 1)Get the arc length corresponds to the given angle on a circle of radius 2.5. (Round your answer to three decimal places.) 45° An ant start at the point (1, 0) on the unit circle and walks counterclockwise a distance of 4 units around the circle. Find the x and y coordinates (correct to 2 decimal places) of the last place of the ant.
21 "for Dummies" eBooks on the topic of math, logic, statistics etc from basic math to Trigonometry to Calculus II. The only oddball in this collection is the Calculus for Dummies book because it is a 93MB scan as opposed to an official eBook. Algebra I Essentials for Dummies ISBN: 0470618349 With its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget. Perfect for students who need to review or reference critical concepts, Algebra I Essentials For Dummies provides content focused on key topics only, with discrete explanations of critical concepts taught in a typical Algebra I course, from functions and FOILs to quadratic and linear equations I for Dummies - 2nd Edition ISBN: 0470559640 Factor fearlessly, conquer the quadratic formula, and solve linear equations There's no doubt that algebra can be easy to some while extremely challenging to others. If you're vexed by variables, Algebra I For Dummies, 2nd Edition provides the plain-English, easy-to-follow guidance you need to get the right solution every time! Algebra II Essentials for Dummies ISBN: 0470618400 Passing grades in two years of algebra courses are required for high school graduation. Algebra II Essentials For Dummies covers key ideas from typical second-year Algebra coursework to help students get up to speed. Free of ramp-up material, Algebra II Essentials For Dummies sticks to the point, with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical Algebra II course, from polynomials, conics, and systems of equations to rational, exponential, and logarithmic functions II for Dummies ISBN: 0471775812 Besides being an important area of math for everyday use, algebra is a passport to studying subjects like calculus, trigonometry, number theory, and geometry, just to name a few. To understand algebra is to possess the power to grow your skills and knowledge so you can ace your courses and possibly pursue further study in math. Algebra II For Dummies is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems. This friendly guide shows you how to get up to speed on exponential functions, laws of logarithms, conic sections, matrices, and other advanced algebra concepts. In no time you'll have the tools you need to: This straightforward guide offers plenty of multiplication tricks that only math teachers know. It also profiles special types of numbers, making it easy for you to categorize them and solve any problems without breaking a sweat. When it comes to understanding and working out algebraic equations, Algebra II For Dummies is all you need to succeed! Basic Math & Pre-Algebra for Dummies ISBN: 0470135372 Get the skills you need to solve problems and equations and be ready for algebra class., and percents, you'll build necessary skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations. Basic Math & Pre-Algebra Workbook for Dummies ISBN: 0470288177 When you have the right math teacher, learning math can be painless and even fun! Let Basic Math and Pre-Algebra Workbook For Dummies teach you how to overcome your fear of math and approach the subject correctly and directly. A lot of the topics that probably inspired fear before will seem simple when you realize that you can solve math problems, from basic addition to algebraic equations. Lots of students feel they got lost somewhere between learning to count to ten and their first day in an algebra class, but help is here! Begin with basic topics like interpreting patterns, navigating the number line, rounding numbers, and estimating answers. You will learn and review the basics of addition, subtraction, multiplication, and division. Do remainders make you nervous? You'll find an easy and painless way to understand long division. Discover how to apply the commutative, associative, and distributive properties, and finally understand basic geometry and algebra. Find out how to: Complete with lists of ten alternative numeral and number systems, ten curious types of numbers, and ten geometric solids to cut and fold, Basic Math and Pre-Algebra Workbook For Dummies will demystify math and help you start solving problems in no time! Calculus Essentials for Dummies ISBN: 0470618353 Just the key concepts you need to score high in calculus From limits and differentiation to related rates and integration, this practical, friendly guide provides clear explanations of the core concepts you need to take your calculus skills to the next level. It's perfect for cramming, homework help, or review. Calculus for Dummies ISBN: 0764524981 Well, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra* Students taking their first calculus course – If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series. * Students who need to brush up on their calculus to prepare for other studies – * Adults of all ages who'd like a good introduction to the subject –* Real-world examples of calculus * The two big ideas of calculus: differentiation and integration * Why calculus works * Pre-algebra and algebra review * Common functions and their graphs * Limits and continuity * Integration and approximating area * Sequences and series Don't buy the misconception. Sure calculus is difficult – but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off – it's simply the next step in a logical progression. Calculus II for Dummies ISBN: 047022522X Got just enough refresher explanations before each set of problems, you'll sharpen your skills and improve your performance. You'll see how to work with limits, continuity, curve-sketching, natural logarithms, derivatives, integrals, infinite series, and more! 100s of Problems! * Step-by-step answer sets clearly identify where you went wrong (or right) with a problem * The inside scoop on calculus shortcuts and strategies * Know where to begin and how to solve the most common problems * Use calculus in practical applications with confidence Differential Equations Workbook for Dummies ISBN: 0470472014 Need to know how to solve differential equations? This easy-to-follow, hands-on workbook helps you master the basic concepts and work through the types of problems you'll encounter in your coursework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every equation. You'll also memorize the most-common types of differential equations, see how to avoid common mistakes, get tips and tricks for advanced problems, improve your exam scores, and much more! Intermediate Statistics for Dummies ISBN: 0470045205 Need to know how to build and test models based on data? Intermediate Statistics For Dummies gives you the knowledge to estimate, investigate, correlate, and congregate certain variables based on the information at hand. The techniques you'll learn in this book are the same techniques used by professionals in medical and scientific fields. Linear Algebra for Dummies ISBN: 0470430907 Does linear algebra leave you feeling lost? No worries —this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction. Logic for Dummies ISBN: 0471799416 Logic concepts are more mainstream than you may realize. There's logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as CSI and Numbers incorporate a variety of logistical studies. Logic For Dummies explains a vast array of logical concepts and processes in easy-to-understand language that make everything clear to you, whether you're a college student of a student of life. LSAT Logic Games for Dummies ISBN: 0470525142 Improve your score on the Analytical Reasoning portion of the LSAT If you're like most test–takers, you find the infamous Analytical Reasoning or "Logic Games" section of the LSAT to be the most elusive and troublesome. Now there's help! LSAT Logic Games For Dummies takes the puzzlement out of the Analytical Reasoning section of the exam and shows you that it's not so problematic after all! Math Word Problems for Dummies ISBN: 0470146605 Everyone remembers story problems, nowadays called "word problems," from elementary school and middle school math. Solving word problems is the latest way to help students who struggle learning basic math skills, as well as to introduce more complicated math concepts. Math Word Problems For Dummies shows students and adult learners how to solve word problems with a method that works for any word problem at any level. Math-wary readers will use basic math to work through problems, focusing on elementary-level skills before moving on to algebra and geometry. Mary Jane Sterling (Peoria, IL), a teacher for more than 25 years, is the author of numerous For Dummies books, including Algebra For Dummies (0-7645-5325-9) and Trigonometry For Dummies (0-7645-6903-1). Pre-Algebra Essentials For Dummies ISBN: 0470618388 Just the critical concepts you need to score high in pre-algebra This practical, friendly guide focuses on critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to standard formulas and simple variable equations. Pre-Algebra Essentials For Dummies is perfect for cramming, homework help, or as a reference for parents helping kids study for exams. Pre-Calculus Workbook for Dummies ISBN: 0470421312 Get the confidence and the math skills you need to get started with calculus! Are 100s of Problems! Detailed, fully worked-out solutions to problems The inside scoop on quadratic equations, graphing functions, polynomials, and more A wealth of tips and tricks for solving basic calculus problems Probability for Dummies ISBN: 0471751413 Packed with practical tips and techniques for solving probability problems Increase your chances of acing that probability exam -- or winning at the casino! Whether Statistics Essentials for Dummies ISBN: 0470618396 Statistics Essentials For Dummies not only provides students enrolled in Statistics I with an excellent high-level overview of key concepts, but it also serves as a reference or refresher for students in upper-level statistics courses. Free of review and ramp-up material, Statistics Essentials For Dummies sticks to the point, with content focused on key course topics only. It provides discrete explanations of essential concepts taught in a typical first semester college-level statistics course, from odds and error margins to confidence intervals and conclusions. This guide is also a perfect reference for parents who need to review critical statistics concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts. Trigonometry Workbook for Dummies ISBN: 0764587818 From angles to functions to identities - solve trig equations with ease Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or worse yet, not know where to begin? No fear - this hands-on-guide focuses on helping you solve the many types of trigonometry equations you encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, you'll sharpen your skills and improve your performance. You'll see how to work with angles, circles, triangles, graphs, functions, the laws of sines and cosines, and more! 100s of Problems! * Step-by-step answer sets clearly identify where you went wrong (or right) with a problem * Get the inside scoop on graphing trig functions * Know where to begin and how to solve the most common equations * Use trig in practical applications with confidence
Mathematics for Elementary Teachers -Text Only - 7th edition Summary: This leading mathematics text for elementary and middle school educators helps readers quickly develop a true understanding of mathematical concepts. It integrates rich problem-solving strategies with relevant topics and extensive opportunities for hands-on experience. By progressing from the concrete to the pictorial to the abstract, Musser captures the way math is generally taught in elementary schools.
More About This Textbook Overview Tr From a review of Algebra, I.M. Gelfand and A. Shen, ISBN 0-8176-3677-3: " Editorial Reviews From the Publisher "Cover[s] all of the basic topics that a high school or beginning university student should be expected to know.... There are...some nice touches; for example, a nice informal discussion showing that the sine of an angle in a right triangle does not depend on whether the sides are measured in inches or centimeters..." —Choice "Covers all the basics of the subject through beautiful illustrations and examples…. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject." — L'enseignement Mathématique "As a teacher I enjoyed this book enormously and I will doubtless borrow many of the plums to spice up my lessons…. [For] that ideal student who is to be prepared to be challenged to think what the subject is really about, and has the patience to excavate the basic ideas for all they are worth before jumping on to the next chapter, it should prove to be a godsend." —The Mathematical Gazette "The authors tried to explain the results of trigonometry as simply as possible…. The exercises include a few problems of each routine type. Most of the problems exhibit a new aspect of the technique or object under discussion. One of the goals of this book is to prepare students for a course in calculus. We recommend it for teachers and students 22, 2005 The best academic book I have ever touched! This book-and any books that are similar to this one-are long overdue and are tremendously needed in classrooms, especially for higher level students. The problem with more of your standard, conventional books that you have at school are that they ONLY tell you how to do something, not why something works like this or that. This is invaluable, for it (the method of solving a problem) then lingers in your brain for a very long time and when you come in contact with some problem not yet the same to it, but somewhat related, you will be able to utilize that knowledge to solve the problem. Whereas by memorizing the steps and 'hows' to do a problem, the person's mind is then very provincial in that area. The person who gave the book two stars above is correct that it is disappointing that there are no solutions, but the overall superb content of the book should put that problem in disguise. Trust me, if you really want to LEARN, buy and read carefully through this book!!!! It will be very beneficial. 2 out of 2 people found this review helpful. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. Anonymous Posted September 24, 2004 A fascinating examination of trigonometry. This clearly written text, which is designed as a supplement to a trigonometry course, is a fascinating study of the subject. After reviewing the geometric prerequisites, the authors cover right triangle trigonometry, the relationship between trigonometry and geometry, unit circle trigonometry, trigonometric identities, graphs of trigonometric functions, and inverse trigonometric functions. The book touches on subjects not normally covered in trigonometry courses. Particularly noteworthy are appendices to the later chapters in which the authors relate trigonometry to Pythagorean triples, use sequences of trigonometric functions to approximate pi, and introduce Fourier series. There are numerous worked examples to give the reader insights that will help her or him solve the many difficult problems in the text. Solutions to the problems are not provided. 2 out of 2 people found this review helpful. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. Avid_Learner Posted January 28, 2009 Perfect I haven't dealt with Trigonometry (or Algebra/Geometry) for over 10 years and now I need it for my work. I found this book on here (sadly it was not easy to find... I found it because I sorted by lowest price).<BR/><BR/>I take it B&N wants you to buy the expensive books rather than the ones that are truly amazing when they are less expensive.<BR/><BR/>Instantly while reading this book I was refreshed with not only the trigonometry I needed but also the geometry and algebra that back it up. It was concise, clear as glass, this author really understands how the human mind learns.<BR/><BR/>I didn't come away feeling as though I'd memorized formulas; each time I closed the book I felt enriched with a greater understanding of math.<BR/><BR/>This book is suitable for brand new students and is better than the textbooks I received in school; but also suitable for review after a long time such as is my case. It's not bloated and it speaks well with it's illustrations. It's very suited for visual learners like myself.<BR/><BR/>There are no solutions to the problems; I found that I did not require any. This book offers true education.<BR/><BR/>Why is this not at schools? And for it's price? It's sad something like this is hidden away, really. Get this in the schools!! Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. Anonymous Posted November 15, 2002 Dont bother with this one The book covers all topis however there are no solutions to the problems. What good is a book without solutions! Dont waste your money 0 out of 1 people found this review helpful. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
Product Description The Candy-Coated World of Calculus. Boost calculus confidence with this dynamic and engaging series that takes students through limits, graphing, derivatives, integrals and more. Fast-paced and full of information, this series will aid retention of key concepts with an easy-to-follow pace and repeated reviews of key concepts. Help your students grasp even the most perplexing functions! The DVD Super Pack contains Modules 1 through 9 plus companion CD-ROM.Module 1: Calculus Basics The Standard Deviants answer a question that has baffled humanity since...oh, about 1700: What is calculus? The two men who created calculus, Newton and Leibniz, aren't around to explain it to you, so the Standard Deviants are going to do the job instead. Plus, we'll review the basics of algebra, graphs, functions and limits. Module 2: Limits The sky's the limit...on the types of limits the Standard Deviants are going to show you. But just as you think you've reached your limit on limits, we'll boldly go off into infinity!Module 3: Derivatives What is an effect, the root of a word, a synonym for "credited" and also a famous mathematical term? The answer: a derivative. The Standard Deviants are going to focus on the derivative's celebrity status in math as the numero uno rate of change.Module 4: Work-Saving Rules You can have your work cut out for you finding derivatives and tangents. The Standard Deviants can lessen your workload with some rules that will make life easier. Rules that make life easier: The power rule, E rule and natural log rule will have you plotting points and drawing curves in no time flat.Module 5: Finding Derivatives The Standard Deviants give you a few more rules to help you survive, thrive and derive in the calculus jungle. The product rule, quotient rule, and chain rule will help you find derivatives - no matter what shape or size they are!Module 6: Derivative Applications Is your brain drained? Do you want a little review? You got it. The Standard Deviants go over all the major concepts and formulas from the first five programs and make sure all this calculus know-how sticks in your head. Then we'll discuss applications of derivatives, like critical points, functions, and derivative tests.Module 7: Figuring Out Curves There are curves that go back and forth, increase and decrease and never seem to stand still. How does one find their extrema? Are the curves concave up or concave down? We'll tackle these questions and many more! Module 8: Practical Applications See how calculus saves the day, no matter what the problem. The Standard Deviants figure out the cheapest sized delivery box for Uncle Skippy's premium edible dirt business, find the instantaneous velocity of a Volkswagen Beetle being chased by stampeding elephants and see how far a chicken can throw an egg.Module 9: The Anti-Derivative Go against the grain as the Standard Deviants tackle the anti-derivative! Suddenly everything is reversed! Pigs can fly, lunch is free, money grows on trees and beggars can be choosers. How does one find the anti-derivative? With a little process called integration.Calculus Companion CD Transform your Standard Deviants School video programs into complete lessons with this supplementary CD-ROM! Each disc contains everything you need to present and reinforce the material covered in the DVD/video modules, including a Teacher's Guide with helpful presentation notes, a Program Guide that lists the most important topics in each program, illustrated QuikNotes with definitions and examples, and a quiz. Also usable with the Standard Deviants videos. Easy-to-access text files in PDF format. Mac and PC compatible.Grade Level: 11+. 234 minutes. 9 DVDs + CD Guide
Buy Used Textbook eTextbook New Textbook We're Sorry Sold Out More New and Used from Private Sellers Starting at $117Elementary And Intermediate Algebra Elementary and Intermediate Algebra Elementary And Intermediate Algebra, 1pass for Mathematicsnow, And Speechbuilder Express Elementary and Intermediate Algebra, 4th Edition Outlines and Highlights for Elementary and Intermediate Algebra by Gustafson, R David and Tussy, Alan S , Isbn : 9780495188742 Summary Algebra can be like a foreign language. But one text delivers an interpretation you can fully understand. Building a conceptual foundation in the "language of algebra," iNTERMEDIATE ALGEBRA, 4e provides an integrated learning process that helps you expand your reasoning abilities as it teaches you how to read, write, and think mathematically. Packed with real-life applications of math, it blends instructional approaches that include vocabulary, practice, and well-defined pedagogy with an emphasis on reasoning, modeling, communication, and technology skills. The authors' five-step problem-solving approach makes learning easy. More student-friendly than ever, the text offers a rich collection of student learning tools, including Enhanced WebAssign online learning system. With INTERMEDIATE ALGEBRA, 4e, algebra makes sense!

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