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Given a reference domain, some boundary conditions and a limited amount of material, which can not fill the whole domain, we want to determine the material distribution inside the domain so that the structure generated will contain the minimum elastic energy. This is called minimum compliance problem, a topic in the field of topology optimization. Our initial goal is to implement the numerical methods in this field to the interesting examples offered in our class, such as the wall cylinder and the plate under distributed pressure, and then analyse the computational results. If time permits, we will consider other optimization objects beside the elastic energy. This book offers detailed discussion on modeling, placing emphasis on where the equations come from and why some variable should be zero or can be ignored. Thus I can learn not only the derivation but also the mechanical insight.
Number Theory (formerly MTH-35) Description: Introduction to the arithmetic properties of the integers including divisibility, congruences, diophantine equations, primes and their distribution, quadratic forms and quadratic reciprocity. Additional topics will be chosen from continued fractions, cryptography, partitions, elliptic curves, modular forms and number fields
Comment: This textbook is very much usable for any beginning Trigonmetry course. I had to... see more Comment: This textbook is very much usable for any beginning Trigonmetry course. I had to supplement the exercise set a bit in a number of sections. Also, I was able to supplement with topics found in the Stitz and Zeager Trigonometry textbook: Also, students found the videos found here to be useful: Comment: I am new Merlot member and am wondering whether this discussion thread is still active or whether it is now closed. Upon... see more Comment: I am new Merlot member and am wondering whether this discussion thread is still active or whether it is now closed. Upon arriving to this site, I was asked if I wished to join but it does say "Material Inactive.״Thank youThis is a remarkable online resource. Allows you to easily access information and download functional templates you can use... see more Comment: This is a remarkable online resource. Allows you to easily access information and download functional templates you can use right away. Can be a little complex, but for the beginning college research, it is indispensable. Comment: A decent array of PowerPoints for the classroom. Very clever PP games. (Presentations will have to be updated.) Some of the... see more Comment: A decent array of PowerPoints for the classroom. Very clever PP games. (Presentations will have to be updated.) Some of the presentation take a little investigation and experimentation to work properly. A good resource. Comment: Good information but font is small and hard to read on some documents. There is no PowerPoint on this site, but there is a... see more Comment: Good information but font is small and hard to read on some documents. There is no PowerPoint on this site, but there is a clever web page which links to graphics which simulates a PowerPoint.
Most widely held works by Consortium for Mathematics and Its Applications (U.S.) For all practical purposes : introduction to contemporary mathematics( Book ) 26 editions published between 1987 and 1997 in English and held by 1,579 libraries worldwide This series provides an understanding of math in both personal matters and the world around us. Relevant applications of mathematics are presented, focusing on contemporary math as a problem solving tool. Against all odds inside statistics( Visual ) 21 editions published between 1988 and 2007 in English and held by 823 libraries worldwide Presents the why as well as the how of statistics using computer animation, colorful on-screen computations, and documentary segments. For all practical purposes : mathematical literacy in today's world( Book ) 12 editions published between 1999 and 2009 in English and held by 375 libraries worldwide [The authors'] goal [for this book is] to help students think logically and critically about the mathematical information that abounds in our society. [This book] stresses the connections between contemporary mathematics and modern society ...-Pref. Statistics decisions through data( Visual ) 7 editions published between 1990 and 1993 in English and held by 223 libraries worldwide An introductory statistics course composed of five hour-long instructional videos. The texts include exercises, group activities, and quizzes. For all practical purposes( Visual ) 8 editions published between 1986 and 2006 in English and held by 165 libraries worldwide A series which stresses the connections between contemporary mathematics and modern society. Presents a great variety of problems that can be modeled and solved by quantitative means. Algebra in simplest terms( Visual ) 10 editions published between 1990 and 1991 in English and held by 164 libraries worldwide Solving equations is a basic operation of all higher math. This set shows algebra's usefulness to retailers, biologists, and even anyone who drives a car. Host Sol Garfunkel walks viewers through realistic problems, highlighting the common trouble spots. College algebra in simplest terms( Visual ) 4 editions published in 1991 in English and held by 125 libraries worldwide Presents the role of algebra in daily life and demonstrates practical applications in the workplace. Uses symbols, charts, pictures, and state-of-the-art computer graphics to illustrate basic algebraic techniques. Reviews problems step-by step, focusing on the methods students find most difficult to grasp. Statistics : the shape of the data by Susan Jo Russell( Book ) 2 editions published between 1989 and 1997 in English and held by 123 libraries worldwide For teaching elementary and middle school students how to collect and analyze real world data. Measuring : from paces to feet by Rebecca B Corwin( Book ) 1 edition published in 1990 in English and held by 107 libraries worldwide Teaches elementary and middle school students how to collect and analyze real world data.
This is a free online textbook designed for the Advanced Algebra instructor. According to the author, he "developed a set of... see more This is a free online textbook designed for the Advanced Algebra instructor. According to the author, he "developed a set of in-class assignments, homework and lesson plans, that work for me and for other people who have tried them. The complete set comprises three separate books that work together:•The Homework and Activities Book contains in-class and homework assignments that are given to the students day-by-day." "•The" target=״_blank״ Concepts Book provides conceptual explanations, and is intended as a reference or review guide for students; it is not used when teaching the class." •The" target=״_blank״ Teacher's Guide provides detailed lesson plans; it is your guide to how the author "envisioned these materials being used when I created them (and how I use them myself) " target=״_blank״ Instructors should note that this book probably contains more information than you will be able to cover in a single school year." This is the Conceptual Explanations part of Kenny Felder's course in Advanced Algebra II. It is intended for students to... see more . According to the OER Commons, "Word 2007 is a word processor designed by Microsoft This manual will show you some more... see more According to the OER Commons, "Word״ This book is written as a series of conversations. In each conversation the participants discuss, argue about, and develop... see more This book is written as a series of conversations. In each conversation the participants discuss, argue about, and develop issues critical to the effective design and instructional use of learning objects. AJAX is an acronym for Asynchronous JavaScript and XML. It is a development technique for creating interactive web... see more AJAX is an acronym for Asynchronous JavaScript and XML. It is a development technique for creating interactive web applications. Unlike classic web pages, which must load in their entirety if content changes, AJAX allows web pages to be updated asynchronously by exchanging small amounts of data with the server behind the scenes. " Algebra for College Students is designed to be used as an intermediate level text for students who have had some prior... see more " Algebra for College Students is designed to be used as an intermediate level text for students who have had some prior exposure to beginning algebra in either high school or college. This text explains the why's of algebra, rather than simply expecting students to imitate examples.
More About This Textbook Editorial Reviews From The Critics This textbook reviews the mathematical symbols and operations of algebra, and reinforces function and graphing concepts for future courses. The authors cover polynomial, rational, radical, exponential, and logarithmic equations, and both linear and nonlinear systems. The eighth edition introduces functions and graphs of linear equations earlier in the text
Very clear and useful. Covers a broad range of mathematics and physics and is actually very straightforward and readable. I've had a copy out from my university library for months and will most likely but it after leaving as it is a very good reference.
Product Description The new edition of this easy-to-understand text, designed for a non-calculus course in statics and strength of materials, requires only a working knowledge of algebra, geometry, and trigonometry. In addition to expanded coverage and better organization of information, it addresses new topics such as accuracy and precision, solution of simultaneous equations, rolling resistance, mechanical properties of materials, composite beams, reinforced concrete beans, plastic analysis of beams, design of shear connectors, and more. New chapter on mechanical properties of materials and an expanded chapter on the design of beams for strength. Students learn to apply basic principles to a variety of problems. Homework problems of various levels of difficult furnished at the end of each chapter, beginning with relatively simple problems to help students gain confidence. Review of trigonometry and algebra included in Chapter 1. Computer program assignments follow regular homework problems in most chapters, requiring students to write computer programs to solve some general problems in the chapter topics. (Any appropriate computer language may be used.)
Features * Objective Based Learning: Introductory section objectives have been expanded to include the "what and why" of the objectives, followed by icons within the text identifying the specific areas of focus. A summary of chapter objectives will now be featured in the chapter summary material. * Mathematical Modeling and Data Analysis: A focus on mathematical modeling and data analysis, specifically establishing a step by step process for understanding word problems and gathering the data from said problems. * Graphical Interpretation:
Introductory and Intermediate Algebra for College Students - With 2 CDS - 3rd edition Summary: TheBlitzer Algebra Seriescombines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum student appeal. Blitzer's personality shows in his writing, as he draws students into the material through relevant and thought-provoking applications. Every Blitzer page is interesting and relevant, ensuring that students will actually use their textbook to achieve success! KEY TOPICS: Variables, Real Numbers, and Mathematical Models; Linear Equations and Inequ...show morealities in One Variable; Linear Equations in Two Variables; Systems of Linear Equations; Exponents and Polynomials; Factoring Polynomials; Rational Expressions; Basics of Functions; Inequalities and Problem Solving; Radicals, Radical Functions, and Rational Exponents; Quadratic Equations and Functions; Exponential and Logarithmic Functions; Conic Sections and Systems of Nonlinear Equations; Sequences, Series, and the Binomial Theorem. MARKET: for all readers interested in algebra
Elementary Mathematical Modeling : Functions and Graph introduction to mathematical modeling uses elementary functions to describe and explore real-world data and phenomena. Helps readers connect math with the world around them through real-world applications of elementary mathematics. Shows how to construct useful mathematical models, how to analyze them critically, and how to communicate quantitative concepts effectively. Uses concrete language and examples throughout to foster quantitative literacy. For anyone interested in gaining a solid foundation in mathematical concepts. (Note: Each chapter begins with a real-world vignette that is revisited as the chapter evolves, and concludes with a Review and a project-style Investigation.)
Precalculus : Graphing Approach - 5th edition Summary: Part of the market-leading ''Graphing Approach Series'' by Larson, Hostetler, and Edwards, ''Precalculus: A Graphing Approach,'' 5/e, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed. Continuing the series' emphasis on student support, the Fifth Edition introduces ''Prerequisite...show more Skills Review.'' For selected examples throughout the text, the ''Prerequisite Skills Review'' directs students to previous sections in the text.''New!'' The ''Nutshell Appendix'' reviews the essentials of each function, discussed in the ''Library of Functions'' feature, and offers study capsules with properties, methods, and examples of the major concepts covered in the textbook. This appendix is an ideal study aid for students.''New!'' ''Progressive Summaries'' outline newly introduced topics every three chapters and contextualize them within the framework of the course.''New!'' ''Make a Decision'' exercises--extended modeling applications presented at the end of selected exercisesets--give students the opportunity to apply the mathematical concepts and techniques they've learned to large sets of real data.''Updated!'' The ''Library of Functions,''.''Updated!'' The ''Chapter Summaries'' have been updated to include the Key Terms and Key concepts that are covered in the chapter. These chapter summaries are an effective study aid because they provide a single point of reference for review.''Updated!'' The ''Proofs of Selected Theorems'' are now presented at the end of each chapter for easy reference.The Larson team provides an abundance of features that help students use technology to visualize and understand mathematical concepts. ''Technology Tips'' ''Technology Support'' notes appear throughout the text and refer students to the ''Technology Support Appendix,'' where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. The ''Technology Support'' notes alsodirect students to the ''Graphing Technology Guide,'' on the textbook's website, for keystroke support for numerous calculator models.Carefully positioned throughout the text, ''Explorations'' engage students in active discovery of mathematical concepts, strengthening critical thinking skills and helping them to develop an intuitive understanding of theoretical concepts.''What You Should Learn'' and ''Why You Should Learn It'' appears at the beginning of each chapter and section, offering students a succinct list of the concepts they will soon encounter. Additionally, this featur726 +$3.99 s/h Acceptable Sierra Nevada Books Reno, NV Biggest little used bookstore in the world! $8.26 +$3.99 s/h Acceptable Blue Cloud Books Phoenix, AZ Blue Cloud Books ??? Hot deals from the land of the sun. $8.6016.46 +$3.99 s/h Good invisibledog Salt Lake City, UT 0618854630 Unmarked text. $19.35 +$3.99 s/h Good SellBackYourBook Aurora, IL 0618854630 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!! $37.68 +$3.99 s/h Good Books Revisited Chatham, NJ Possible retired library copy, some have markings or writing
Mathematics Mathmatics Course Descriptions Mathematics Courses (MAT) Placement in mathematics courses for those with no previous college mathematics credit is determined on the basis of high school mathematics credit, high school mathematics GPA, mathematics scores on the SAT or ACT and scores on the mathematics placement test given at registration time each semester. A review of elementary and intermediate algebra designed to assist students in developing the skills necessary for taking MAT 122. Fundamentals of Mathematics or MAT 141. College Algebra. Prerequisite: placement level 0 (zero). Four hours institutional credit (institutional credit is not applicable to the 126 hours required for graduation). Only offered on a credit/no credit basis. These courses are a two-course sequence of mathematics content course (not method course) designed to prepare students to teach elementary and middle school mathematics for understanding, as envisioned by the National Council of Teachers of Mathematics, and as described in their document Principles and Standards for School Mathematics. The courses will examine deeply those topics in mathematics which are relevant for elementary and middle school teaching. MAT 111 focuses on the problem solving and arithmetic including why standard algorithms work, properties of arithmetic, and applications of elementary mathematics. MAT 112 focuses on the problem solving and geometry including why various standard formulas and properties in geometry are valid. Prerequisite: MAT 040 or placement level 2 for MAT 111 and MAT 111 for MAT 112. MAT 111 is three hours and MAT 112 is three hours for early grade majors and four hours for middle grade majors. (Note. (1) These courses only fulfill the general education core mathematics requirement for elementary and middle grade education majors. (2) These courses are not equivalent to either MAT 122 or MAT 14 This course will introduce a variety of topics chosen from the following: Number systems, finite and infinite sets, geometry, topology, chaos theory, probability, and game theory. This course aims to help students to develop an appreciation for the beauty of mathematics, and for the usefulness of mathematical thinking, by examining particularly surprising results in classical and contemporary mathematics. Prerequisite: MAT 040 or placement level 1. (Note: This course fulfills the core requirement in mathematics, but does not serve as a prerequisite for any other course.) Three hours. The course will cover complex numbers, solution of equations and inequalities, techniques of graphing, and the study of various functions: linear, quadratic, polynomial, rational, exponential, and logarithmic. Designed for those who have had two years of high school algebra, but need more depth in algebraic topics to prepare for enrollment in MAT 142, 144 or STA 251. Prerequisite: MAT 040 or placement level 2; not open to students with credit for any mathematics course (or equivalent) numbered 142 or higher unless special permission is granted by the instructor. Four hours. The course will cover analytical trigonometry, systems of equations, matrices and determinants, linear programming, solution of polynomial equations, conic sections, mathematical induction, the binomial theorem, permutations and combinations, and introductory probability. Designed to meet the requirements of various major programs (including biology, business and elementary education/middle grades certification), and to provide preparation for the calculus sequence. Prerequisite: MAT 141 or placement level 3; not open to students with credit for any mathematics course (or equivalent) numbered 145 or higher unless special permission is granted by the instructor. Four hours. The course will cover systems of linear equations, matrices, linear programming, mathematics of finance and elementary differential and integral calculus. Emphasis will be placed on applications to finance and management problems. Prerequisite: MAT 141 or placement level 3. Four hours. An introduction to the theory of probability. The course will cover combinatorics, laws of probability, discrete and continuous random variables and distributions, expectation, variance, and if time permits, other topics. Prerequisite: MAT 247. Three hours. The course will cover first order differential equations, second and higher order linear equations, series solutions, the Laplace transform, systems of first order equations, linear second order boundary value problems. Both analytic and numerical techniques are studied. Prerequisite: MAT 146. Four hours. Proofs in mathematics are both intimidating and mysterious to most people. This course hopes to dispel some of that mystery as well as equip students to both read and write mathematical proofs. Besides a review of logic and mathematical nomenclature, students will be required to tackle proofs from a variety of different fields of mathematics. Prerequisite: MAT 146. Three hours. 'S' 'W' This course will develop the algebra of vectors and matrices, including finding the inverse of a matrix, subspaces, basis and dimension of vector spaces, linear transformations, isomorphisms. Inner and cross products will be treated. Special types of matrices will be discussed, such as the Jordan Normal form. Eigenvalues and eigenvectors will be treated. Prerequisite: MAT 146. Three hours. The objective of this course is to teach students axiomatic reasoning without the aid of diagrams, explore what can be deduced from neutral geometry (without the Euclidean Fifth Postulate, or, equivalently, the Hilbert Parallel Axiom for Euclidean Geometry), explore aspects of Euclidean Geometry, then, replace the Euclidean Fifth Postulate with the Hyperbolic Parallel Postulate, and show that Hyperbolic Geometry is as self-consistent as Euclidean Geometry. The historical developments, philosophical implications and Hyperbolic Trigonometry should be of particular use to future secondary education mathematics instructors. Prerequisite: MAT 290 or permission of instructor for Math Edu majors for MAT 360; MAT 360 for MAT 361. Three hours each. Quantitative Methods Courses (STA) An introductory course in statistical science used in scientific research investigations. Topics considered include the nature and importance of statistics, quantification, measurement, probability, elementary research design, the collection and scoring of research results, measures of central tendency, the normal distribution, correlational analysis, statistical inference, analysis of variance and the analysis of categories and ranks. Computer applications will be stressed. Prerequisite: MAT 040 or higherlevel mathematics course, or placement level 2 or higher. Four hours. This course explores methods of data collection and analysis for making decisions related to business, economics, and other organizational issues. Topics include descriptive statistics, correlation, the Normal distribution, sampling, surveys, statistical inference, hypothesis testing, and regression. Applications focus on real data analyzed with statistical software. Students learn to think critically about conclusions drawn from data and to apply statistical methods in their own studies. Prerequisite: MAT 141 or higherlevel mathematics course, or placement level 3 or higher. Four hours.
mathematics.com - ENGINEERING.com Interactive material to download or work with online; articles on current technology topics; resources and links of interest to mathematicians; technology products offered for sale. Online calculators and applets for geometry, trigonometry, calculus, ...more>> Mathematics (SparkNotes.com) - WebCT.com & iTurf Inc. Over 100 guides for mathematics ranging from pre-algebra topics to advanced work in calculus, written by students and recent graduates of Harvard University. The site also includes message boards for beginner, high school, and advanced math, calculus, ...more>> Mathematics - Student Helpmate - Chris Divyak Search or browse this archive of questions about algebra, calculus, geometry, statistics, trigonometry, and other college math; then pay for access to answers. To submit your own problem to Student Helpmate, type your question or upload it as a file; ...more>> Math Everywhere, Inc. (MEI) Online Internet mathematics courses that are written in interactive notebooks using Mathematica. Take a whole course, or part of a course in calculus, pre-calculus, differential equations, or the geometry of n-space with matrices. This program offersmathmistakes.info - Russell Blyth A selection of common mistakes (in context) made by students in algebra, trigonometry and calculus, along with explanations, and online flashcards on algebra, trigonometry and calculus topics (more resources in development). Olympiads for Elementary and Middle Schools An international mathematics competition for elementary and middle school students. Individual students can take one exam each month from November to March. The site includes a few sample problems and information about ordering materials and joining the ...more>> Mathomatic - George Gesslein II Mathomatic is a small, portable, general purpose CAS (Computer Algebra System) that can solve, simplify, and combine algebraic equations. It does some calculus and is very easy to use. ...more>>
Links Breadcrumbs Maple Ta Maple T.A. is an online assessment tool that is built into Blackboard. Although any instructor can use the application to build online tests, it may be most appealing to faculty in math and science due to its built-in math functions and mathematical versatility. Faculty can use this software to display mathematical notation in their questions and students can create free-form mathematical responses. Hundreds of sample questions, that can be used as-is or modified, are available within the software. Maple T.A. also provides an abundance of statistical information at both the course level and individual student level. For example, on the entry exams, in addition to a list of students' final scores, faculty can access the dates on which students took the exam and the amount of time they spent on it. The percentage of students who answered each question correctly as well as an individual student's answers can be determined. This type of information is extremely useful in identifying weaknesses in the calculus sequence, as well as weaknesses for individual students. Maple T.A. ™ has partnered with the Mathematics Association of America (MAA) in order to maintain the functional standard of the product.
Mathematics 2, Essential When we paint a room, put up a fence, buy a rug, or wrap a present, we are using shapes. Essential Math 2 deals with the nature and property of shapes such as circles, triangles and squares. In doing so, this course provides an introduction to geometry and algebra. Essential Math 2 also acquaints students with the metric system of measurement. What others are saying: I have so far found the service especially satisfactory. Ever since I started receiving a different kind of first page form with a barcode, I've been receiving all my mail from the American School much sooner than I expect it. Many thanks to the American School for your excellent service. — Akashi, California
Mathematics for Health Sciences - 82 edition Summary: Students will learn basic math skills, the use of measurement systems, and strategies of problem solving needed in health science courses. This text is designed for active learning--students are asked to answer questions that follow the introduction of each new topic. Students can compare their responses with the answers provided in the margins to know if they are ready to go on to the next subsection. Exercise sets and self-tests, with their answers, are also provid...show moreed. Proportions are used extensively; dimensional analysis is emphasized. ...show less PAPERBACK Fair 081850478112412480818504785
College Algebra : Concepts and Contexts - 11 edition Summary: This book bridges the gap between traditional and reform approaches to algebra encouraging users to see mathematics in context. It presents fewer topics in greater depth, prioritizing data analysis as a foundation for mathematical modeling, and emphasizing the verbal, numerical, graphical and symbolic representations of mathematical concepts as well as connecting mathematics to real life situations drawn from the users' majors58.31
MATH 74 Transition To Upper Division Mathematics Course info & reviews The course will focus on reading and understanding mathematical proofs. It will emphasize precise thinking and the presentation of mathematical results both orally and in written form. The course is intended for students who are considering majoring in mathematics but wish additional training.
Galois' Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the... more...
The field of binary Logics has two main areas of application, the Digital Design of Circuits and Propositional Logics. In both cases it is possible to teach the theoretical foundations and to do some exercises, but in both cases the examples that can be done in class and by hand are far away from examples that are relevant for practical problems.Many interesting problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations as certain parameters vanish or become infinite. This book introduces the problems involving singular limits based on the concept of weak or variational solutions. more... Introduces the theory of nonlinear dispersive equations to graduate students in a constructive way. Dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev spaces, this textbook uses the linear Schrodinger equation to describe properties enjoyed by general dispersive equations. more... The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves... more... At the 19th Annual Conference on Parallel Computational Fluid Dynamics held in Antalya, Turkey, in May 2007, the developments and implementations of large-scale and grid computing were presented. This book comprises of the invited and selected papers of this conference. more... Everyday math skills can be painlessly learned and easily mastered, transforming readers from a person who doesn't know the meaning of APR into someone who understands credit card rates. Ryan's guide is broken into sections which review basic arithmetic from fractions to percents. more... The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics... more... One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas... more... In September 2006, research leaders in the field of coastal engineering, fluid mechanics, and wave theory met at Cornell University to celebrate the 60th birthday of Prof. Philip L-F Liu. This volume is a compilation of the research papers presented at the symposium, and includes both review and new research papers. Topics such as nonlinear wave theory,... more...
Related Subjects 9th Grade Math: Inequalities In mathematics, an inequality is a statement about the relative size or order of two objects, or about whether they are the same or not. The notation a < b means that a is less than b. The notation a > b means that a is greater than b. The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size. In each statement above, a is not equal to b. These relations are known as strict inequalities. The notation a < b may also be read as "a is strictly less than b". In contrast to strict inequalities, there are two types of inequality statements that are not strict: The notation a ≤ b means that a is less than or equal to b (or, equivalently, not greater than b) The notation a ≥ b means that a is greater than or equal to b (or, equivalently, not smaller than b) Many 9th grade math students find inequalities difficult. They feel overwhelmed with inequalities homework, tests and projects. And it is not always easy to find inequalities tutor who is both good and affordable. Now finding inequalities help is easy. For your inequalities homework, inequalities tests, inequalities projects, and inequalities tutoring needs, TuLyn is a one-stop solution. You can master hundreds of math topics by using TuLyn. Our inequalities videos replace text-based tutorials in 9th grade math books and give you better, step-by-step explanations of inequalities. Watch each video repeatedly until you understand how to approach inequalities problems and how to solve them. Tons of video tutorials on inequalities make it easy for you to better understand the concept. Tons of word problems on inequalities give you all the practice you need. Tons of printable worksheets on inequalities let you practice what you have learned in your 9th grade math class by watching the video tutorials. How to do better on inequalities: TuLyn makes inequalities easy for 9th grade math students. How Others Use Our Site I Would like to re-learn all the math lessons I\`ve had since the 6th grade, Mostly because i slept throughout the 6th grade to 9th grade. I\`ll be stuck in 9th grade again next year, and i don\`t want it to happen again.. (And i was watching Clannad and i suddenly got jealous of Kotomi Ichinose) yes, nerdy, i know. And i don`t care. To prepare for the 9th grade. Apply rules for solving equations and inequalities. I ned to take some test ,so i ned to learn more about 9th grade math. Because i am in 9th grade n im supposed 2 be in the 11th grade and i was told this could catch me up. It will help me with my son who`s entering 9th grade but struggles to understand teacher`s explanations and this will allow for him to practice at home. I am a resource math teacher to 8th and 9th graders and I need more resources. My daughter is in 9th grade and I don`t know how to do her math homework. Algebra - 9th grader - deciding which method to use when problem types are in random order. I am teaching special ed students algebra and geometry on grade level. I have no materials for bringing them up from 5th grade - 7th grade level to 9th grade -10th grade level. Tutoring my 9th grade son. I teach math to 9th grade -12th grade at a small city school in North Carolina. Knowing that each student in NC has to score levels 3 or 4 on the EOC Algebra 1 test to graduate, any real-life application type problems would be beneficial to the success of my students. Knowing also that matrces are heavily tested on the NC EOC test, this website appears that it would be helpful. Our textbooks do not offer many examples of matrices . Thank you. This site will help in teaching both 6th grade and 8th grade math in solving equations and inequalities. Need help with learning how to graph inequalities using x and y coordinates. I am a mathematics teacher and your web site can help me making my assessments and worksheets for the pupils of my class of 8th and 9th grades.
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
An essential tool for standardized tests, the Spectrum Math series offers grade-appropriate coverage of basic arithmetic and math skills. Each book features drill and skill practice in math fundamentals, as well as applications of mathematics in everyday settings. Chapter Pre-Tests, Chapter Tests, Mid-Book Tests and Final Tests all contribute to an extended familiarity with developmental, problem-solving and analytical exercises. An assignment record sheet, record of test scores sheet and answer key are included. Fantastic book Easy to explain and great for learning independent study. Share this review: 0points 0of0voted this as helpful. Review 2 for Spectrum Math, 2007 Edition, Grade 4 Overall Rating: 3out of5 Good for worksheets Date:April 2, 2013 poohrona Age:35-44 Gender:female Quality: 4out of5 Value: 5out of5 Meets Expectations: 3out of5 This book is a good source for worksheets to use in addition to another teaching source. My problem with this is that it doesn't expand much on any one thing and I have had to find additional materials to go along with this. Share this review: 0points 0of0voted this as helpful. Review 3 for Spectrum Math, 2007 Edition, Grade 4 Overall Rating: 5out of5 Date:November 10, 2009 Lisa Perdue This book gives good examples. I really like the way the book is laid out. I highly recommend this book.
Sc in Mathematical Finance This part-time, modular MSc is flexibly designed for those in full-time employment in the UK and overseas. It covers the most important technical and quantitative aspects of finance in regular use in financial institutions. Nice and Noughtie Numbers This course shows how numbers are fundamental to many aspects of our civilization. It covers topics such as counting systems, prime numbers, the importance of zero, musical scales, bell ringing, the calendar and seasons, and encryption of messages. Mathematical finance This flexible, part-time Programme is designed to allow those working full-time to develop expertise in mathematical finance without compromising their professional work. Basic Statistics for the Social Sciences The aim of this course is to provide a good grounding in the basic statistical methods used in the social sciences - in particular in Business Studies, Economics, Psychology and their applications. You Can Count on It - Maths in Finance In this brief course we shall look at how mathematics contributes to finance and business. Our course is suitable for people with previous experience of mathematics at the sixth-form level and aims to provide an elementary introduction to the mathematics. Alternatively you can perform a keyword search on all our courses using the 'Find courses' box on this page.
Welcome The Franklin High School Mathematics course offerings address the learning standards defined by the Massachusetts Mathematics Curriculum Frameworks and the National Council of Teachers of Mathematics. The Massachusetts Mathematics Frameworks comprise five strands: Number Sense and Operations, Patterns, Relations, and Geometry; Measurement; and Data Analysis, Statistics and Probability. A more detailed description of each learning standard in the state frameworks may be found on the Department of Education's web site: Curriculum Frameworks. The goals of the Franklin High School Mathematics Department are to help every student to become more reasonable and rational thinkers who can apply knowledge in their everyday lives. Through active participation in their courses, students learn the structure and nature of mathematics. They also develop analytical skills that help them apply basic principles to new areas of study and everyday living. Mathematics courses utilize new technologies to facilitate computation and enable students to visualize the mathematics. The department recommends that all students have their own graphing calculator, which enables students to investigate concepts using multiple forms of representation and extends the range of the curriculum. Mathematics courses, most of which are offered at the College Preparatory and Honors levels include
If you provide us with a few extra details when you register you will receive a free publication and become an Associate of ATM. In your basket: Nothing yet Mathematics for Primary and Early Years: Developing Subject Knowledge How the publisher describes it: "This task-driven text emphasizes strategies and processes and is very different from the usual style of mathematics textbooks. For example, algebra is treated as a way of thinking mathematically, rather than merely manipulating symbols. Each of the sections is designed to stand alone so that they can be studied in any order or dipped into as needed." Review by Matthew Reames In brief: Unfortunately misnamed, this book is not a guide to primary and early years mathematics. Instead, it is a self-study text for people hoping to improve their mathematical understanding and confidence. "A useful resource for people wishing to brush up on their knowledge of mathematical ideas and concepts up to GCSE level." Mathematics for Primary and Early Years: Developing Subject Knowledge is not a guide to primary mathematics at all. Instead, it is part revision book, part refresher course of maths to GCSE level. Written as part of the series Developing Subject Knowledge, this book is one of several used in an Open University course as part of the Foundation Degree in Early Years. Each chapter covers a different mathematical strand: number, measures and proportion, statistics, algebra, geometry, chance, and proof. The book is designed to be a self-study text for people who are trying to build their confidence in mathematics. While the book seems rather useful as a basic mathematical reference text (if encountering gradians, for example, turn to page 53 for a description), it seems that the title is unfortunately misleading: those looking for a maths revision guide will miss it while those hoping for help developing their knowledge of primary and early years maths will be rather disappointed. Matthew Reames • Former Head of Mathematics, St Edmund's Junior School, Canterbury, now PhD student in mathematics education at the University of Virginia
Book Description: Dugopolski's College Algebra and Trigonometry: A Unit Circle Approach, Fifth Edition gives students the essential strategies to help them develop the comprehension and confidence they need to be successful in this course. Students will find enoughcarefully placed learning aids and review tools to help them do the math without getting distracted from their objectives. Regardless of their goals beyond the course, all students will benefit from Dugopolski's emphasis on problem solving and critical thinking, which is enhanced by the addition of nearly 1,000 exercises in this
Mathematics Lab The Math Laboratory, in conjunction with the Mathematics and Computer Science Department, is a resource for students who need academic assistance and support in mathematics. Support with assignment completion, examination preparation, study skills, and test-taking skills, as well as assistance in using computers with math assignments, is provided by Mathematics learning specialists.
MathDork Tutorials are the fastest way to learn the basic principles of Algebra. These lessons jump into your brain! They are based on 10 years of private tutoring experience. Learn Algebra the easy way, by viewing animations. MathDork takes over where textbooks leave off. The rigorous approach taken by most textbooks is necessary, but does not always address the need for a conceptual approach that helps many learners. MathDork uses animation to teach the concepts, helping the student to integrate both teaching methods.
Vector Calculus and Applications Module aims: This module is an introduction to vector calculus and its applications especially fluid dynamics. It lays down some basic principles using a number of simplifying assumptions. It examines how one can use vector formalism and calculus together to describe and solve many problems in two and three dimensions. For example, the rules that govern the flow of fluids and the motion of solids can be described using vector calculus, with resulting laws of motion described by partial differential equations rather than ordinary differential equations. The emphasis will be on inviscid, incompressible flows: viscous flow is the subject of later modules. Applications include the design of aeroplanes, car body shapes and the flows of liquids and gases through pipes. These problems raise important questions, such as: How is flight possible? How can one minimise drag? How do vortices form? What is pressure and how does it interact with the flow? Physical applications include meteorology (fluid dynamics applied to weather forecasting and events such as tornadoes and hurricanes) and oceanography (fluid dynamics applied to ocean currents, tides and waves). This module is a prerequisite for a number of more specialist modules in the third year. Please note that full specifications are not currently available for download. This usually indicates that the module isn't being taught in this current academic year and details will be available soon. Please get in contact if you have any further questions about this module or programme structure.
Printing Books Lesson Grade: 6-8 Periods: 1 Standards: Author: Unknown Unknown Students explore the relationships among lines, slopes, and y-intercepts in the context of printing their algebra textbooks. Students use a spreadsheet to facilitate their exploration. This activity is based on an idea from Navigating Through Algebra in Grades 6-8 (NCTM, 2001). Before students begin to work through each of the three options, ask them to circle the one they predict will be the best solution to the problem. Put students in pairs to discuss their predictions. On the chalkboard, record the names of the students under the option number they have selected (1, 2, or 3). Leave this information on the chalkboard to discuss toward the end of the lesson. This problem involves a number of different tasks. First, tables and graphs for each situation need to be made. Using a spreadsheet makes this problem much easier. For example, you can use the Printing Books spreadsheet. In order to create a graph, you will need to right click on the hyperlink, and choose "save target as" to save this file to your computer. Then you will be able to use the Chart Wizard to create graphs. The figure below shows the costs of the three plans for up to 2500 books. The copy center's plan will be the most expensive, and the printing company's the least expensive if all 2,250 books are produced at one location. Below is a graphical version of this data. Students will note the slopes of each of the printing options. Students may also note the point of intersection of all three lines. If each high school can use a different printing company, which choice should each make? The figure below displays additional data and a graph on which the zoom feature allows us to see more clearly where the costs for different plans intersect. At this point students should revisit their predictions from the beginning of the lesson. Using the information recorded on the chalkboard, ask the students who predicted the correct option to explain their predictions. Pose the following change to the scenario to the class: Suppose that these additional conditions apply: Western High School will need 400 textbooks next year. Eastern High School will need 550 textbooks next year. Northern High School will need 1400 textbooks next year. Students should return to their partners from the beginning of the lesson and discuss this new "twist" to the scenario. Each pair of students should submit a written proposal to the Board of Education defending their choice. On the basis of these data, students may write something similar to the following: Western High School will need 400 textbooks for next year, so the cheapest way of having these books made would be to use the local copy center. It would cost $7,300 dollars for these books. Eastern High School needs 550 books. The cheapest place to go would be the school district's in-house copy center. It would cost $9,256.25. Northern High School needs 1400 books. The cheapest way to get these books would be to go with the printing company. This would cost $18,300. All together, these three orders would cost $34,856.25. If all 2350 books were produced by one company, the cheapest choice would be the printing company. This would cost $27,325. It actually would cost less to produce all the books together, rather than letting the individual schools order their texts. Learning Objectives Identify ways that the table, the graph, and the equation provide information to solve the problem Explore relationships among lines, slopes, and y-intercepts Common Core State Standards – Mathematics Grade 7, Expression/Equation CCSS.Math.Content.7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that ''increase by 5%'' is the same as ''multiply by 1.05.'' Grade 8, Expression/Equation CCSS.Math.Content.8.EE.B.5Grade 8, Expression/Equation CCSS.Math.Content.8.EE.B.6 UseGrade 8, Functions CCSS.Math.Content.8.F.B.4
The unifying theme of this text is the development of the skills necessary for solving equations and inequalities, followed by the application of those skills to solving applied problems. An earlier introduction to the coordinate system, graphing, and functions is a focus for the fourth edition. Tables, graphs, and other visuals have been added to give students practice interpreting different forms of data display. Applications have been added throughout the text to help demonstrate concepts, motivate students, and to give students practice using new skills.
The second edition of Akst/Bragg's Basic Mathematics through Applications brings you even more of a good thing!Throughout the text, motivating real-world applications, examples, and exercises demonstrate how integral mathematical understanding is to student mastery in other disciplines, a variety of occupations, and everyday situations. A distinctive side-by-side format, pairing each example with a corresponding practice exercise, encourages students to get actively involved in the mathematical content from the start. Unique Mindstretchers target different levels and types of student understanding in one comprehensive section problem set per section. Mindstretchers incorporate related investigation, critical thinking, reasoning, and pattern recognition exercises along with corresponding group work and historical connections. Compelling Historical Notes give students more evidence that mathematics grew out of a universal need to find efficient solutions to everyday problems. Plenty of practice exercises provide ample opportunity for students to thoroughly master basic mathematics skills and develop confidence in their understanding. Finally, new MyMathLab icons in the margins of the text indicate to students that there is a video clip, animated example, or practice exercise for them to explore on-line if you take advantage of the package deal. Making the transition to calculus means being prepared to grasp bigger and more complex mathematical concepts. "Precalculus: Functions and" "Graphs" is designed to make this transition seamless, by ... The Seventh Edition of Calculus and Its Applications builds on its reputation as one of the most student-oriented and clearly written Applied Calculus texts available. The optional use of technology ...
More About This Textbook Overview Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the "Rule of Four" – graphical, numeric, symbolic/algebraic, and verbal/applied presentations – to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique. Readers will also gain access to WileyPLUS, an online tool that allows for extensive drills and practice. Calculus teachers will build on their understanding in the field and discover new ways to present concepts to
Book DescriptionProduct Description Review From the reviews: a nice introduction to the foundations of applications of geometry to computer graphics and computer-aided design….A useful textbook. Zentralblatt MATH Mathematics students often ask where they can find a nice introduction to computer graphics and computer-aided design; professors have also been known to pose the same question. They will all find an answer here: Marsh's book should guide them effectively and painlessly towards the applications of mathematics and geometry in graphics and CAD. Computer-Aided Design 32 (2000) From the reviews of the second edition: "This is a mathematics textbook on the basics of the geometry involved in computer graphics and computer-aided design, written at an undergraduate level suitable for students of mathematics, computer science, and engineering. … All of the book's topics are presented in a clean and concise way, with nice illustrations and attention to both geometric ideas and practical issues of computing. … This book would be useful for instructors who want a specific reference … ." (Adam Coffman, Mathematical Reviews, 2005h) "Images generated by a computer are ubiquitous, they are used in science, in engineering, and by the entertainment business. This textbook is an introduction to the mathematics behind these images. … This exposition is intended for a broad audience with basic mathematical knowledge (vectors, matrices, calculus)." (P. Schmitt, Monatshefte für Mathematik, Vol. 151 (4), 2007) "The title says it all. … covers exactly what you would expect: theory and background for applying geometric techniques for visualization on a computer. … This book is part of the SUMS (Springer Undergraduate Mathematics Series). The theory and applications are explained well, and moreover the text contains numerous examples, problems, and fully worked solutions. The book was written with students in computer science, engineering as well as of mathematics in mind … ." (Pieter Audenaert, Bulletin of the Belgian Mathematical Society, 2007) From the Back Cover Focusing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). An introduction to transformations of the plane and three-dimensional space describes how objects can be constructed from geometric primitives and manipulated. This leads into a treatment of projections and the method of rendering objects on a computer screen by application of the complete viewing operation. Subsequently, the emphasis is on the two principal curve and surface representations, namely, Bézier and B-spline (including NURBS). As in the first edition, applications of the geometric theory are exemplified throughout the book, but new features in this revised and updated edition include: the application of quaternions to computer graphics animation and orientation; discussions of the main geometric CAD surface operations and constructions: extruded, rotated and swept surfaces; offset surfaces; thickening and shelling; and skin and loft surfaces; Over 300 exercises are included, some new to this edition, and many of which encourage the reader to implement the techniques and algorithms discussed through the use of a computer package with graphing and computer algebra capabilities. A dedicated website also offers further resources and links to other useful websites. Designed for students of computer science and engineering as well as of mathematics, the book provides a foundation in the extensive applications of geometry in real world situations. This text has a novel approach to entry level computer graphics using homogeneous coordinates entirely. I struggled a bit with the use of these representations in perspective transformations. However once I got it I found the derivations and formulas to be easy to get and easy to use. The book has an extensive set of exercises with complete answers. I deducted one star because the theoretical aspects of homogeneous transformations could use expansion and simplification. This book is unusual in a way I wish more math and computer science books would follow. What you get is a brief description of the mathematics, the formulas that are useful, and a completely worked out example with illustrations. Although Computer is in the title there is no source code in the book. But the examples are worked out in such detail that is easy to translate them into code. And then you can use the numerical results of the examples to test each step in your own code. Beautiful. So, looking for parametric formulas for quadrics, or quaternions, or frenet frames for Bezier curves? You will find just what you need to make it work for you. This book is packed only with the most useful real-world math for computer graphics. What it leaves out is a lot of explanation as to why any of those topics may matter to you. It also avoids a lot of the theoretical math and extraneous factors that aren't essential to subject. This is also probably not the best tutorial for beginners but would be a great supplement to any of the core computer graphics textbooks. My recommendations are Practical Linear Algebra: A Geometry Toolbox to get you up to speed with the math and Computer Graphics Using Open GL (2nd Edition) to get your head oriented.
This second, updated edition of the admired introduction to discrete mathematics is a detailed guide both to the subject itself and to its relationship with other topics including set theory, probability, cryptography, graph theory...
Peer Review Ratings Overall Rating: This is a 41- slide Power Point presentation with audio designed for Pre-Calculus Algebra students to help them better grasp the terminology and concepts of parabolas including focus, directrix, axis of symmetry, and equations of the form (x-h)^2=4p(y-k) et al. This is one of several modules created by the same author. See other reviews of Logarithm Change of Base and Inverse Functions. A common introductory page with links to each module would be useful for outside users. Learning Goals: To provide an audio/visual demonstration of parabolas and their various features and characteristics. Target Student Population: High school and college students Prerequisite Knowledge or Skills: Basic algebra and some familiarity with a graphing calculator Type of Material: Tutorial Recommended Uses: Student tutorial or classroom supplement. Technical Requirements: Macromedia Flash Movie Player. The audio files do not perform effectively with a dial-up connection. Evaluation and Observation Content Quality Rating: Strengths: The PowerPoint presentation with audio is well done and covers the geometric definition of a parabola thoroughly in its 41 slides. Graphs are shown of y = +/- x^2 and x = +/- y^2. The equations (x-h)^2=4p(y-k) and (y-k)^2=4p(x-h) are presented and explored along with their graphs. Concerns: The concluding slide(s) would have been enhanced by a complete graph/diagram of a parabola and a summary of the key points covered in the presentation. Potential Effectiveness as a Teaching Tool Rating: Strengths: The audio/visual presentation is a fairly self-contained unit on the nature of a parabola and its equation. Focus, directrix, axis of symmetry are explained and illustrated. The audio track gives additional explanations rather than just reading the slide content. The slides include text, graphs and calculator. Concerns: There is no opportunity for interaction on the part of the user other than navigating forwards or backwards through the slides. Deliberate use of 'opposite of x' rather than 'negative x' may confuse some users. Brief comment on the existence of other conic sections or their applications would be useful. Ease of Use for Both Students and Faculty Rating: Strengths: The presentation provides navigation buttons to move forward or backward between slides. Nice use of color to identify stationary and moving points. Good, slow, clear narration. Concerns: There is no jump feature to allow users to return to the beginning of the presentation or to a specified slide
CBD Price: $39.13 ( Usually ships in 24-48 hours. ) Trigonometry, a work in the collection of the Gelfand School Program, is the result of a collaboration between two experienced pre-college teachers, one of whom, I.M Gelfand, is considered to be among the most distinguished living mathematicians. Trigonometry covers all the basics of the subject through illustrations and examples. Geometric relationships are rewritten in trigonometric form and extended, while trigonometric functions are geometrically motivated. The text then makes a transition to the study of algebraic and analytic properties of trigonometric functions, in a way that provides a solid foundation for more advanced mathematical discussions. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject. There is no teacher's guide, workbook or answer key for this book. Solutions are provided for some of the problems. 229 pages, paperback. CBD Price: $19.95 ( In Stock ) "Sine of acute angle in a right triangle is the ratio of the opposite side to the hypotenuse. Let's examine the properties of sine." If such words fill your heart with horror, then this is the book for you. Formal style and dry language is deliberately avoided at all costs, and scientific information is presented in the form of conversations between a father-an expert in the field-and his daughter and son. There is no teacher's guide or workbook. Answers are provided at the back of the book. Full answers are provided at the authors' website. This book is recommended for high school and college students and teachers, or for independent mathematics study. 203 pages, softcover.
Course Outline Institution: Clackamas Community College Course Title: Fundamentals of Arithmetic Course Prefix/#: MTH 010 Type of Program: Developmental Credits: 4 Date: December 21, 2006 Outline Developed by: Kathy Taylor Last Review Date: July 1, 2008 Course Description: This course is designed to teach the basic concepts of arithmetic in a lecture-laboratory setting. Length Of Course: 42 lecture hours Grading Criteria: Letter grade or Pass / No Pass. Prerequisite: None Required Textbook: Basic Mathematical Skills with Geometry (Seventh Edition), by Baratto and Bergman; McGraw Hill Required Materials: Students may be required to use a scientific calculator, ruler, pencil and paper. Course Objectives: This course is intended to review operations on whole numbers, elementary fraction concepts, operations on decimals, and measurement. Student Learning Upon completion of this course, the successful student will be able to accomplish the Outcomes: following:  Use mental arithmetic, paper and pencil algorithms, and a calculator as computation tools in solving mathematical problems.  Represent the operations of arithmetic using visual models for whole numbers and decimals.  Use the operations of arithmetic on whole numbers, selected fractions, and decimals  Learn to use the operations of arithmetic on whole numbers, selected fractions, and decimals.  Use equivalent forms of a problem, to make comparisons between forms.  Estimate the results of computation.  Round the results of computation.  Understand the concepts which underlie the algorithms of arithmetic.  Reason and draw conclusions from numerical information.  Understand and apply the concepts of perimeter, area, and volume.  Understand the English system of measurement and the metric system of measurement; and be able to translate measurements within each system.  Use both pencil and paper algorithms and visual models to fine averages. Major Topic Outline: Addition and Subtraction of Whole Numbers: Decimal place-value system; the language and properties of whole numbers; adding whole numbers, rounding, estimation, and order; subtraction of whole numbers; solving word problems with addition and subtraction. Multiplication of Whole Numbers: The language and properties of subtraction, multiplying whole numbers, order of operations, solving word problems involving multiplication, powers of whole numbers. Division of Whole Numbers: The language of division, division of whole numbers, order of operations, solving word problems involving division, finding the average. Introduction to Fractions with denominators which are powers of 10: The language of fractions; proper fractions, improper fractions, and mixed numbers; equivalent fractions; simplifying fractions. Addition and Subtraction of Fractions with denominators which are powers of 10. Adding fractions with a common denominator, finding the least common denominator, adding fractions with unlike denominators, subtracting fractions, adding and subtracting mixed numbers, applications involving fractions. Addition, Subtraction, and Multiplication of Decimals: Place value in decimal fractions, adding decimals, subtracting decimals, multiplying decimals, rounding decimals. Division of Decimals: Dividing decimals by whole numbers, dividing decimals by decimals, converting from decimal form to fractional form. Metric and English System of Measurement: Metric and English units of length, weight and volume. Geometry Perimeter and area, circumference and area of circles, area of parallelograms and triangles, area of combined figures Suggested CLASS HOURS TOPIC Timeline 1 Place Value, Introduction to our Number System 3 Addition of Whole Numbers, Modeling, Rounding, Estimating 2 Subtraction of Whole Numbers, Modeling, Rounding, Estimating 1 Perimeter 4 Multiplication of Whole Numbers, Modeling, Rounding, Estimating 1 Powers and Order of Operations 3 Perimeter, Circumference, Area and Volume, Modeling 3 Division of Whole Numbers, Modeling, Estimating 2 Averages, Modeling 3 Introduction to Fractions, Denominators are Powers of 10 3 Addition and Subtraction of Fractions, Denominators are Powers of 10 5 Addition, Subtraction, and Multiplication of Decimals 2 Division of Decimals 2 Metric and English System 7 Review, Tests and Final Exam
MATH 5485 – Introduction to Numerical Methods I Fall 2007 Marcel Arndt Lab Project: Bridge Construction In this lab project, we investigate the static behavior of bridges built from steel trusses like the one shown in Figure 1. When some loading is applied to the bridge, for example due to the weight of cars going over it, the forces get distributed among all trusses. However, not all trusses will exhibit the same force, rather some will carry more load than others, depending on the design of the bridge. Heavily loaded trusses are more likely to fail than less loaded trusses. Hence it is of crucial importance for bridge engineers to compute theses forces, identify possible points of failure, and reinforce the structure where necessary to prevent catastrophes. At the same time, one wants the bridge to be as lightweight and efficient as possible to keep material costs low. Numerical simulation allows this to be achieved without performing extensive experiments with real bridges and therefore considerably reduces construction time and cost. In this lab project, you will: • Learn about the mathematical modeling of the static behavior of truss bridges. • Learn how to reformulate this model to make it accessible by computers. • Learn how to implement and numerically solve the problem for a given bridge. • Build your own bridge which provides the best load distribution and thus is safest! This text will guide you through the whole process and provide a step-by-step instruction. Work carefully through the text to understand all aspects of modeling and implementation. It is important to follow all details, especially the sometimes subtle indices, otherwise you will run into trouble when it comes to the actual computation later. You will encounter several tasks in the project. Your job is to perform these tasks. This will finally lead you to a complete solution of the bridge construction project. It is a good idea to work through the entire text first before you start working on the tasks to get an impression of the big picture. Figure 1: A truss bridge with two foundations over a river valley. 1 1.5 2 4 1 0.5 0 1 3 5 0 0.5 1 1.5 2 2.5 3 3.5 4 Figure 2: A simple mechanical structure with 5 nodes and 7 trusses. Nodes 1 and 5 are fixed to the ground. You will need to submit a term paper by Monday, October 29, 2007. This term paper shall include the solutions to all tasks, including the programs you wrote and graphs of your results. Your term paper will be graded and counts as the first midterm. Additionally, submit the input files of the bridge you constructed by email to arndt@math.umn.edu. There will be a competition among students: The stability of all bridges will be ranked, and the most stable ones get extra points! 1 Description of the Bridge The bridges we investigate here are mechanical structures which are built from steel trusses. A truss is a thin straight rod. The trusses are joined together at their endpoints. The junction points are called the nodes. Figure 2 shows a simple mechanical structure with 5 nodes and 7 trusses. Before we can discuss loading and forces, we need to describe the structure mathematically. First, we define the nodes. Assume our bridge consists of N nodes, numbered 1, 2, . . . , N . We denote the position of the i-th node by xi = (xi,1 xi,2 ) ∈ R2 . (1) (Note that we carry out everything in two-dimensional space here to keep things simple, hence xi ∈ R2 . However, the generalization to the three-dimensional setting would be straightforward.) A few nodes rest on a foundation or are fixed to the shoreline to keep the bridge in place and carry the load. We denote these nodes as fixed, and the remaining ones as free. Thus we need to keep track of the type of the node as well. Let M denote the number of free nodes. As N was the total number of nodes, we have M ≤ N . The structure of the bridge from Figure 1 is shown in Figure 3. Here fixed nodes are black, and free nodes are white. For this bridge, we have N = 47 and M = 41. Then, there are K trusses, each of which connects two nodes. For each truss, we need to specify these two nodes. Instead of storing the coordinates again (which we already have in form of the vectors xi ), it is better to store the node numbers, ranging from 1 to N . Hence for k = 1, 2, . . . , K we introduce two variables tk,1 , tk,2 ∈ {1, 2, . . . , N }, (2) meaning that the k-th truss connects nodes tk,1 and tk,2 . These variables fully specify the structure. For example, the simple structure displayed in Figure 2 can be described as shown in Table 1. Next, when some loading is applied to the bridge, the nodes move a certain amount from their original position, except for the fixed nodes which are tied to the ground. For real structures such as bridges, the 2 2000 24 9 19 17 11 20 22 23 33 42 40 34 43 45 46 47 1500 18 21 41 44 10 8 12 13 5 6 32 35 36 29 30 1000 16 4 39 28 14 37 15 3 38 27 500 7 2 31 26 0 1 25 0 1000 2000 3000 4000 5000 6000 7000 Figure 3: Structure of the bridge from Figure 1. The black nodes are fixed, and the white nodes are free. Trusses Nodes k tk,1 tk,2 i xi,1 xi,2 type 1 1 2 M =3 1 0.0 0.0 fixed 2 1 3 N =5 2 1.0 1.5 free 3 2 3 3 2.0 0.0 free 4 2 4 K =7 4 3.0 1.5 free 5 3 4 5 4.0 0.0 fixed 6 3 5 7 4 5 Table 1: Mathematical description of the simple structure shown in Figure 2. nodes don't move much since steel constructions are pretty stiff, but they indeed do move a little bit. We denote the displacement of node i by ui = (ui,1 ui,2 ) ∈ R2 , (3) that is, node i moves from xi to xi + ui under loading. Since the fixed nodes cannot move, we have ui = 0 whenever node i is fixed. (4) The node positions xi without loading are quantities given by the bridge, whereas the displacements ui are the main unknowns to be computed at the end of the day. Because of (4), we only need to consider the displacements ui of the free nodes i. 2 Mathematical Modeling Now, lets come to the mathematical modeling. First, we relate the displacement ui of all nodes i to the elongation ek of truss k. The original length lk of truss k is lk := xtk,2 − xtk,1 = (xtk,2 ,1 − xtk,1 ,1 )2 + (xtk,2 ,2 − xtk,1 ,2 )2 . (5) Under loading, this length lk changes to (xtk,2 + utk,2 ) − (xtk,1 + utk,1 ) . (6) 3 xj +uj xi +ui xj xi Figure 4: Deformation of nodes i and j from original positions xi and xj to xi + ui and xj + uj . The elongation of truss k is therefore given by (xtk,2 + utk,2 ) − (xtk,1 + utk,1 ) − xtk,2 − xtk,1 , (7) see Figure 4 for an illustration. Formula (7) turns out to be too complicated for the subsequent calculations because it leads to nonlinear equations. However for small deformations, we have approximately (xtk,2 + utk,2 ) − (xtk,1 + utk,1 ) ≈ xtk,2 − xtk,1 + nk · (utk,2 − utk,1 ) (8) where xtk,2 − xtk,1 nk := (9) xtk,2 − xtk,1 is the normal vector pointing from node tk,1 to node tk,2 . Thus we define the (approximate) elongation of truss k as ek := nk · (utk,2 − utk,1 ). (10) The elongation ek is positive if the truss k is stretched and negative if it is compressed. Equation (10) relates the elongation to the displacement. Note that this relationship is linear. Second, we relate the elongations to forces. This is called the constitutive relation. Here we assume that the trusses act like Hookean springs, that is, the force fk on truss k is proportional to its relative elongation ek /lk : ck fk := ek . (11) lk This is a reasonable assumption for steel trusses if the displacement is small. The constant ck > 0 is called the elastic modulus and describes the stiffness of the truss. Large values of ck correspond to hard and thick material where you need a strong force to effect a certain elongation, whereas small values of ck correspond to soft and thin material where already small forces suffice to effect a large elongation. In our application, the trusses all consist of the same material, steel, but we allow for different truss thicknesses. Therefore ck varies with the thickness of the truss. Third, we relate the forces to each other. According to Newton's First Law, the bridge is in a stable state if the sum of all forces acting on each free node i vanishes. This is called the force balance. In our application, there are two types of forces: internal forces caused by the tension of the trusses, and external forces caused by external loading: vehicles going over the bridge, wind forces, gravitational forces due the 4 weight of the bridge itself and so on. The internal forces are the fk from above, whereas the external loading ext ext is given by the vectors fiext = (fi,1 fi,2 ) ∈ R2 for i = 1, 2, . . . , N . The directional force exerted by truss k on node i is −fk nk if i = tk,1 and f k nk if i = tk,2 , (12) taking into account the direction of the normal vector nk . The force balance at the free node i is thus given by f k nk − fk nk − fiext = 0. (13) k: tk,2 =i k: tk,1 =i Note that the equations (13) are linear conditions on the fk . At a fixed node, the ground is supposed to absorb all forces, so there is no force balance there. 3 Matrix Notation Equations (10), (11), and (13) together give linear conditions on the unknown displacements ui of the free nodes. In this section, we will figure out how to translate this linear system into matrix notation. The unknowns we need to solve for are the 2-vectors ui of displacements for all free nodes i, whereas the fixed nodes are left out due to (4). To enumerate the free nodes, we introduce variables mi which map overall node numbers to free node numbers. This means we assign a unique free node number mi with 1 ≤ mi ≤ M to each free node i. (Recall that M denotes the number of free nodes.) Moreover, we let mi = 0 whenever node i is a fixed node. Thus the mapping not only enumerates the free nodes, but also keeps track of whether a node is free or fixed. This way, we avoid to introduce another variable to store the type of the node. For example, the mapping for the structure given in Figure 2 and Table 1 can be defined as follows: i mi 1 0 2 1 3 2 4 3 5 0 Our unknowns are the 2-vectors ui = (ui,1 ui,2 ) with mi = 0. We now subsume these M unknown 2-vectors to the large common vector u = (u1 u2 . . . u2M ) ∈ R2M by means of u2mi −1 = ui,1 , u2mi = ui,2 for all i = 1, 2, . . . , N with mi = 0. ext ext ext Similarly, we subsume the external forces fiext to the large common vector f ext = (f1 f2 . . . f2M ) ∈ R2M : ext ext ext ext f2mi −1 = fi,1 , f2mi = fi,2 for all i = 1, 2, . . . , N with mi = 0. Then, we subsume all elongations ek and forces fk to large common vectors e = (e1 e2 e3 · · · eK ) ∈ RK and f = (f1 f2 f3 · · · fK ) ∈ RK . (14) Since relationship (10) between the displacements ui and the elongations ek is linear, there must be a matrix B ∈ RK×2M such that e = Bu. (15) The matrix B is called the incidence matrix. 5 Task 1 Figure out the precise definition of the incidence matrix B and the normal vectors nk . Since this will be needed for the implementation later, it is useful to do this in a pseudo-code style like B = zero-matrix of size K x 2M for k = 1...K n(k,1) = <something> n(k,2) = <something> add <something> to B(<index1>,<index2>) ... end Be aware that it is extremely important to get the indices completely right, otherwise your implementation will produce garbage later! The constitutive relation (11) can obviously be written as f = Ce (16) with the diagonal matrix   c1 /l1  c2 /l2  C =  ∈ RK×K . (17)   ..  .  cK /lK Then, let us come to the force balance. Task 2 Show that the force balance (13) can be written as B T f = f ext , (18) that is the matrix related to the force balance is the transpose of the incidence matrix. Finally, we put it all together. Recall that we have Bu = e, Ce = f , (19) T ext B f =f , so we obtain Au = f ext where A = B T CB. (20) This is the linear equation we need to solve! It turns out that the matrix A ∈ R2M×2M is regular for most structures. Hence for any external loading ext f , there exists a unique solution u. However, in rare cases the matrix happens to become singular. There are two possible reasons for this: 1. Insufficient fixed nodes. A fully connected structure needs at least two fixed nodes to stabilize against translations and rotations (called rigid body motions). 2. Malformed nodes. Avoid free nodes with two or less trusses. For nodes with three trusses only, make sure no two of them are parallel, see Figure 5. If you encounter a singular matrix A, check whether your structure fulfills these conditions. 6 1.5 6 7 1 2 1 3 5 0.5 0 4 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Figure 5: Malformed Nodes. Node 1 is malformed since it has only three trusses (1–2, 1–3, and 1–4), two of which are parallel (1–2 and 1–3). Node 5 is well-formed. 4 Implementation Let us recall what variables are given by the specification of the bridge (input data) and what variables need to be computed (output data). The input data is: • Numbers M , N , and K • Node positions xi ∈ R2 for i = 1, 2, . . . , N and their types (free or fixed) • Truss connectivity tk,1 and tk,2 for k = 1, 2, . . . , K • Elastic moduli ck for k = 1, 2, . . . , K • External loading fiext for i = 1, 2, . . . , N The output data is: • Node displacements ui ∈ R2 for i = 1, 2, . . . , N • Truss elongations ek for k = 1, 2, . . . , K • Truss forces fk for k = 1, 2, . . . , K First, let us discuss the input data. The input data will be read from files. Observe that the list of input data consists of data numbered from 1 to N , associated with the nodes, and data numbered from 1 to K, associated with the trusses, except for the scalar numbers M , N , and K. Thus it makes sense to store all node-based data together in one file, and all truss-based data together in another file. For easy human readability, we choose a plain text format. For the node-based data, we agree on the following format. For each node (free or fixed), there is one line in the file, ordered by node numbers. Each line consists of (in this order): xi,1 xi,2 0 if node is free or 1 if node is fixed ext fi,1 ext fi,2 The entries are separated by at least one blank. The file is named as (name of bridge).nodes. 7 The trusses are stored in a similar way. Each line in the file (name of bridge).trusses consists of the entries tk,1 tk,2 ck Note that we do not need to specify the numbers M , N , and K explicitly. N is implicitly given by the number of lines in the nodes file, M by the number of lines in the nodes file whose third entry is 0, and K by the number of lines in the trusses file. For example, the simple structure from Figure 2 and Table 1 is stored as: File simple.nodes: 0.0 0.0 1 0.0 0.0 1.0 1.5 0 0.0 0.0 2.0 0.0 0 0.0 -2.0 3.0 1.5 0 0.0 0.0 4.0 0.0 1 0.0 0.0 File simple.trusses: 1 2 1 1 3 1 2 3 1 2 4 1 3 4 1 3 5 1 4 5 1 (Do not deviate from the format defined here, since otherwise it would become difficult for the grader to compare the different solutions later.) Task 3 Write a MatLab function readbridge with the name of the bridge as input argument. The function shall read the bridge data from the two files and compute the mapping mi . It shall return the following variables: x (matrix of size N × 2) map (vector of size N ) fext (matrix of size N × 2) t (vector of size K × 2) c (vector of size K) M, N, K (scalars) Note: The built-in MatLab function textscan is useful here. Now we have all necessary input data, so we can come to the actual computation. Task 4 Write a MatLab program bridge which first calls readbridge to get the input data. Then compute the normal vectors ni and the matrix B as figured out in Task 1. Assemble the matrix A from (20) and the right hand side f ext . Solve the linear system for u using one of your own solvers developed as homework. Make sure your solver stops with an error message if the matrix A happens to be singular. Compute the elongations e and the forces f from (15) and (16), respectively. 8 After having determined the unknowns, we need to interpret the results. Instead of printing large tables of numbers, it is more useful to extract certain quantities. Here the following quantities are of interest: 1. Maximal force: maxk \|fk \| 2. Maximal elongation: maxk \|ek \| 3. Maximal relative elongation: maxk \|ek \|/lk Task 5 Extend your program from Task 4 to determine these quantities. It is reasonable to assume that a truss will fail if its relative elongation exceeds a certain value. Thus the relative elongation is especially useful to identify possible points of failure of the bridge. However, we do not only want to discover that our bridge might fail under some given loading. We rather want to know which truss is endangered so we can reinforce it by increasing its thickness or by adding more trusses nearby to better balance the load. To this end, we visualize our solution. The graph shall show: 1. The nodes at their deformed positions xi + ui . 2. The trusses with color coding of the relative elongation: Blue means minimal elongation, green to yellow medium elongation, and red to brown maximal elongation. Task 6 Write a MatLab function plotbridge which plots the bridge as stated above and add it to your main program from Task 4. Now you are ready to actually compute a bridge by yourself! Task 7 Download the data for the bridge shown in Figure 1 from Run your program to compute the above mentioned quantities and create the corresponding graphs for the following loading regimes: ext ext 1. f11,2 = −0.1, all other fi,j = 0 (vertical point load) ext ext 2. f23,2 = −0.1, all other fi,j = 0 (vertical point load) ext ext 3. fi,2 = −0.01 for i = 9, 11, 17, 19, 20, 22, 23, 33, 34, 40, 42, 43, 45, 46, all other fi,j = 0 (uniform vertical load on the whole road surface) ext ext 4. f42,1 = 0.1, all other fi,j = 0 (horizontal point load, e.g. caused by wind) Describe and interpret your results. ext Figure 6 shows how the bridge from Figure 1 looks like under the loading f20,2 = −0.1. 5 Bridge Optimization After having computed a given bridge, we now climb up to the next step. The ultimate interest of bridge engineers is not to evaluate a given bridge, but to design a new one which is as stable and efficient as possible. Of course there are conditions to be met: The bridge must fit with the geometry of the river valley, and there is only a limited amount of material. Task 8 Build your own bridge according to the rules described below and submit the two input files (in the format discussed above) by email to arndt@math.umn.edu. 9 2000 24 9 19 17 11 33 42 40 34 43 45 46 47 20 22 23 1500 18 41 44 0.06 10 12 21 35 36 29 30 8 13 6 32 5 1000 16 39 28 14 4 37 0.04 15 3 38 27 500 7 2 31 26 0.02 0 1 25 0 0 1000 2000 3000 4000 5000 6000 7000 ext Figure 6: Bridge with loading f20,2 = −0.1. You may build your own bridge from scratch, or you may start with the bridge given here and improve it. For example, one can read off from Figure 6 that the truss between nodes 1 and 2 is highly endangered: The brown color indicates the highest relative elongation, see the color bar. So it makes sense to improve the structure at this point by increasing the elastic modulus of the truss 1–2 or adding more nodes and trusses close to it. Your bridge must comply with the following rules: 1. At most 100 nodes, i.e. N ≤ 100. K 2. The amount of material for the trusses is limited to k=1 ck lk ≤ 100000. 3. There must be nodes at (0 1800) and (7200 1800). Along the straight line between these two nodes, there must be additional nodes with distance 600 or less. These nodes shall all be connected by trusses to form the road surface. 4. The only possible points for fixed nodes are: (compare Figure 3) • (0 y) with 1350 ≤ y ≤ 1800 (left shoreline) • (7200 y) with 1350 ≤ y ≤ 1800 (right shoreline) • (1800 0) (left foundation in the river) • (5400 0) (right foundation in the river) 5. No intersecting trusses. There will be a competition among students: The stability of all bridges will be ranked, and the most stable ones get extra points! Stability is measured as follows. The following loads are applied to the bridge: 1. Vertical point load fiext = (0 −0.1), individually for each node i on the road surface. 2. Horizontal point load fiext = (0.1 0), individually for each node i on the road surface. For each loading regime, the maximum relative elongation is determined. Then the maximum of these values is taken over all loading regimes. The bridge with the smallest maximum value is best. Don't forget to submit this number for your bridge
Maths - clifford / Geometric Algebra - Further ReadingGeometric Fundamentals of Robotics... Geometric Algebra for Physicists - This is intended for physicists so it soon gets onto relativity, spacetime, electrodynamcs, quantum theory, etc. However the introduction to Geometric Algebra and classical mechanics is useful. Geometric Computing for Perception Action Systems: Concepts, Algorithms, and Scientific Applications (Hardcover). This is the only book I have so far come across that has a reasonable explanation of 'motors' and why it is useful to use 4D Geometric algebra to represent kinematics of solid bodies (in chapter 2). The book is quite a slim volume considering that it covers both fundamental concepts and practical applications. Therefore I think you will need to have a good understanding of Geometric Algebra before starting on this book. Geometric Algebra for Computer Science: An Object-oriented Approach to Geometry. This book stresses the Geometry in Geometric Algebra, although it is still very mathematically orientated. Programmers using this book will need to have a lot of mathematical knowledge. Its good to have a Geometric Algebra book aimed at computer scientists rather than physicists. There is more information about this book here. Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.
Activity Book Composite Mathematics For ... (Paperback) This is a supplement book with main course book. the book is full of Maths activities for classes I to V. Efforts have been made to present questions in all possible forms, so that a child grasps the concepts better. Details Of Book : Activity Book Composite Mathematics For ... Book: Activity Book Composite Mathematics For Class I Author: Dr.R.S.AggarwalVikas Aggarwal ISBN: 8121931266 ISBN-13: 9788121931267 Binding: Paperback Publisher: SChand
BEFORE USING THE CALCULATOR FOR THE FIRST TIME... Be sure to perform the following procedure to load batteries, reset the calculator, and adjust the contrast before trying to use the calculator for the first time. 1. Making sure that you do not accidently press the o key, attach the case to the calculator and then turn the calculator over. 5. Press m. * The above shows the CFX-9850 * The above shows the fx-9750G (9950)G(B) PLUS screen. PLUS screen. • If the Main Menu shown above is not on the display, press the P button on the back of the calculator to perform memory reset. • Statistical Regression Graph Example • When you draw a graph or run a program, any comment text normally appears on the display in blue. You can, however, change the color of comment text to orange or green. Example: To draw a sine curve 1. KEYS Alpha Lock Normally, once you press a and then a key to input an alphabetic character, the key- board reverts to its primary functions immediately. If you press ! and then a, the keyboard locks in alpha input until you press a again. Quick-Start Welcome to the world of graphing calculators. Quick-Start is not a complete tutorial, but it takes you through many of the most common functions, from turning the power on, to specifying colors, and on to graphing complex equations. When you're done, you'll have mastered the basic operation of this calculator and will be ready to proceed with the rest of this user's guide to learn the entire spectrum of functions available. Quick-Start defc to highlight RUN and then 2. Use press This is the initial screen of the RUN mode, where you can perform manual calculations, and run programs. BASIC CALCULATIONS With manual calculations, you input formulas from left to right, just as they are written on paper. Quick-Start 1. Press SET UP 2. Press to switch the set up display. cccc1 3. Press (Deg) to specify degrees as the angle unit. 4. Press to clear the menu. 5. Press to clear the unit. cfsefw 6. Press REPLAY FEATURES With the replay feature, simply press to recall the last calculation that was performed. Quick-Start FRACTION CALCULATIONS You can use the key to input fractions into calculations. The symbol " { " is used to separate the various parts of a fraction. Example: 1 1. Press b$bf$ 2. Press bg+dh$ Indicates 6 Converting a Mixed Fraction to an Improper Fraction While a mixed fraction is shown on the display, press to convert it to an improper fraction. Quick-Start DUAL GRAPH With this function you can split the display between two areas and display two graphs on the same screen. Example: To draw the following two graphs and determine the points of intersection Y1 = X(X + 1)(X – 2) Y2 = X + 1.2 !Zcc1 1. Quick-Start 3. Use , and to move the pointer again. As you do, a box appears on the display. Move the pointer so the box encloses the area you want to enlarge. 4. Press , and the enlarged area appears in the inactive (right side) screen. Quick-Start TABLE FUNCTION The Table Function makes it possible to generate a table of solutions as different values are assigned to the variables of a function. Example: To create a number table for the following function Y = X (X+1) (X–2) 1. Handling Precautions • Your calculator is made up of precision components. Never try to take it apart. • Avoid dropping your calculator and subjecting it to strong impact. • Do not store the calculator or leave it in areas exposed to high temperatures or humidity, or large amounts of dust. 1 or 2 kbytes of memory free (unused) at all times. In no event shall CASIO Computer Co., Ltd. be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials. Getting Acquainted — Read This First! About this User's Guide uFunction Keys and Menus • Many of the operations performed by this calculator can be executed by pressing function keys 1 through 6. The operation assigned to each function key changes according to the mode the calculator is in, and current operation assignments are indicated by function menus that appear at the bottom of the display. 1. Key Markings Many of the calculator's keys are used to perform more than one function. The functions marked on the keyboard are color coded to help you find the one you need quickly and easily. Function Key Operation The following describes the color coding used for key markings. Color Key Operation Orange... 2. Selecting Icons and Entering Modes This section describes how to select an icon in the Main Menu to enter the mode you want. uTo select an icon 1. Press m to display the Main Menu. Currently selected icon The above shows the CFX-9850 GB PLUS screen. Selecting Icons and Entering Modes Icon Mode Name Description TABLE Use this mode to store functions, to generate a numeric table of different solutions as the values assigned to variables in a function change, and to draw graphs. RECURsion Use this mode to store recursion formulas, to generate a numeric table of different solutions as the values assigned to variables in a function change, and to draw graphs. Selecting Icons and Entering Modes 3 4 5 3. Use the f and c cursor keys to move the highlighting to the item whose setting you want to change. 4. Press the function key (1 to 6) that is marked with the setting you want to make. Selecting Icons and Entering Modes 3. Display k About the Display Screen This calculator uses two types of display: a text display and a graphic display. The text display can show 21 columns and eight lines of characters, with the bottom line used for the function key menu, while the graph display uses an area that measures 127 (W) ×... Display • Direct Command Execution Example: Selecting executes the DRAW command. k Exponential Display The calculator normally displays values up to 10 digits long. Values that exceed this limit are automatically converted to and displayed in exponential format. You can specify one of two different ranges for automatic changeover to exponential display. 4. Contrast Adjustment Adjust the contrast whenever objects on the display appear dim or difficult to see. uTo display the contrast adjustment screen Highlight the CONT icon in the Main Menu and then press w. CFX-9850(9950)GB PLUS, fx-9750G PLUS CFX-9850G PLUS uTo adjust the contrast Press the e cursor key to make the display darker and the d cursor key to make it lighter. 5. When you keep having problems… If you keep having problems when you are trying to perform operations, try the following before assuming that there is something wrong with the calculator. k Get the Calculator Back to its Original Mode Settings 1. 1-1 Before Starting Calculations... Before performing a calculation for the first time, you should use the set up screen to specify the angle unit and display format. k k k k k Setting the Angle Unit (Angle) 1. Display the set up screen and use the f and c keys to highlight "Angle". 2. 1 - 1 Before Starting Calculations... u u u u u To specify the number of significant digits (Sci) Example To specify three significant digits 2 (Sci) 4 (3) Press the function key that corresponds to the number of significant digits you want to specify ( = 0 to 9). 1 - 1 Before Starting Calculations... k k k k k Inputting Calculations When you are ready to input a calculation, first press A to clear the display. Next, input your calculation formulas exactly as they are written, from left to right, and press w to obtain the result. 1 - 1 Before Starting Calculations... ! Relational operator =, G , >, <, ≥, ≤ @ And (logical operator), and (bitwise operator) # Or (logical operator), or (bitwise operator), xor, xnor • When functions with the same priority are used in series, execution is per- formed from right to left. 1 - 1 Before Starting Calculations... k k k k k Stacks The unit employs memory blocks, called stacks , for storage of low priority values and commands. There is a 10-level numeric value stack , a 26-level command stack , and a 10-level program subroutine stack . An error occurs if you perform a calculation so complex that it exceeds the capacity of available numeric value stack or command stack space, or if execution of a program subroutine exceeds the capacity of the subroutine stack. 1 - 1 Before Starting Calculations... k k k k k Overflow and Errors Exceeding a specified input or calculation range, or attempting an illegal input causes an error message to appear on the display. Further operation of the calculator is impossible while an error message is displayed. The following events cause an error message to appear on the display. 1 - 1 Before Starting Calculations... k k k k k Graphic Display and Text Display The unit uses both a graphic display and a text display. The graphic display is used for graphics, while the text display is used for calculations and instructions. The contents of each type of display are stored in independent memory areas. 1 - 1 Before Starting Calculations... u u u u u To insert a step Example To change 2.36 to sin2.36 c.dgx ddddd • When you press ![ the insert location is indicated by the symbol ''t''. The next function or value you input is inserted at the location of ''t''. To abort the insert operation without inputting anything, move the cursor, press ![ again, or press d, e or w. 1-2 Memory k k k k k Variables This calculator comes with 28 variables as standard. You can use variables to store values to be used inside of calculations. Variables are identified by single- and θ . letter names, which are made up of the 26 letters of the alphabet, plus The maximum size of values that you can assign to variables is 15 digits for the mantissa and 2 digits for the exponent. 1 - 2 Memory 2. Press w again to display the memory status screen. Number of bytes still free 3. Use f and c to move the highlighting and view the amount of memory (in bytes) used for storage of each type of data. The following table shows all of the data types that appear on the memory status screen. 1 - 2 Memory k k k k k Clearing Memory Contents Use the following procedure to clear data stored in memory. 1. In the memory status screen, use f and c to move the highlighting to the data type you want to clear. If the data type you select in step 1 allows deletion of specific data 2. 1-3 Option (OPTN) Menu The option menu gives you access to scientific functions and features that are not marked on the calculator's keyboard. The contents of the option menu differ according to the mode you are in when you press the K key. See the Command List at the back of this user's guide for details on the option (OPTN) menu. 1-4 Variable Data (VARS) Menu To recall variable data, press J to display the variable data menu. {V-WIN}/{FACT}/{STAT}/{GRPH}/{DYNA} {TABL}/{RECR}/{EQUA}/{TVM} See the Command List at the back of this user's guide for details on the variable data (VARS) menu. • Note that the EQUA and TVM items appear for function keys (3 and 4) only when you access the variable data menu from the RUN or PRGM Mode. 1 - 4 Variable Data (VARS) Menu • The table contents recalled by the above operation are stored automatically in Matrix Answer Memory (MatAns). • An error occurs if you perform the above operation when there is no function or recursion formula numeric table in memory. 1 - 4 Variable Data (VARS) Menu • The coefficients and solutions recalled by the above operation are stored automatically in Matrix Answer Memory (MatAns). • The following conditions cause an error to be generated. — When there are no coefficients input for the equation —... 1-5 Program (PRGM) Menu To display the program (PRGM) menu, first enter the RUN or PRGM Mode from the Main Menu and then press ! W. The following are the selections available in the program (PRGM) menu. • {COM} … {program command menu} •... 2-1 Basic Calculations k k k k k Arithmetic Calculations • Enter arithmetic calculations as they are written, from left to right. • Use the - key to input a negative value. • Use the - key for subtraction • Calculations are performed internally with a 15-digit mantissa. The result is rounded to a 10-digit mantissa before it is displayed. 2-2 Special Functions k k k k k Answer Function The unit's Answer Function automatically stores the last result you calculated by pressing w(unless the w key operation results in an error). The result is stored in the answer memory. u u u u u To use the contents of the answer memory in a calculation Example 123 + 456 = 579... 2 - 2 Special Functions k k k k k Using the Replay Function The Replay Function automatically stores the last calculation performed into replay memory. You can recall the contents of the replay memory by pressing d or e. If you press e, the calculation appears with the cursor at the beginning. 2 - 2 Special Functions 6.9 × 123 = 848.7 Example 123 ÷ 3.2 = 38.4375 AbcdaaA!W6(g) 5(:)g.j*aA!W 5(^)aA/d.cw Intermediate result at point where " ^ " is used. • Note that the final result of a multistatement is always displayed, regardless of whether it ends with a display result command. 2-3 Function Calculations k k k k k Function Menus This calculator includes five function menus that give you access to scientific functions that are not printed on the key panel. • The contents of the function menu differ according to the mode you entered from the Main Menu before you pressed the K key. 2 - 3 Function Calculations About Logical Operations • A logical operation always produces either 0 or 1 as its result. • The following table shows all of possible results that can be produced by AND and OR operations. Value or Expression A Value or Expression B A AND B A OR B... 3-1 Before Performing a Calculation The following describes the items that are available in the menus you use when performing Solve, differential/ quadratic differential, integration, maximum/ minimum value, and Σ calculations. P.27 When the option menu is on the display, press 4 (CALC) to display the function analysis menu. 3-2 Differential Calculations [OPTN]-[CALC]-[d/dx] To perform differential calculations, first display the function analysis menu, and then input the values shown in the formula below. f(x) Increase/decrease of Point for which you want to determine the derivative d/dx ( f (x), a, Ax) ⇒ ––– f (a) The differentiation for this type of calculation is defined as: f (a + Ax) –... 3-3 Quadratic Differential Calculations [OPTN]-[CALC]-[d After displaying the function analysis menu, you can input quadratic differentials using either of the two following formats. f(x) Final boundary ( = 1 to 15) Differential coefficient point ––– ( f (x), a, n) ⇒ ––– f (a) Quadratic differential calculations produce an approximate differential value using the following second order differential formula, which is based on Newton's polynomial interpretation. 3 - 3 Quadratic Differential Calculations Input 3 as point , which is the differential coefficient point. Input 6 as , which is final boundary. • In the function f(x), only X can be used as a variable in expressions. Other variables (A through Z, r, θ... 3 - 4 Integration Calculations • Pressing A during calculation of an integral (while the cursor is not shown on the display) interrupts the calculation. • Always use radians (Rad Mode) as the angle unit when performing trigono- metric integrations. •... 3-6 Summation (Σ) Calculations [OPTN]-[CALC]-[Σ(] To perform Σ calculations, first display the function analysis menu, and then input the values shown in the formula below. α β 6(g)3(Σ() Distance between partitions Last term of sequence Initial term of sequence Variable used by sequence β... 3 - 6 (Σ) Summation Calculations • You can use only one variable in the function for input sequence • Input integers only for the initial term of sequence and last term of sequence • Input of and the closing parentheses can be omitted. If you omit , the calculator automatically uses = 1. Chapter Complex Numbers This calculator is capable of performing the following operations using complex numbers. • Arithmetic operations (addition, subtraction, multiplication, division) • Calculation of the reciprocal, square root, and square of a complex number • Calculation of the absolute value and argument of a complex number •... 4-2 Performing Complex Number Calculations The following examples show how to perform each of the complex number calculations available with this calculator. k k k k k Arithmetic Operations [OPTN]-[CPLX]-[i] Arithmetic operations are the same as those you use for manual calculations. You can even use parentheses and memory. 4 - 2 Performing Complex Number Calculations k k k k k Complex Number Calculation Precautions • The input/output range of complex numbers is normally 10 digits for the mantissa and two digits for the exponent. • When a complex number has more than 21 digits, the real part and imaginary part are displayed on separate lines. Chapter Binary, Octal, Decimal, and Hexadecimal Calculations This calculator is capable of performing the following operations involving different number systems. • Number system conversion • Arithmetic operations • Negative values • Bitwise operations Before Beginning a Binary, Octal, Decimal, or Hexadecimal Calculation with Integers Selecting a Number System Arithmetic Operations... 5-1 Before Beginning a Binary, Octal, Decimal, or Hexadecimal Calculation with Integers You can use the RUN Mode and binary, octal, decimal, and hexadecimal settings to perform calculations that involve binary, octal, decimal and hexadecimal values. You can also convert between number systems and perform bitwise operations. •... 5-2 Selecting a Number System You can specify decimal, hexadecimal, binary, or octal as the default number system using the set up screen. After you press the function key that corresponds to the system you want to use, press w. u u u u u To convert a displayed value from one number system to another Example To convert 22... 6 - 1 Before Performing Matrix Calculations Specify the number of rows. Specify the number of columns. • All of the cells of a new matrix contain the value 0. • If "Mem ERROR" remains next to the matrix area name after you input the dimensions, it means there is not enough free memory to create the matrix you want. 6 - 1 Before Performing Matrix Calculations k k k k k Deleting Matrices You can delete either a specific matrix or all matrices in memory. u u u u u To delete a specific matrix 1. While the MATRIX list is on the display, use f and c to highlight the matrix you want to delete. 6-2 Matrix Cell Operations Use the following procedure to prepare a matrix for cell operations. 1. While the MATRIX list is on the display, use f and c to highlight the name of the matrix you want to use. 2. Press w and the function menu with the following items appears. •... 6 - 2 Matrix Cell Operations u u u u u To insert a column Example To insert a new column between columns 1 and 2 of the following matrix : Matrix A = 3(COL)e 2(INS) u u u u u To add a column Example To add a new column to the right of column 2 of the following matrix :... 6-3 Modifying Matrices Using Matrix Commands [OPTN]-[MAT] u u u u u To display the matrix commands 1. From the Main Menu, select the RUN icon and press w. P.27 2. Press K to display the option menu. 3. Press 2 (MAT) to display the matrix operation menu. The following describes only the matrix command menu items that are used for creating matrices and inputting matrix data. 6 - 3 Modifying Matrices Using Matrix Commands Matrix name • An error occurs if memory becomes full as you are inputting data. • You can also use the above format inside a program that inputs matrix data. u u u u u To input an identity matrix Use the matrix operation menu's Identity command (1) to create an identity matrix. 6 - 3 Modifying Matrices Using Matrix Commands k k k k k Modifying Matrices Using Matrix Commands You can also use matrix commands to assign values to and recall values from an existing matrix, to fill in all cells of an existing matrix with the same value, to combine two matrices into a single matrix, and to assign the contents of a matrix column to a list file. 6 - 3 Modifying Matrices Using Matrix Commands Example 2 To combine the following two matrices : K2(MAT)5(Aug)1(Mat) aA,1(Mat)aBw • The two matrices you combine must have the same number of rows. An error occurs if you try to combine two matrices that have different numbers of rows. u u u u u To assign the contents of a matrix column to a list file Use the following format with the matrix operation menu's Mat→List command (2) to specify a column and a list file. 6 - 4 Matrix Calculations • The two matrices must have the same dimensions in order to be added or subtracted. An error occurs if you try to add or subtract matrices of different dimensions. • For multiplication, the number of columns in Matrix 1 must match the number of rows in Matrix 2. 6 - 4 Matrix Calculations Example Obtain the determinant for the following matrix : Matrix A = –1 –2 3(Det)1(Mat)aAw • Determinants can be obtained only for square matrices (same number of rows and columns). Trying to obtain a determinant for a matrix that is not square produces an error. Chapter Equation Calculations Your graphic calculator can perform the following three types of calculations: • Linear equations with two to six unknowns • High-order equations (quadratic, cubic) • Solve calculations Before Beginning an Equation Calculation Linear Equations with Two to Six Unknowns Quadratic and Cubic Equations Solve Calculations What to Do When an Error Occurs... 7-1 Before Beginning an Equation Calculation Before beginning an equation calculation you have to first enter the correct mode, and you must also clear the equation memories of any data that might be left over from a previous calculation. k k k k k Entering an Equation Calculation Mode In the Main Menu, select the EQUA icon to enter the Equation Mode. 7-2 Linear Equations with Two to Six Unknowns You can use the procedures described here to solve linear equations with unknowns that match the following formats: x + b y = c Two unknowns x + b y = c Six unknowns x + b y + c... 7 - 2 Linear Equations with Two to Six Unknowns k k k k k Solving Linear Equations with Three Unknowns Example To solve the following linear equations for , and – 2 = –1 –5 = –7 1. While in the Linear Equation Mode (SIML), press 2 (3), because the linear equations being solved have three unknowns. 7 - 2 Linear Equations with Two to Six Unknowns • Internal calculations are performed using a 15-digit mantissa, but results are displayed using a 10-digit mantissa and 2-digit exponent. • This unit performs simultaneous linear equations by placing the coefficients inside of a matrix. 7-3 Quadratic and Cubic Equations This calculator can also solve quadratic and cubic equations that match the following formats (when G G G G G • Quadratic: • Cubic: k k k k k Specifying the Degree of an Equation While in the Equation Mode, press 2 (POLY) and then specify the degree of the equation. 7 - 3 Quadratic and Cubic Equations • Internal calculations are performed using a 15-digit mantissa, but results are displayed using a 10-digit mantissa and 2-digit exponent. • An error occurs whenever the unit is unable to solve the equations. •... 7 - 3 Quadratic and Cubic Equations k k k k k Changing Coefficients You can change a coefficient either before or after you register it by pressing w. u u u u u To change a coefficient before registering it with w Press the A key to clear the current value and then input another one. 7-4 Solve Calculations You can determine the value of any variable you are using without having to solve the equation. Input the equation, and a table of variables appears on the display. Use the table to assign values to variables and then execute the calculation to obtain a solution and display the value of the unknown variable. 7 - 4 Solve Calculations • Solve uses Newton's method to calculate approximations. The following can sometimes occur when this method is used. —Solutions may be impossible to obtain for certain initial estimated values. Should this happen, try inputting another value that you assume to be in the vicinity of the solution and perform
この書籍内から Review: Complex Analysis: An Introduction to the Theory of Analytic Functions of Complex Variable ユーザーレビューレビュー全文を読む Review: Complex Analysis: An Introduction to the Theory of Analytic Functions of Complex Variable ユーザーレビュー - Ronald Lett - Goodreads A beautiful exposition of complex analysis. One warning, though: you should have a good understanding of complex algebra and calculus before reading this text, as it is dense.レビュー全文を読む Information for Math 503, fall 2007 For example, one edition of the classical text of Ahlfors entitled Complex analysis; an introduction to the theory of analytic functions of one complex ... ~greenfie/ mill_courses/ math503a/ instruct.html
College Teachers - Internet Projects The Math Forum hosts a project called Ask Dr. Math. It provides students (primarily K-12) all over the world with a place to pose their questions about mathematics. Not only is this a great service to the students, but it is also a lot of fun for the "doctors." As this project becomes more and more popular, the demand for doctors increases too. If you know of any college students who would like to spend a little time answering fun and challenging math questions on the Internet, please let us know. Stan Wagon, a professor in the Mathematics and Computer Science Department at Macalester College, poses a mathematics problem to his students every week. The problems are meant to be accessible to first-year college students, so very little background is needed to understand or solve them. They are also sent out by electronic mail and an archive of some older Problems of the Week is also maintained at Macalester. The archives of the Macalester Problems of the Week are housed at the Math Forum. A database containing materials designed to help teach a CHANCE course or a more standard introductory probability or statistics course. The aim of CHANCE is to make students more informed, and critical, readers of current news that uses probability and statistics as reported in daily newspapers such as "The New York Times" and the "The Washington Post" and current journals and magazines such as "Chance," "Science," "Nature," and the "New England Journal of Medicine." Chance News, a biweekly news letter that provides abstracts of articles in current newspapers and journals. Links are made to the full text of the article when it is available and to resources at other Web sites. Discussion questions are provided for many of the articles. Syllabi of previous CHANCE courses and articles that have been written about the CHANCE course. Teaching aids by topic, descriptions of activities, data sets, videotapes, and other resources that may be useful in teaching a CHANCE course and/or other introductory statistics or probability courses.
Customers Who Bought This Also Bought... Connect the process of problem solving with the content of the Common Core. The first of a series, this book will help mathematics educators illuminate a crucial link between problem solving and the Common Core State Standards. Anticipating what students will do--what strategies they will use--in solving a problem Monitoring their work as they approach the problem in class Selecting students whose strategies are worth discussing in class Sequencing those students' presentations to maximize their potential to increase students' learning Connecting the strategies and ideas in a way that helps students understand the mathematics learned By connecting the CCSSM to previous standards and practices, the book serves as a valuable guide for teachers and administrators in implementing the CCSSM to make mathematics education the best and most effective for all studentsThis book focuses on essential knowledge for teachers about geometry. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. "The authors provide a commonsense approach for those who work directly with classroom teachers to support and improve teaching and learning. Easily read, this book lays out a simple plan for success as a mathematics coach." —Emily S. Rash, Mathematics Specialist Monroe City School District, LA This e-book only companion to Rich and Engaging Mathematics Tasks Grades 5-9 (NCTM #13516) contains more than 50 additional articles and tasks! A valuable resource to any mathematics teacher, this rich collection of mathematical tasks will enliven students' engagement in mathematical thinking and reasoning and help them succeed in the classroom. Please note: This product can only be purchased via NCTM's Online catalog. Non-web payment methods, such as POs, cannot be used to purchase this item. If you have questions, please call NCTM's Customer Service Department at 800-235-7566. The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
... read moreProduct Description: erve presents the fundamental concepts of algebra illustrated by numerous examples- and, in many cases, the theory is further explicated by suitable sequences of exercises. The author's aim is to introduce the concepts of higher mathematics while bringing the reader to a more thorough understanding of elementary mathematics. His lucid explanations cover these major areas: OUR NUMBER SYSTEM: Sets, Cardinal Numbers, Order Relations, Real Numbers, Fields and Number Systems, more. THEORY OF NUMBERS: Divisibility, Prime Numbers, Bases, Division Algorithm, Decimal Notations, Linear Congruences, more. THEORY OF POLYNOMIALS: Rational Functions, Irreducible Polynomials, Functions, Limits, Continuity, Derivatives, more. THEORY OF EQUATIONS: Zeros of a Polynomial, Change of a Variable, Number of Roots, Quartic Equations, more. DETERMINANTS AND MATRICES: Historical Development, Permutations, Inversions, Transpositions, Cramer's Rule, more. CONSTRUCTIONS: The Algebraic Viewpoint, Classical Constructions, Mechanical Angle Trisectors, Linkages, more. GRAPHICAL REPRESENTATIONS: Euclidean and Complex Spaces, Conic Sections, Quadric Surfaces, Curve Tracing, more. While intended for students who have previously studied college mathematics through calculus, this book has also been successfully used where calculus was not a prerequisite. It provides a very easily followed presentation and may also be used as an introductory or supplementary textbook. For prospective teachers of secondary mathematics, for students preparing for specialized advanced undergraduate courses in mathematics, and for the general reader in search of a firmer grasp of the essentials of algebra, there is no better, more helpful guide than Meserve
AEPA Math Everything You Need to Know About AEPA Math AEPA Math refers to the Mathematics test of the AEPA (the Arizona Educator Proficiency Assessments) examinations. AEPA Mathematics is one of the subjects that an AEPA examinee, who wants to be a Mathematics educator, takes to show his or her proficiency in the subject. Based on the scores obtained in the AEPA Mathematics section, the examinee is awarded the certification of a Maths educator. APEA Math Format The questions of the AEPA Math section are aimed at testing the mathematical concepts of entry-level educators of Arizona schools. The questions are of objective type with multiple choice answers. The subareas on which an AEPA Math examinee will be tested are as follows: Number Sense- This section tests the knowledge and conceptual clarity in topics related to Basic Arithmetic, such as, Ratio and Proportion, Percentage, Factors, Decimals, Number Theory, and Discrete Mathematics. This section also tests one's knowledge in the field of Real Numbers and Complex Numbers, and Imaginary Numbers. Data Analysis and Probability- This section tests one's knowledge of concepts in Probability and Descriptive Mathematics. All areas associated with the concept of Probability can be tested in this test. Hence, it is important for an AEPA Math examinee to brush up on this section in an in-depth manner. The skills of gathering data, organizing it into a meaningful report, and then analyzing the report, are also tested by this educator assessment examination. Algebra, Mathematical Patterns and Functions- This section of AEPA Math, evaluates an examinee's concepts in Basic Algebra, Algebraic Equations and their relations. It also tests the knowledge of Linear Algebra and Matrix Algebra. An examinee should be thorough with his knowledge of Quadratic Equations, Inequalities, and algebraic functions in order to clear this test. The AEPA Math examinee's concepts of Logarithmic, Polynomial and Exponential functions should be good to answer the questions posed in this section. Geometry and Measurement- This section tests an examinee's concepts of Basic Geometry, Three-dimensional Geometry, Co-ordinate Geometry, and the usage of algebra in geometry. The AEPA Math examinee's concepts of Vector Geometry and Transformational Geometry are also tested in this section. Trigonometry and Basics of Calculus- This section aims to assess the AEPA Math examinee's skills in Basic Trigonometry and Calculus, and the appropriateness of their application in different situations. Mathematical Structure and Logic- This section presents questions that test the examinees skills in applying Mathematical logic, Mathematical communication and Mathematical reasoning. Questions on the concepts of Axiomatic Domain Theory are also included in this section. Percentage Distribution of the Six Sections of AEPA Math The Number Sense, and Data Analysis and Probability sections, cover 14 percent of the test paper, each. The Patterns, Algebra and Functions; Geometry and Measurement; Trigonometry and Calculus; and Mathematical Structure and Logic sections, each cover 18 % of the AEPA Math test paper. For more information on the different sections of AEPA Mathematics and the syllabus in these subjects, please visit AEPA Math Test Duration The time for completion of the AEPA Math section is four hours. Can Calculators Be Used in AEPA Math Tests? The AEPA examinees are allowed to perform calculations using calculators in AEPA Math test, but they have to use the calculator provided to them at their test center. They cannot use their personal calculators in the examination hall. The testing authorities will give them scientific calculators to work on the Mathematics section of AEPA. Conclusion The AEPA Math section is tough, as it covers a wide range of topics at an in-depth level. One must take the advice of AEPA Math experts (only people who have passed AEPA Maths) in preparing for this test. Alongside one can't take the help of good study material and practice test papers, adequately, before appearing for this Maths test to attain the desired
8 Answers Response moderated "Solving equations and such" sounds more like high-school maths to me. You can always revisit your old high-school math books if you still have them. They are usually pretty good (but tend to repeat the same concepts ad absurdum, you can skip some of the excercises once you feel you've grasped the concept). If you are looking for a no-bullshit, as straight forward as possible, intro to college math i can warmly recommend the Schaum's Outline series. There is even one especially for college maths They are short and to the point and very effective at quickly teaching you the subject of interest, but you do still have to put in the work. When I was reviewing my math prior to starting college, this site was especially helpful. If you are actually wanting college-level math, you will need to be more specific about what it is you are wanting to learn. It doesn't seem like you need to "learn" math (correct me if I'm wrong), but to "review" it. Any bookstore will have shelves full of various grade-level review books, and you can pick the topics you feel weak in. They have simple text (since they're not generally trying to teach from scratch) and loads of exercises with answers supplies—and techniques to follow if you get into trouble. What level of math did you leave off at? It is hard to recommend a book without knowing where you are. This James Stewart text is a classic Calculus book. Doesn't matter what edition you get. They are used all across the country in college calc classes, and it did a good job teaching me the subject. Highly recommend. If you are not there yet, stash the idea for future use. I've come to realize that math is so much more than just solving textbook problems. I had to get to partial differential equations to realize it, though. Math is basically a language humans have developed over millenia to explain how the world works. If you are intimidated by the subject (many people are), I suggest an indirect approach – consider looking back at how mathematics evolved, its history. Learning math through history would have been much more interesting to me. I just read Zero: The Biography of a Dangerous Idea, which kind of takes this approach. It gets a little technical towards the end, and would be a much better read if you understand basic calculus and basic physics, but you may still find it interesting. And here now I am assuming you haven't studied calc yet…don't be offended, I'm just not sure at all where you are. If you understand why an equation is, you can derive it from nothing and don't need to memorize it. This is what I like about math – there is always an explanation as to why. It is very logical. Unlike physics where everything simply is because it is. @lilkoi I seriously don't remember. It was in high school though, I have been out for about 6 years now and will be starting from scratch, this time doing college algebra and triginometry I guess. I want to do the basic Gen Eds so I can get them out of the way.
Trigonometry - 2nd edition Summary: Engineers trying to learn trigonometry may think they understand a concept but then are unable to apply that understanding when they attempt to complete exercises. This innovative book helps them overcome common barriers to learning the concepts and builds confidence in their ability to do mathematics. The second edition presents new sections on modeling at the end of each chapter as well as new material on Limits and Early Functions. Numerous Parallel Words and Math...show more examples are included that provide more detailed annotations using everyday language. Your Turn exercises reinforce concepts and allow readers to see the connection between the problems and examples. Catch the Mistake exercises also enable them to review answers and find errors in the given solutions. This approach gives them the skills to understand and apply trigonometry45 +$3.99 s/h Acceptable BookCellar-NH Nashua, NH 0470222719 Has heavy shelf wear, corner wear, highlighting, underlining & or writing. CD-ROM or supplement may not be included. The book is still a good reading copy.A portion of your purchase of this...show more
Course: Integrated Algebra 1, 1st Semester Textbook: Mathematics 1: McDougal Littell Cost: $69.48 Notetaking Guide: Mathematics 1: Georgia Notetaking Guide Cost: $1.50 Prerequisite: 8th Grade Standard Introduction to Algebra / Geometry and Teacher Recommendation Teacher: Mrs. Radford Email: Kathy_radford@gwinnett.k12.ga.us Website: Process Standards interwoven throughout the mathematics program are that students will: IAI 1. use appropriate technology to solve IAI 11. communicate mathematical thinking mathematical problems coherently and clearly to peers, teachers and others IAI 2. build new mathematical knowledge through IAI 12. analyze and evaluate the mathematical problem solving thinking and strategies of others IAI 3. solve problems that arise in mathematics and in IAI 13. use the terminology and language of other contexts mathematics to express mathematical ideas precisely IAI 4. apply and adapt a variety of appropriate IAI 14. recognize and use connections among strategies to solve problems mathematical ideas to solve problems. IAI 5. monitor and reflect on the process of IAI 15. explain how mathematical ideas mathematical problem solving interconnect and build on one another to produce a coherent whole IAI 6. recognize reasoning and proof (evidence) as IAI 16. recognize and apply mathematics in contexts fundamental aspects of mathematics outside of mathematics IAI 7. make and investigate mathematical conjectures IAI 17. create and use pictures, manipulatives, models and symbols to organize, record and communicate mathematical ideas IAI 8. investigate, develop and evaluate mathematical IAI 18. select, apply and translate among arguments and proofs mathematical representations to solve problems IAI 9. select and use various types of reasoning and IAI 19. use representations to model and interpret methods of proof physical, social and mathematical phenomena IAI 10. organize and consolidate mathematical thinking through communication These goals will provide the direction for assessment and instruction. Attainment of these goals is facilitated by the students' demonstration of the following Academic Knowledge and Skills (AKS). GCPS Unit 1: Linear Functions (4 weeks)  IAI 20: Represent functions using function notation. ( MM1N1)  IAI 21: Graph the basic functions f(x) = x, and f(x) = \|x\|. ( MM1N1)  IA1 domain, range, and intercepts. (MM1N1)  IAI 26: Compare rates of change of linear functions. (MM1A1) GCPS Unit 2: Polynomials & Quadratic Functions (7 weeks)  IAI 20: Represent functions using function notation. (MM1A1)  IAI 21: Graph the basic functions f(x) =x2. (MM1A1)  IAI zeros, and maximum and minimum values. (MM1A1)  IAI 24: Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior. (MM1A1)  IAI 31: Add, subtract, multiply, and divide polynomials. (MM1A2)  IAI 32: Expand binomials using the Binomial Theorem. (MM1A2)  IAI 34: Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + 2 2 2 2 2 2 2 2 2 y) = x + 2xy + y ; (x - y) = x - 2xy + y ; (x + y)(x - y) = x - y ; (x + a)(x + b) = x + x (a + b) + ab (MM1A2)  IAI 35: Use area and volume models for polynomial arithmetic. (MM1A2)  IAI 36: Solve quadratic equations in the form ax2+ bx + c = 0, where a = 1, by using factorization and finding square roots where applicable. (MM1A3)  IAI 38: Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x2+ bx + c = 0. (MM1A3) GCPS Unit 3: Algebra: Cubic, Square Root, & Rational Functions (7 weeks)  IAI 21: Graph the basic functions f(x) = x3, f(x) = √x, and f(x) = 1/x. (MM1A1)  IAI 22: Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes. (MM1A1)  IAI 23: Investigate and explain the characteristics of a function: domain, range, intervals of increase and decrease, and end behavior. (MM1A1)  IAI 25: Recognize sequences as functions with domains that are whole numbers. (MM1A1)  IAI 26: Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families. (MM1A1)  IAI 27: Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither. (MM1A1)  IAI 28: Explain how any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x). (MM1A1)  IAI 29: Simplify algebraic and numeric expressions involving square root. (MM1A2)  IAI 30: Perform operations with square roots. (MM1A2)  IAI 31: Add, subtract, multiply, and divide polynomials. (MM1A2)  IAI 33: Add, subtract, multiply, and divide rational expressions. (MM1A2)  IAI 34: Factor special products limited to the formula: (x + y)3 = x+ 3 x2y + 3xy2+ y3, (x - y)3 = x3 . 3x2y + 3xy2 – y3 (MM1A2)  IAI 37: Solve equations involving radicals such as √x + b = c, using algebraic techniques. (MM1A3)  IAI 39: Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1. (MM1A3) Resources  The Textbook is available online at The login is "radfordstudent" and the password is "math01". The activation code is 2420086-10.  Each student will be given a Notetaking Guide replaceable for a $1.50 fee. Materials Students are responsible for bringing the following materials to class on a daily basis: * Textbook * Pencil & Pen * Graph Paper Notetaking guide Paper, either in a 3 ring binder or a spiral notebook Scientific Calculator Make-Up Work/Cheating 1. Work missed due to absences must be turned in within one week of returning to school. A grade of 0 will be given for work that is not made up in the appropriate time interval. 2. All tests and quizzes missed due to absences must be made-up at a time that can be agreed upon by both the teacher and student. This date must be within one week of the student returning to school. 3. Assignments that are due on the day of an absence are due the first day the student returns to school. 4. Late work WILL NOT BE ACCEPTED. Late work is defined as work that is assigned while a student is present in class and not turned in to the teacher when expected. 5. Copying another student's paper, either partially or in full will result in the grade of zero for BOTH students involved. A warning is given for the first offense and a referral for any offense there after. It is the student's responsibility to cover their own work and to keep their eyes on their own paper. Sharing of work will not be tolerated. Grading Each student's semester average will be computed using the following percentages: TESTS 40% A: 90 - 100 QUIZZES 15% B: 80 – 89 DAILY/TASKS 20% C: 74 - 79 9 WEEK BENCHMARK 5% D: 70 - 73 PERFORMANCE EXAM 5% F: 00 – 69 FINAL EXAM (EOCT) 15% Extra Help: Tutoring is available before and after school most days. A list of teachers and times will be available by the second week of school. Please check with the teacher ahead of time so that we may plan accordingly. Tests: Tests will be announced at least 2 days ahead of time and will be given throughout the semester. If you are not present the day of the class review it is expected that you will review on your own and be prepared to take the test with the class. Daily/Tasks: You can expect to have an assignment most days. Daily work includes homework, notes, homework quizzes, and tasks. Quizzes: Quizzes will be given periodically. A quiz may not be announced ahead of time. Benchmark Statement: Benchmark assessments will be given at the 9th week into the grading period. It will be a cumulative multiple-choice assessment. ACCEPTABLE USE POLICY All students must agree to the acceptable use policy before using computer technology at Archer High school. Every time you sign on to use a computer this policy will be displayed. The "Acceptable Use Policy" states, "The internet is intended for educational purposes only. It is against school policy to submit, publish, or display any defamatory, inaccurate, abusive, obscene, profane, sexually oriented, threatening, racially offensive, or illegal material. Students may not access E-mail or chat sessions or computer hacking web sites of any kind. Students may not upload or download any software, etc. or make changes to any part of this computer. This includes but is not limited to the hard drive. By logging into this computer, YOU ARE ACCEPTING RESPONSIBILITY of what internet sites are viewed and any other inappropriate activities that may occur. All violations of the county and school ACCEPTABLE USE POLICY will result in a disciplinary referral to the Administration of Archer High School." GATEWAY REMINDER I understand that I will be assessed for learning of the AKS by the High School Gateway Test in the Spring of my 10th grade year. I must earn a passing score for all parts of the test in order to earn a regular Gwinnett County diploma. Should I not pass the Gateway, I will have the opportunity for academic interventions and to retake the failed portion(s) of the Gateway. In addition to the High School Gateway Test, graduation requirements include passing scores on the Georgia High School Graduation Tests and earning adequate Carnegie Units. Parent Contact: GRADES WILL BE SENT HOME ELECTRONICALLY ON A WEEKLY BASIS! *Progress Reports will go out at 6 and 12 weeks*** Tutoring: A list of non-school tutors is available on the teacher website. Reminder, these people are not endorsed by the school. For more information you must call the person. Books: Students will need to bring their books to class daily. There will NOT be any extra books in the classroom. Integrated Algebra 1 Fall 2009-2010 Kathy Radford I have read and understand the information presented in this document. I will, to the best of my ability as a student or parent, work to fulfill the aforementioned requirements. ____________________________________ _________________________ Student name (Please Print) Student signature / Date ____________________________________ Student email (Please Print) __________________________________ __________________________ Parent Name (please print) Parent signature / Date ________________________________________________ Parent email (Please Print) Progress reports will be emailed weekly, usually on Fridays. If you want to receive a weekly update, please provide your email address above. * The teacher reserves the right to make changes as he/she deems
Discrete Mathematics For Computer Science 9781930190863 ISBN: 1930190867 Pub Date: 2005 Publisher: Key College Publishing Summary: "Discrete Mathematics for Computer Science" is the perfect text to combine the fields of mathematics and computer science. Written by leading academics in the field of computer science, readers will gain the skills needed to write and understand the concept of proof. This text teaches all the math, with the exception of linear algebra, that is needed to succeed in computer science. The book explores the topics of bas...ic combinatorics, number and graph theory, logic and proof techniques, and many more. Appropriate for large or small class sizes or self study for the motivated professional reader. Assumes familiarity with data structures. Early treatment of number theory and combinatorics allow readers to explore RSA encryption early and also to encourage them to use their knowledge of hashing and trees (from CS2) before those topics are covered in this course. Bogart, Kenneth P. is the author of Discrete Mathematics For Computer Science, published 2005 under ISBN 9781930190863 and 1930190867. One hundred twenty four Discrete Mathematics For Computer Science textbooks are available for sale on ValoreBooks.com, nine used from the cheapest price of $4.50, or buy new starting at $23.31
Special Functions of Mathematics for Engineers, Second Edition Modern engineering and physical science applications demand a thorough knowledge of applied mathematics, particularly special functions. These typically arise in applications such as communication systems, electro-optics, nonlinear wave propagation, electromagnetic theory, electric circuit theory, and quantum mechanics. This text systematically introduces special functions and explores their properties and applications in engineering and science. Publishers' note: This new softcover printing of the Second Edition of Special Functions of Mathematics for Engineers, originally published by McGraw-Hill in 1992, includes known corrections to the text and formulas. Because of the importance of this material in modern engineering, SPIE The International Society for Optical Engineering and Oxford University Press are republishing it to make it available to the engineering, science, and mathematics communities. Modern engineering and physical science applications demand a more thorough knowledge of applied mathematics particularly special functions than ever before. These functions typically arise in applications such as communication systems, electro-optics, nonlinear wave propagation, electromagnetic theory, electric circuit theory, and quantum mechanics, among others. This book systematically introduces important special functions and explores their properties and applications in engineering and science. The book is suitable as a classroom textbook in courses dealing with higher mathematical functions or as a reference text for practicing engineers and scientists. The second edition includes numerous applications drawn from a variety of fields, including fiber optics, statistical communication theory, vibration phenomena, and fluid mechanics. Whenever possible, related applications are discussed in the chapter introducing the special function. The volume includes a brief review of calculus concepts, such as infinite series and improper integrals, because of their close association with special functions. Each chapter includes exercises to facilitate learning. Larry C. Andrews is a professor of mathematics at the University of Central Florida and a member of the Department of Electrical and Computer Engineering. Dr. Andrews is also an associate member of the Center for Research and Education in Optics and Lasers (CREOL). Along with special functions, his research interests include laser beam propagation through random media, detection theory, and signal processing.
College Algebra - 3rd edition Summary: These authors have created a book to really help students visualize mathematics for better comprehension. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition, the authors have added a variety of new tools to help students better use the book for maximum effectiveness to not only pass the course, but truly understa...show morend the material
Michael Hunt on Scheme and algebra High school math teacher Michael Hunt reports on his first three weeks of class: Class periods are 40 minutes twice a week and 45 minutes three times a week. We've completed day 12 (that is, 9.5 instructional days) and completed the area-of-ring problem today. We've also done convert3 along the way. My goal is to finish the first extended exercise with the ping-pong game (hopefully by Christmas). For context, the majority of my students "took" Algebra One at various (mostly private) schools in and around Houston last year in eighth grade, but did not score well enough on our diagnostic test to place out of Algebra One and into Geometry in ninth grade. A small minority of my students took Pre-algebra in eighth grade. A still smaller minority are repeating Algebra One, having failed it here as ninth graders last year. The pace deliberately favors these minorities of students and appears to be as fast as about 50% of the students can go. At the start, most of these students were unfamiliar with the word "function" and many could not either remember or apply the order of operations rules, for examples. Many are challenged to correctly compute arithmetic expressions without the use of a calculator. In fairness, students here historically have not been exposed to the word "function" in Algebra One until the last several weeks of the course. I am enthusiastically pleased so far with the results we've achieved in Algebra One, using Scheme. Nearly all of the students are now appropriately using words like "function" (and even composite function), "evaluate," and "substitute." I was thrilled to have been able to introduce the word "function" on the first instructional day, particularly with these students, without overwhelming them with all of the usual conceptual and notational overhead as well as I was thrilled to see so many students grasp this fundamental mathematical concept so effortlessly!
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The introduction describes this text as one which could be used for either an undergraduate or a graduate course. The text incorporates technology as a means of reducing computation and allowing students to create their own examples. It is written so as to accommodate either Mathematica or a freeware program entitled Groups, Algorithms and Programming (GAP). As an example of how this can simplify life for undergraduates, both Mathematica and GAP can verify (by brute force) that A5 is simple. However, such a brute force analysis doesn't really help us to see why A5 is a simple group. Based on my experience, undergraduate students will find the effort required to learn Mathematica or GAP notation to exceed the reward of creating the examples. The MAA software package Exploring Small Groups is much easier to use. Additionally, Excel will create modular arithmetic tables very easily. The table of contents suggests a traditional order of topics, with group theory being explored in full prior to the introduction of rings. However, the section and chapter headings often don't match up with what is actually covered. Homework problems are grouped at the end of each chapter. In the chapters I looked closely at, many of the key ideas and examples (e.g., the dihedral groups) appear only in homework problems. This book does not appear to be of sufficient depth or rigor for a graduate text, but the organization of the text makes it inappropriate for undergraduates as well. I outline some of those difficulties below, focusing on four of the chapters. Chapter One: Understanding the Group Concept As is common, the notion of a group is first introduced through the symmetries of an equilateral triangle. In this case the author introduces Terry the Dancing (equilateral) Triangle. Terry can perform six dance steps each of which corresponds to one of the six members of . Unfortunately, the pictures illustrating Terry's six moves do not illustrate results of the dance moves as described. Instead, the only pictures provided are taken from "the animation close to the completion of each step." As a result a rotation of 120 degrees clockwise is illustrated by a figure which appears to have been rotated 60 degrees. The figures illustrating the three reflections show triangles with are no longer equilateral! I think the reader deserves a set of pictures of Terry after he has completed each step. Without that it is not possible to verify the group table that the author presents. The result is that what could have been a very clever introduction is confusing. The confusion quickly deepens. After stating each of the group axioms in terms of dance steps (STAY is the name used for the "identity dance step.") At this point the group axioms have not yet been stated in any other terms, only described as dance steps, but we immediately proceed to the following proposition PROPOSITION 1.1 If y is an inverse of x, then x is the only inverse of y. While the Proposition as stated is true, I'm almost certain it was meant to be stated as: "if x is an inverse of y then x is the only inverse of y." At least that's what its "proof" proves! The next example considered is modular arithmetic. The first example is addition mod 10, but the notation used is a dot. That is a + b (Mod 10) is symbolized by a.b. As a result, we see (on page 7) the equation x.0 = 0.x = x. While true in this context, it is likely to be very confusing to beginning students. Part of the confusion is due to the Mathematica syntax which uses MultTable for any Cayley Table for a group, so that any group operation is "multiplication." The chapter also contains proofs of several facts from elementary number theory. Several of these proofs use the well-ordering of the positive integers, even though this theorem is never explicitly stated. I think these concepts are better reserved for a "chapter 0" (as Gallian and others do in their texts). The chapter concludes with the formal definition of a group. It does not, in my opinion, have enough examples of groups to give beginning students an idea of the richness of the group concept. Chapter Two: The Structure within a Group There is way too much information here for an undergraduate course. Among the topics (covered in 20 pages) are: generators, subgroups, cyclic groups, the group of units mod n, and some more number theory. At the undergraduate level, each of these concepts is probably worth a chapter in its own right. Here are examples of how condensed things are: The subgroup structure of cyclic groups is explored only in the homework. The group of units in Zn is defined in the middle of a paragraph in chapter 1. Some 16 pages later, Euler's totient function is proved to count the number of generators of Zn and an example of the group of units is given. S3 is defined, but there is no reference to the fact that this is part of a family of groups which will appear again in Chapter 5. Chapter 4: Mappings between Groups Here again, the material is highly condensed. The motivating example of an isomorphism is between a quotient group of the octahedral group and S3! After defining isomorphism, the author proceeds to an enumeration, with proofs, of all the groups (up to isomorphism) of order 8. D4 appears, of course — but the only time we have previously encountered this group is as problem 6 in chapter 1. In fact, there is no discussion of the dihedral groups to this point outside of D3 and D4. I can't imagine a typical undergraduate understanding, much less appreciating what's going on here. Why do we care how many groups of order 8 there are? The author then proceeds to proofs of the three classic isomorphism theorems. The only examples of these are in the exercises. I think undergraduates need lots more examples of actual isomorphisms before we lay all this theory on them. Chapter 9: Introduction to Rings The first section in this chapter begins by listing a few sets which admit two binary operations. We then leave ring theory altogether for a brief excursion into Cantor's set theory! The author defines a countable set and proves that the rational numbers are countable and that the real numbers are not. He then returns to the idea of two binary operations without any explanation as to what the previous few pages were about. The first example of a ring is Z6, the second is the quaternions. There is a discussion of zero divisors and the fact that elements which are not zero divisors don't always have inverses, but the notion of the group of units in Zn is not discussed. A great deal of space is devoted to the syntax needed to enter ring definitions into Mathematica and GAP — the result is that there are far fewer examples than I would like to see in an initial treatment of the ring concept. At this point, I think it fair to conclude that this text is not competitive with the many fine undergraduate and graduate texts available. I would not recommend this book as either an undergraduate or a graduate text. It is too condensed for an undergraduate text and doesn't provide enough depth for a graduate text. In addition, the presentation style is not conducive to student learning. While the use of Mathematica or GAP has great potential, it is not sufficient to overcome the deficiencies I observed in these five chapters. In fact, the numerous explanations of the use of Mathematica and GAP obscure the presentation. I think these would be more helpful as an appendix or a separate manual. Richard Wilders is Marie and Bernice Gantzert Professor in the Liberal Arts and Sciences and Professor of Mathematics at North Central College. His primary areas of interest are the history and philosophy of mathematics and of science. He has been a member of the Illinois Section of the Mathematical Association of America for 30 years and is a recipient of its Distinguished Service Award.
Preparing Mathematics for IIT JEE How to study Mathematics for IIT JEE and other Engineering Entrances Examinations? This question has been asked to me more number of times than any other question (by both students and their parents). Studying Strategy: Theory Part ØTheory part of any topic, is the most important part. ØTheory prepares your mind to solve problems and should be only studied slowly. Don't be in any kind of hurry while studying theory, ØAllow your mind to absorb every detail. ØAfter finishing a particular section, try reading it again. ØNow, when you're reading it for the second time, then it should be done in a little different manner. Here, you must try to teach the topic to yourself as if you are your own teacher. This will certainly help you in identifying you doubts which can lead to actually getting them clarified. ØAt the end, try to summarize the topic in your own way. Summarizing is compulsory for any section/topic and you must do it yourself. It gives you the overall idea about the topic, and helps you identify your strengths and weaknesses in the topic. How to Solve a Question ? 1.Reading the question properly : A lot of (a huge lot) students start attempting a question before even reading it properly. The most important aspect of a question is the question itself. A lot of students are unable to do a lot of problems Just because they don't understand the question properly. 2.Clarity about objective : Make up your mind about exactly what is asked in a particular question. 3.Analyze the given data : Read every piece of information carefully and try to use all the details to generate your solution. In some problems, if I get stuck and can't move ahead, then I follow this strategy. I'll see what all conditions/data is provided to me in the question and then I think how can I use it to my advantage. How to Solve Exercises I have mostly observed that a lot of students solve exercises like this: "They'll solve one question, open the back page and tally their answer. If it is right, then happily they'll move on to the next question. Otherwise, they'll go to their teacher for the correct solution." Demerits of the Above Approach are 1.It allows you to take a break whenever you want, thus decreasing your concentration span. 2.It doesn't have any feedback system i.e. you can't judge yourself in this manner. 3.It can't give you any idea of where you stand, your weaknesses, strengths etc. 4.It is not a very effective. 5.It is very boring. 'The 10-Problem Approach' 1.Select 10 problems. 2.Fix a time-frame - 20 to 30 mins (depending on your level) 3.Now, solve these 10 problems as if you're writing an exam. 4.Learn to leave the problem if you're getting stuck and a lot of time is being wasted. This will definitely help you in examination to identify solvable problems. 5.After finishing the 10 problems, re-attempt the questions which you did not get in the first time. 3.By checking your score, you can judge yourself about the clarity of your topic. 4.Helps you identity your strengths and weaknesses. 5.In the long run. you can see your success chart. By looking at your achievements, slowly you'll become more confident person and confidence is everything in IIT JEE. If you don't have confidence, then you can't get a great rank. 6.You can tell whether you're doing silly mistakes or not. 7.It will help in improving your calculation speed and accuracy. Generally students after getting the idea, leave the question (skip the calculation) and move on(Very BIG problem found in many students). 8.In order to score better in your 10 problems, you'll be compelled to do all the calculations and get the final answer.
027368180X 9780273681809 Essential Mathematics for Economic Analysis:"The book is by far the best choice one can make for a course on mathematics for economists. It is exemplary in finding the right balance between mathematics and economic examples."Dr Roelof J Stroeker, Erasmus University, Rotterdam."The writing style is superb…it manages to allow intuitive understanding whilst not sacrificing mathematical precision and rigour."Dr Steven Cook, University of Wales SwanseaEssential Mathematics for Economic Analysis provides an invaluable introduction to mathematical analysis and linear algebra for economists. Its main purpose is to help students acquire the mathematical skills they need in order to read the less technical literature associated with economic problems. The coverage is comprehensive, ranging from elementary algebra to more advanced material, whilst focusing on all the core topics usually taught in undergraduate courses on mathematics for economists. Back to top Rent Essential Mathematics for Economic Analysis 2nd edition today, or search our site for Knut textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson.
Description: This is an online text on universal algebra with a strong emphasis on applications and examples from computer science. The text introduces some basic algebraic concepts, such as signatures, algebras, homomorphisms, initial algebras, free algebras, and illustrates them with numerous interactive applications to computer science topics.
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Introduction to the Mathematics of Money: Saving and Investing - 07 edition Summary: This is an undergraduate textbook on the basic aspects of personal savings and investing with a balanced mix of mathematical rigor and economic intuition. It uses routine financial calculations as the motivation and basis for tools of elementary real analysis rather than taking the latter as given. Proofs using induction recurrence relations and proofs by contradiction are covered. Inequalities such as the Arithmetic-Geometric Mean Inequality and the Cauchy-Schwarz Inequality are use...show mored. Basic topics in probability and statistics are presented. The student is introduced to elements of saving and investing that are of life-long practical use. These include savings and checking accounts certificates of deposit student loans credit cards mortgages buying and selling bonds and buying and selling stocks. The book is self contained and accessible. The authors follow a systematic pattern for each chapter including a variety of examples and exercises ensuring that the student deals with realities rather than theoretical idealizations. It is suitable for courses in mathematics investing banking financial engineering and related topics
Statistics, Functions, and Rates of Change 1. To expose students to concepts in elementary statistics 2. To review basic concepts of algebra (including function notation, linear functions, and exponential functions) 3. To expose students to the concept of the derivative 4. To prepare students for MGT 235 Text Bruce Bowerman and Richard O'Connell. Business Statistics in Practice, Third Edition. McGraw-Hill, 2004. Course Notes: functions, linear functions, the distributive property and factoring, percentages, exponential growth, simplifying rational expressions, limits, average rate of change, introduction to derivatives (15 days) This material is to be covered to the extent that time allows. * Note: At appropriate places in this course, time should be allotted to elaborate on the historical aspects relevant to the subject.
Math Study Study Skillsoutlines good study habits and provides students with study strategies and tips to improve in areas such as time management, organization, and test-taking skills. With a friendly and relatable voice, Alan Bass addresses the misgivings and challenges many students face in a math class, and offers techniques to improve their study skills, as well as opportunities to practice and assess these techniques. This math study skills workbook is short enough to be used as a supplement in a math course, but can also be used as a main text... MORE in a study skills class.
Handed out a Mathematica sheet with a skeleton of an analysis, and used this information to thoroughly discuss what would have to be filled in for a complete analysis. Students should end their project with a summary of function behavior, making sure they include ALL intervals that are determined by key points. Day 44: Wednesday, 11/13 Worked on an Extreme Value Theorem type of problem from section 4.2. Completed problem # 18 from section 4.6. Collected "Plans" for the work students will do for the analysis of function for the final project. Day 43: Tuesday, 11/12 In lab. Worked on a family of functions exercise (# 35 from section 4.4) in class with students in preparation for next part of the final mathematica project. Discussed key ideas both for using Mathematica, as well as for working with this particular type of problem. Finished discussing exercise 34 from section 4.2, emphasizing the first derivative test and the second derivative test. Explained that students would use one or the other, but not typically both, to determine if the critical points they found were actually local max or local mins. Discussed how to find possible points of inflection, and discussed how you would use a graph of the second derivative to determine if you had a point of inflection for the original function. Monday, all students should come to class. Those who are not retaking the test will pick up the First Parts of the final project, and can go to the math lab to work. Those retaking the test will use class time on Monday for that activity. Worked on # 34 from section 4.2, and used it as an opportunity to review a lot of ideas involving trig. Handed out a yellow sheet covering some material for # 34 using Mahtematica. We will continue to discuss this problem in class on Friday. Day 39: Tuesday, 11/5 Hand back tests. Students will have an opportunity to take a re test on Monday, 11/11. If a student retakes the test, the grade on the retake will be the one that counts. Handed out a sheet on Information from Chapter 4. Worked on a problem from section 4.4 with students in the lab, showing them a number of things about using Mathematica for finding and analyzing critical points of the function, as well as finding and verifying points of inflection. The function we used had a clear turning point, but had two hidden points of inflection that are very difficult to see graphically. Day 38: Monday, 11/4 Test Hand back GW 5 with answers. Day 37: Friday, 11/1 Review for test. Test on Monday. Covers all material on the Practice Exercise Sheet for Unit Day 36: Wednesday, 10/30 Covered section 4.5 - L'Hopital's Rule for indeterminate forms. Did # 8, 10 and 14 as examples from page 296. Asked students to read the examples in the text book that deal with other indeterminate forms. Test will be on Monday. We will start Chapter 4 tomorrow. Friday will be a review day. Day 34: Monday, 10/28 Teacher out - Sick Day. Students should continue work on GW, and practice with derivatives. Day 33: Friday 10/25 Answered a few questions on practice homework. Reviewed information about inverses, and inverse functions. Started section 3.6. Worked with Sin, Cos and Tan, and talked about restricted domains so that we were working with a piece of the function which was 1 to 1. Developed the rule for the derivative of the sin inverse function using implicit differentiation. Students should work on section 3.1 - 3.5 over the weekend, and should also work on the GW 5. We will do some examples of finding derivatives for functions involving the inverse trig functions on Monday. Day 32: Wednesday 10/23 Talked a little more about GW 5. Handed back quizzes, and reinforced that students MUST be working with this material on a regular basis, and must be spending focused time ensuring they know the rules and how and when to use them. Covered section 3.5: Implicit Differentiation. First showed the example of a circle, where we solved for y in terms of x. Then showed how to use implicit differentiation to arrive at the answer. Reinforced that we are still finding the derivative which is the slope of the line tangent to a curve at a point. Day 31: Tuesday, 10/22 Worked with students to input a function, and it's Linearization. Talked about how the function L[x,a] could be used to generate any tangent line to the function it was associated with at the point x = a. Reviewed with students how to graph both functions in one window, and talked briefly about the focus of the next Graded Homework. Handed out GW 5, and had students work on the part that involved creating graphs and tables for the functions f and g and their linearizations. Day 30: Monday, 10/21 Quiz given at the beginning of class. Handed back GW 4 and discussed briefly. Did some more problems using the chain rule. Day 29: Friday, 10/18 Answered some questions from the practice exercises. Began the Chain rule. Worked on a number of examples Day 28: Wednesday, 10/16 Discussed the derivatives of the trig functions. Had students draw the sin curve, and sketch the derivative of this using skills from Chapter 2. We noticed it looked like the cosine curve. Then had students sketch the graph of the derivative of the cosine function, and saw that it looked like the opposite of the sine curve. Developed the derivative of the tangent by using the quotient rule. Also developed the derivative of the sec by using the fact that it is 1/cos x and used the quotient rule. Reviewed the other rules, and did a few examples. Announced that there would be a quiz on Monday on sections 1, 2 and 3. The quiz will focus only on the basic skills, not on the conceptual problems. Day 27: Friday, 10/11 Handed cards out to students with their mid term grades on them, and asked them to make sure it agreed with their own computation. Discussed the product rule and quotient rule, and did a number of examples. Have a great Holiday weekend! Practice finding derivatives on at least one day! Day 26: Wednesday, 10/9 Presented how to think about finding the derivative of an exponential function from both a graphical and an algebraic point of view. Proved to the students that the derivative of an exponential function is some constant multiple of that same exponential function. Worked numerically to see what the constant was. Demonstrated the connection between the constant we found through a limiting process, and the ln(base). We cannot yet prove this is the derivative, but have a strong inclination that it is! Day 25: Tuesday, 10/8 Handed back tests, and talked briefly about what was required to really "know" the material at hand. Worked on Mathematica with students to input a cube root function, and to create the appropriate tables of difference quotients that help us determine whether or not a derivative exists at a particular point for the function. Handed out GW 4, and explained that question 2 would entail the same type of work. Question 1 will explore the concept of where a derivative may not exist, and we will work on the required tables together in lab tomorrow. Began section 3.1 - and covered the rules for derivatives up to the exponential functions. Day 23: Friday, 10/5 Test. Gave each student the take home piece, which is due at the beginning of class on Monday. Day 22: Wednesday, 10/2 Reviewed answers to Sheet 4 and 5. Reviewed for test # 2. Test is on Friday, and will cover sections 2.6, the parts of 2.7 that we discussed, and 2.8 The In class Test WILL NOT have a table of derivative values on it, or a harder function to work with in terms of finding a derivative algebraically. These will be on a take home part for the test. The in class test WILL expect that students can algebraically find the derivative of a quadratic function. Day 21: Tuesday, 10/1 Handed back GW 3. Spent a little time discussing a few things about the assignment. Used the Exploring Derivatives sheet 3 to walk students through how we would sketch a graph of the derivative based on the graph of a function. Had students try this on their own with sheet 4. Also worked through the data for the derivative and second derivative from Sheet 3. Day 20: Monday, 9/30 Discussed the idea of a second derivative. Worked on the yellow sheets on derivatives (Sheet 2, Sheet 3 , Sheet 4 and 5). These sheets help to relate the information from the gold sheet to both graphs and tables of values. Day 19: Friday, 9/27 Handed out Sheet for Exploring Derivatives - Sheet 1, and used that information to help students understand the relationship between a function and it's derivative. We examined what was true about the derivative if a function was increasing, decreasing, turning, concave up or concave down. Day 18: Wednesday 9/25 Discussed exactly what the values in the tables we created on Mathematica represented: Each value is an Average Rate of Change between 2 points. We picked a particular value, and clearly wrote out what it represented very specifically. Worked through finding a derivative as a function of x. Worked through the function we had previously used to find the derivative at a point, and instead found the derivative as a function. Day 17: Tuesday 9/24 Handed back Test# 1 with answer key. Also gave out a Gold sheet with an extra point opportunity for Success Strategies, and encouraged students to take advantage of doing a Test Analysis and meeting with Lou. I must receive this within one week for credit. Introduced new terminology for the slope of the secant line that we developed yesterday. Called it the Average Rate of Change (ARC) or the Difference Quotient. Worked with students on creating the definition of the Difference Quotient in Mathematica, and then setting up tables to explore the limiting value of the Average Rates of change between 5 and 5 + h. Emphasized the terminology and notation. Had students complete the work in Mathematica for that section. Day 16: Monday, 9/23 Answered questions on GW 3 which is due in at the BEGINNING of class tomorrow. Papers should already be printed and stapled before class. Students WILL NOT be allowed to print their assignments in the computer room. Began section 2.6 - discussed how we would approach finding the slope of a line tangent to a function at a given point by using what we already know about slope between two points. Showed how we would set up the slope of a secant line in general terms of a and h, and discussed that the limit of these slopes as h approached 0 from both sides would be the slope of the tangent line. Worked on Exercise 4, and set up the general form of the slope of a secant line if x = 1 was our point of interest. Day 15: Friday, 9/20 Test # 1 Day 14: Wednesday, 9/18 Review for Test # 1. Discussed the procedure for getting Success Strategy Points for the Practice Exercises. Emphasized that packets would ONLY be collected at the beginning of the test. No packets would be considered later. The Purple Practice Exercise sheet MUST be completely filled out in order for points to be awarded. Discussed the composition of the test, how it was laid out, and how to best prepare for the test. Day 13: Tuesday, 9/17 Students had the opportunity in the lab to work on Graded Work 3. Day 12: Monday, 9/16 Handed back GW 2 with answers chosen from student papers. Discussed some of the issues that I saw with the assignment, and explained why I chose the answer papers I did. Again reiterated that graded work was supposed to be an example of the student's best work! Explanations were ESSENTIAL, and needed to be written in a manner that another student from the class would understand what was being done and why. Covered section 2.4 - continuity. Wrote what the three conditions for continuity were, and went through how to use the definition step by step to determine if a function was continuous at a point. Again, students should be reading some of the additional work in the text book to supplement what we discussed in class. Day 11: Friday, 9/13 Handed out Graded Work 3 and spent some time in class discussing it. Students should be reading through the assignment this weekend, and potentially starting it on Mathematica. At the very least, students need to have started the assignment by lab time on Tuesday. This project will take several hours to complete clearly and completely Covered section 2.3 - Algebraically computing limits. Went through a number of exercises, and showed students some algebraic "tricks" to use if plugging the value directly into the expression led to indeterminate form (0/0). Students should be reading through the examples worked out in the text book for additional information before beginning the practice exercises in this section. Day 10: Wednesday, 9/11 Handed back Quiz 1 to AM class (had handed it back on Monday to PM class). Had students enter grades on the back of their success Strategies grade sheet. Again emphasized how important it was for students to make sure they are keeping track of their grades throughout the semester. Reminded students to continue working with tables. They will also be using Section 13 from their manuals on the next graded work, so they should review that work too. Quickly reviewed what we had done on Monday, and picked up discussion from there. Reminded students to be reading the textbook so that they are "hearing" the information again. Pointed out some particularly good areas of the book. Worked on exercise 4 from section 2.5, as well as # 22. Students should be working on practice exercises from sections 2.2 and 2.5. TEST on this unit will be given on Friday, September 20th. Day 9: Tuesday, 9/10 Mathematica quiz in class. After finishing the quiz, students began work on Section 14 of their manual. Students MUST continue work with tables outside of class. Day 8: Monday, 9/9 Collected GW 2. Handed out Practice Exercises for Unit 1 (Purple) Reminded students that these were not really optional.... though I did not collect them and grade them. Students CAN get success strategy points for the practice exercises. Discussed making sure to put the cursor at the end of a plot command line but inside the last ] if manual positioning is on, and you want to add some features to the command. You MUST type a comma between different commands. Talked briefly about quiz tomorrow. Began section 2.5, Limits involving infinity. Looked at a situation as we approached a particular input value where the function was undefined, but where from one side the output values increased without bound, and from the other side, the output values decreased without bound. Showed the symbolic notation, and talked about why the language in the book is somewhat problematic. We will finish section 2.5 on Wednesday. Day 7: Friday, 9/6 Handed out some practice quizes that I have given in earlier semesters for Mathematica. Discussed that there were elements missing on these quizzes that students needed to be comfortable with - including e^x, ln(x) the cube root function, and the trig functions. These are just meant as a starting place for students, not as a mirror image of what the quiz next Tuesday will be like. Pointed out some key definitions in the text book for section 2.2. I do not write all of this on the board, as it is in the book, but students must be reading their book, and potentially adding to their notes. Emphasized the definition of a limit, and the fact that a limit is a real number. Worked through Exercise 6 on page 102 with the class, using this as a way to talk again about one and two sided limits. Worked through most of Example 4 on page 98 in the text book, using that as a way to explain why a numerical approach is not always sufficient. Students should make sure they are reading the text book to supplement the material we cover in class. Day 6: Wednesday, 9/4 Began section 2.2. Worked with a rational function that was not defined at 1, and established how we would investigate this situation numerically, verbally, symbolically and graphically. Established the patterns I expect students to use in terms of "getting close" to an input value. Emphasized that the language is important. We will continue with this material on Friday. Students should be working on Graded work 2, as well as Mathematica outside of class. Day 5: Tuesday, 9/3 Allowed students to work on sections 1 - 6 from the Mathematica manual if they had encountered problems over the weekend. Collected the hard copy of this material from all students by the end of class, and had students make sure they emailed me the file in the event that I have to look at it. Students who had completed sections 1 - 6 worked on sections 7 - 13. Emphasized that there would be a quiz on all the core skills contained in sections 1 - 13 except for section 7 during the next lab. Students MUST be practicing regularly with the material outside of class. They will not have access to any instructions for the quiz. Day 4: Friday, 8/30 Handed out the green Success Strategies Grade Sheet. Handed out the Take Home Replacement for Quiz 1 (Blue). Students need to print out a hard copy for class on Tuesday, and have an electronic copy available to send me during lab on Tuesday. Handed out instructions for signing into WebAssign (sheet is not available electronically - see me if you didn't get one). There will be a specific assignment involving that program next week. If students bought a new book from our bookstore, they should have received an access card that gives them free access to this site for the semester. All students have a 14 day trial period available. Had students meet together in small groups to continue to get to know others in the class. Quickly reviewed the review questions 1, 2, 3 that students had worked on on Monday. Had students continue working on exercise # 6. Students MUST be working on Mathematica outside of class. Also, remember that Graded Work 1 is due on Friday. Day 2: Tuesday 8/27 Met in computer lab. Showed students how to log in to nsflab account with the password reason. Showed them how to open and begin working in Mathematica. Referenced them to the manual, as we worked through parts of section 1 and 2 to familiarize them with writing text, inserting mathematics in a text region, and defining and graphing functions. Emphasized how important it was to be consistently working with Mathematica over the next couple of weeks so as to become proficient with the 7 basic skills. Students will be completing work on sections 1 through 6 in lieu of a quiz in lab next Tuesday. I will show students how to save their work in their Angel Toolbox by the end of this week to ensure they have access to their work on Tuesday. Had students fill out Course Information cards. Had students meet some other students in class, and begin to discuss the first three questions from the Chapter 1 review. Students should have notes in the blue books provided for each of these questions. We will review answers on Wednesday.
Middle School Course Offering will be posted shortly, please check back Math The 21st century takes us into a new era in mathematics education. Changes in technology have made mathematics an alive and dynamic science in itself, as well as an integral part of our daily lives. Now, more than ever before, educating students for life requires that we provide all students with a strong mathematical background. Elementary Program The mathematical instructional approach implemented in kindergarten and first grade classrooms and is based on the recognition of mathematical concepts in the everyday experiences of children. Beginning in elementary school, the mathematics program focuses on the development of critical thinking and problem solving strategies. The use of various manipulatives enables children to enjoy a hands-on approach to learning. Computer software is used to facilitate the acquisition of math skills. Students participate in small group activities where they learn to listen and consider the ideas of others in solving problems. Students continually communicate mathematical ideas and solutions and explain their reasoning. Middle School Program At the middle school level, students continue to use manipulatives, calculators and computer software, as well as paper and pencil, mental math, and estimation where appropriate. Real-life applications and cooperative learning are incorporated into the program. Communication skills of reading, writing and discussion are further developed. Grades six, seven and eight are taught by interdisciplinary teams and students are able to connect mathematics to other disciplines. Honor students accelerate in grade eight and take the NYS regents course, Integrated Algebra, culminating with a regents exam in June. All other eighth grade students take a pre-algebra course in preparation for Integrated Algebra in grade nine. Additionally, seventh graders take the Math Seminar course, which introduces students to explorations of mathematics that extend and enrich the current curriculum with topics such as origami, fractals and Sierpinski's Triangle, and magic squares. High School Program At the high school level, the mathematics department follows the new New York State curriculum of Integrated Algebra, Geometry and Algebra 2 Trigonometry. Students completing the required sequence of courses are offered electives, highlighted by our AP Statistics and Computer Science classes. Within the department, over 200 students are enrolled in Advanced Placement courses, including AP Calculus AB, AP Calculus BC, AP Statistics, and AP Computer Science. Those who do not wish to take Advanced Placement math courses may choose from Honors College Calculus, Advanced Computer Programming, Pre-Calculus or College Prep Algebra. The high percentage of students taking four or more years of mathematics is a measure of the success of our program. Technology The use of technology is expanding throughout the district. Since graphing calculators are allowed on state assessments, students receive instruction on the use of these devices. Graphing calculators are also used to enhance teaching in calculus, pre-calculus and elective mathematics courses. Teacher Workshops Mathematics teachers are continously staying up to date with the ever changing standards our students are accountable for understanding. All along, we continue to keep a focus on instruction that fosters perseverence, critical and logical thinking while also enfusing joy within our practice. The accomplishments of the mathematics department are the result of dedicated professionals, involved parents, and motivated students striving for excellence
Find a Cortaro MathIn Algebra students will learn to solve equations (1st and 2nd degree) by connecting and disconnecting numbers and letters that represent numbers. I will ask them to "al-jabr". It was once known as the Cossic Art. "Coss" is Latin for "the thing
Description 102 Combinatorial Problems consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. The text provides in-depth enrichment in the important areas of combinatorics by systematically reorganizing and enhancing problem-solving tactics and strategies. The book gradually builds combinatorial skills and techniques and not only broadens the student's view of mathematics, but is also excellent for training teachers102 Combinatorial Problems: From the Training of the USA Imo Team102 Combinatorial Problems: From the Training of the USA Imo Team
Mathematics All students in Years 10 and 11 follow a course in Mathematics appropriate to their ability and needs. For the majority of students this will lead to a final GCSE examination. In formulating the courses on offer to the students, regard has been taken of three main principles:- 1. That the methods of teaching and assessment aim to develop the full potential of the individual. 2. That the methods of teaching and assessment should enable each student to demonstrate what they know rather than what they do not know. 3. That the examination and coursework should not undermine the confidence of the candidate. Students are taught in sets comparable to their ability. Movement between sets is possible at various times during the year. Students cover the following courses, depending upon which set they are placed. Our overall intention is to develop the Mathematical ability of the individual to its full potential. Further information on the various courses on offer is available from any Mathematics teacher. Any students deemed to be near the C/D border potentially will be allocated an extra period of "Study Plus" Mathematics to help ensure they reach the desired C grade
9781565770Saxon Advanced Math: Student Edition Second Edition 1996 Advanced Mathematics fully integrates topics from algebra, geometry, trigonometry, discrete mathematics, and mathematical analysis. Word problems are developed throughout the problem sets and become progressively more elaborate. With this practice, high-school level students will be able to solve challenging problems such as rate problems and work problems involving abstract quantities. Conceptually oriented problems that help prepare students for college entrance exams (such as the ACT and SAT) are included in the problem sets
Prerequisites: High School Algebra I, II and Geometry or Math Placement Testing/Evaluation before registration. For students who need to improve their algebraic skills before taking a higher level course such as MATH 160 or 161, this course focuses on algebraic topics deemed most important for success in college mathematics and its applications. Topics covered include the real number system, linear equations and inequalities, word problems, polynomials and factoring, rational algebraic expressions, exponents and radicals, quadratic equations, irrational equations, graphs of equations, systems of equations, and logarithmic and exponential functions. [syllabus]
Download CK-12 Middle School Math Concepts - Grade 8 Table of Contents Loading Contents Description CK-12 Foundation's Middle School Math Concepts - Grade 8 is a standard, complete middle school school math course covering common core 8th grade standards. This preview version is being released in stages several chapters at a time.
Groups and Geometry Peter M. Neumann, Gabrielle A. Stoy, and the late Edward C. Thompson Description This volume presents the Oxford Mathematical Institute notes for the enormously successful advanced undergraduate and first-year graduate student course on groups and geometry. The book's content closely follows the Oxford syllabus but covers a great deal more material than did the course itself. The book is divided into two parts: the first covers the fundamentals of groups, and the second covers geometry and its symbiotic relationship with groups. Both parts contain a number of useful examples and exercises. This book will be welcomed by student and teacher alike as a lucidly written text on an important topic.
math concepts for professional chefs and culinary students Ideal for students and working professionals, Math for the Professional Kitchen explains all the essential mathematical skills needed to run a successful, profitable operation. From scaling recipes and converting units of measure, to costing ingredients and setting menu prices, it covers crucial information that will benefit every foodservice provider. Written by three veteran math instructors from The Culinary Institute of America, the book utilizes a teaching methodology based on daily in-classroom practice. The entirety of the standard culinary math curriculum is covered, including conversions, determining yields, purchasing, portioning, and more. This is a thorough, comprehensive main text for culinary students as well as a great kitchen reference for working professionals Math for the Professional Kitchen will be an invaluable resource not only in the classroom but also in the kitchen as students embark on their professional careers, where math skills play a crucial role in the ever-important bottom line.
Based on fundamental principles from mathematics, linear systems, and signal analysis, digital signal processing (DSP) algorithms are useful for extracting information from signals collected all around us. Combined with today's powerful computing capabilities, they can be used in a wide range of... In a field as rapidly expanding as digital signal processing, even the topics relevant to the basics change over time both in their nature and their relative importance. It is important, therefore, to have an up-to-date text that not only covers the fundamentals, but that also follows a logical... Published August 27
״MATH GRAPHING XL is a powerful & unique 1D graphing calculator to graph mathematical expressions of arbitrary... see more ״MATH GRAPHING XL is a powerful & unique 1D graphing calculator to graph mathematical expressions of arbitrary complexity. It can help students improve their math skills by developing some visual intuition of mathematical expressions or advanced users who need some scientific capabilities only available with expensive desktop software.MATH GRAPHING XL provides the following functionalities:- Multiple expressions with quasi-unlimited number of variables can be combined to produce simple or complex formulas,- Interactive sliders can be created to visually investigate the role of important parameters on the graphical representation of the formulas,- Trace mode to display coordinates and derivative of marker on selected curve,- Solver tool to solve y = f(x) where x or y are unknown, or find local/global minima/maxima/extrema (NEW!),- Formula graphs can be saved to the device's Photos Album, or the formulas be exported through email with embedded graphs,- A list of favorite formulas can be created for editing or archival purposes,- Several formulas can be plotted simultaneously in different colors and styles,- Customizable graph and formula appearance: axes labels, title, curve color and style, ticks number, grid, wallpaper, font, font size, etc.- Single-precision calculator supporting variables, multiple expressions, and on-the-fly evaluation (NEW!).Example of mathematical expression:# Gabor functionx = 0:1:100sigma = 1:50; freq = 0:0.1; phase = 0:180u = cos(2pi(x-50)freq+phasepi/180)v = e^(-((x-50)^2)/(2sigma^2))y = uvplot(u,'lr'); plot(v,'lg'); plot(y,'lw')xlabel('time'); ylabel('amplitude')title('Gabor')״Cost of this app is $9My intention was to showcase how literacy activities can be incorporated into core subjects, such as mathematics, in such a... see more My intention was to showcase how literacy activities can be incorporated into core subjects, such as mathematics, in such a way that makes content fun, yet educational. Math is often an area that deters and confounds students, so I knew I wanted the lesson to be visually appealing and motivational, as well as educational, so I choose to adopt a top secret mission theme to help students learn to add. Not only does this app include educational videos, superior visuals, and user- friendly language, but the makers of this app... see more Not only does this app include educational videos, superior visuals, and user- friendly language, but the makers of this app incorporated 4 levels of Bloom's Taxonomy. The levels of Bloom's included in the game are knowledge, comprehension, analysis, and application. Data analysis is one of the subjects covered in the mathematics section. What's good about this app is that it teaches across the board. Reading, science and math are all incorporated. Also, this app is 100% free from third party advertisement. Cost is $4.99.
Relationship to Outcomes: Students who have successfully completed this course should have achieved: Course Outcomes ABET Outcomes An ability to apply knowledge of mathematics, science, and engineering A An ability to identify, formulate, and solve engineering problems E An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice. K Expanded Course Description: Engineering Computational Problem Solving Matlab Technical Computing Environment Interactive workspace Scalar mathematics Accuracy and computational limitations Files and File Management Definitions and commands Saving and restoring information Designing, editing, and executing scripts Scalar Mathematics Trigonometry Complex numbers Two-dimensional graphics Arrays and Array Operations Vector and matrix arrays Array operations Array plotting Mathematical Functions Signal representation, processing, and plotting Polynomial functions Functions of two variables User-defined functions Data Analysis Maximum and minimum Sums and products Statistical analysis and random number generation Selection Programming Relational and logical operators Flow control Loops Selection statements and functions Vectors, Matrices, and Linear Algebra Vectors and matrices Solutions to systems of linear equations Curve Fitting and Interpolation Least squares curve fitting One-dimensional and two-dimensional interpolation Integration and Differentiation Symbolic Mathematics Symbolic objects, variables and expressions Operations on symbolic expressions Differentiation and integration Textbooks: A. Gilat, MATLAB: An Introduction with Applications, Wiley. D. Smith, Engineering Computation with MATLAB, Addison Wesley. Software: Matlab (student edition) Computer Use: Students are required in problem assignments to write substantial programs in the MATLAB technical computing environment. Engineering Design Statement: Students are asked to design programs to solve problems in which the problem statement is only partially defined. Students must describe and define the problem, define specifications, design and implement an algorithm to meet the specifications, test the algorithm with a variety of data, and redesign the algorithm as needed. The nature of the assignments require iterative refinements of the solution algorithm.
Guys, I need some help with my algebra assignment. It's a really long one having almost 30 questions and it covers topics such as 10th std state syllabus maths very important objectives with answers and steps, 10th std state syllabus maths very important objectives with answers and steps and 10th std state syllabus maths very important objectives with answers and steps. I've been trying to solve those questions since the past 4 days now and still haven't been able to solve even a single one of them. Our teacher gave us this assignment and went on a vacation, so basically we are all on our own now. Can anyone show me the way? Can anyone solve some sample questions for me based on those topics; such solutions would help me solve my own questions as well. I have a way out for you and trust me it's even better than buying a new textbook. Try Algebrator, it covers a rather elaborate list of mathematical topics and is highly recommended. With it you can solve various types of problems and it'll also address all your enquiries as to how it came up with a particular answer. I tried it when I was having difficulty solving questions based on 10th std state syllabus maths very important objectives with answers and steps and I really enjoyed using it. Thanks for the detailed instructions, this sounds great. I wished for something just like Algebrator, because I don't want a software which only solves the exercise and gives the final result, I want something that can actually show me how the exercise has to be solved. That way I can understand it and after that solve it without any help, not just copy the answers. Where can I find the program?
Math 60 (Pre-Algebra) Online Fall Semester 2013 CRN: 73766 Section: OL2 Final Exam is on Friday December 6, 8:00 to 9:10 AM (70 minutes allowed) in our class room, SV3K. Get there early for a little extra time. Bring your calculator for the exam. You are not allowed to use a cell phone for a calculator, phones must be turned off and put away. As was done for midterms, you'll use backside of exam sheets for scratch paper, you will not be allowed to use your own paper. The exam was produced by the Math Department. It is closed book and will cover the entire course. There are 25 questions on the exam. 16 questions are multiple choice covering Student Learning Outcomes (SLO's). The rest you will give the answer. Many questions will be of similar type as the midterms so review your midterm exams. Questions on subjects covered since the last midterm will be on the exam. These subjects are Percentages with Applications (Chapter 8), Reading Graphs (9.2), Plotting Points and Linear Equations (9.4), and Measurements (Chapter 10). For units of measurements, know how to convert between inches, feet and yards. Know how to add measurements given in feet and inches. For metric measurements, know how to convert between basic units and centi, for example 1 centimeter = .01 meter and 1 meter = 100 centimeters. Know how to convert between basic units and kilo, for example 1 kilometer = 1000 meters. There will be no conversions between English and Metric systems. Know how to compute area and circumference of circles. Those formulas can be useful in everyday life plus you will need to know them in Math 70 and Math 102 -- so you may as well learn them now. You will be given the value to use for π. FinalReview.pdf See this link for review questions (produced by AVC Math Department). Answers are at the end.
Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition.
Course Description Description This course is designed to extend skills in problem solving, to foster mathematical creativity, and to introduce the fundamentals of proof. Students learn to think at an advanced level as they tackle challenging problems. Topics addressed in this course will draw from: number theory set theory algebra geometry Each week, students explore a different math topic or problem-solving strategy in depth, and practice both non-routine and contest problems. Additionally, they will learn to create inductive and deductive proofs, with a focus on the proper use of notation and terminology and precision in their writing. The web-based virtual classroom provides interactive and team-building experiences for students. Each topic covered in the course is independent of the other topics. One topic is taught a week on a continuous repeating basis. Students will not necessarily start with "Topic 1" in their first week of enrollment, but all topics will be covered in a 3-month enrollment. When all topics are covered, a student then takes the final exam. Materials Needed There are no required materials for this course. List of Topics The following topics will be covered in the course: Patterns, Sequences and Series Sets and Venn Diagrams Numbers and Counting Primes and Factorizations Rational, Real, and Complex Numbers Exponents and Roots Modular Arithmetic and Bases Relations and Functions Angles, Triangles, and Triples Coordinate Geometry Circles Virtual Classroom Session Times Session Times This course uses an online virtual classroom with text, drawing, and video tools to hold group discussions. Instructions and details are posted on the course website for enrolled students. Virtual Classroom Demo Demo Click on the image below to view a demo of Adobe Connect: System Requirements All CTYOnline courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer). Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc). This course uses an online classroom for individual or group discussions with the instructor. The classroom works on standard computers with the Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile app.
Offering 8 subjects including precalculus
Our intuitions about sets, numbers, shapes, and logic all break down in the realm of the infinite. Seemingly paradoxical facts about infinity are the subject of this course. We will discuss what infinity is, how it has been viewed through history, why some infinities are bigger than others and how a finite shape can have an infinite perimeter. This will very likely be quite different from any mathematics course you have ever taken. Surprises at Infinity focuses on ideas and reasoning rather than algebraic manipulation, though some algebraic work will be required to clarify big ideas. The class will be a mixture of lecture and discussion, based on selected readings. You can expect essay tests, frequent homework, and writing assignments. No prerequisites. Offered typically every one to two yearsThe first in a three-semester calculus sequence, this course covers the basic ideas of differential calculus. Differential calculus is concerned primarily with the fundamental problem of determining instantaneous rates of change. In this course we will study instantaneous rates of change from both a qualitative geometric and a quantitative analytic perspective. We will cover in detail the underlying theory, techniques, and applications of the derivative. The problem of anti-differentiation, identifying quantities given their rates of change, will also be introduced. The course will conclude by relating the process of anti-differentiation to the problem of finding the area beneath curves, thus providing an intuitive link between differential calculus and integral calculus. Those who have had a year of high-school calculus but do not have advanced placement credit for MATH 111 should take the calculus placement exam to determine whether they are ready for MATH 112. Students who have .5 unit of credit for calculus may not receive credit for MATH 111. Prerequisites: solid grounding in algebra, trigonometry, and elementary functions. Students who have credit for MATH 110Y-111Y may not take this courseThis course focuses on choosing, fitting, assessing, and using statistical models. Simple linear regression, mulitple regression, analysis of variance, general linear models, logistic regression, and discrete data analysis will provide the foundation for the course. Classical interference methods that rely on the normality of the error terms will be thoroughly discussed, and general approaches for dealing with data where such conditions are not met will be provided. For example, distribution-free techniques and computer-intensive methods, such as bootstrapping and permutation tests, will be presented. Students will use statistical software throughout the course to write and present statistical reports. The culminating project will be a complete data analysis report for a real problem chosen by the student. The MATH 106-206 sequence provides a thorough foundation for statistical work in economics, psychology, biology, political science, and many other fields. Prerequisite: MATH 106 or MATH 116. Offered every spring major majorIn biological sciences, mathematical models are becoming increasingly important as tools for turning biological assumptions into quantitative predictions. In this course, students will learn how to fashion and use these tools to explore questions ranging across the biological sciences. We will survey a variety of dynamic modeling techniques, including both discrete and continuous approaches. Biological applications may include population dynamics, molecular evolution, ecosystem stability, epidemic spread, nerve impulses, sex allocation, and cellular transport processes. The course is appropriate both for math majors interested in biological applications, and for biology majors who want the mathematical tools necessary to address complex, contemporary questions. As science is becoming an increasingly collaborative effort, biology and math majors will be encouraged to work together on many aspects of the course. Coursework will include homework problem-solving exercises and short computational projects. Final independent projects will require the development and extension of an existing biological model selected from the primary literature, using mathematical software like Mathematica, Matlab, R, or Maple. Students will make a poster presentation of their results. Prerequisites: This course will build on (but not be limited by) an introductory-level knowledge base in both subjects, including MATH 111 and either BIOL 112 or BIOL 113. Interested biology and math majors lacking one of the prerequisites are encouraged to consult with the instructor. Offered every other year. Coding theory, or the theory of error-correcting codes, and cryptography are two recent applications of algebra and discrete mathematics to information and communications systems. The goals of this course are to introduce students to these subjects and to understand some of the basic mathematical tools used. While coding theory is concerned with the reliability of communication, the main problem of cryptography is the security and privacy of communication. Applications of coding theory range from enabling the clear transmission of pictures from distant planets to quality of sound in compact disks. Cryptography is a key technology in electronic security systems. Topics likely to be covered include basics of block coding, encoding and decoding, linear codes, perfect codes, cyclic codes, BCH and Reed-Solomon codes, and classical and public-key cryptography. Other topics may be included depending on the availability of time and the background and interests of the students. Other than some basic linear algebra, the necessary mathematical background (mostly abstract algebra) will be covered within the course. Prerequisite: MATH 224, or permission of the instructor. Offered every two to three years. Differential equations arise naturally to model dynamical systems such as often occur in physics, biology, chemistry, and economics, and have given major impetus to other fields in mathematics, such as topology and the theory of chaos. This course covers basic analytic, numerical, and qualitative methods for the solution and understanding of ordinary differential equations. Computer-based technology will be used. Prerequisite: MATH 224 or PHYS 245 or permission of the instructor. Offered every spring. This course is a first introduction to real analysis. "Real" refers to the real numbers. Much of our work will revolve around the real number system. We will start by carefully considering the axioms that describe it. "Analysis" is the branch of mathematics that deals with limiting processes. Thus the concept of distance will also be a major theme of the course. In the context of a general metric space (a space in which we can measure distances), we will consider open and closed sets, limits of sequences, limits of functions, continuity, completeness, compactness, and connectedness. Other topics may be included, if time permits. Prerequisites: MATH 213 and MATH 222. Junior standing is usually recommended. Offered every year. The course starts with an introduction to the complex numbers and the complex plane. Next students are asked to consider what it might mean to say that a complex function is differentiable (or analytic, as it is called in this context). For a complex function that takes a complex number z to f(z), it is easy to write down (and make sense of) the statement that f is analytic at z if exists. In the course we will study the amazing results that come from making such a seemingly innocent assumption. Differentiability for functions of one complex variable turns out to be a very different thing from differentiability in functions of one real variable. Topics covered will include analyticity and the Cauchy- Riemann equations, complex integration, Cauchy's theorem and its consequences, connections to power series, and the residue theorem and its applications. Prerequisite: MATH 224. Offered every other year. Abstract Algebra II picks up where MATH 335 ends, focusing primarily on rings and fields. Serving as a good generalization of the structure and properties exhibited by the integers, a ring is an algebraic structure consisting of a set together with two operations--addition and multiplication. If a ring has the additional property that division is well-defined, one gets a field. Fields provide a useful generalization of many familiar number systems: the rational numbers, the real numbers, and the complex numbers. Topics to be covered include: polynomial rings; ideals; homomorphisms and ring quotients; Euclidean domains, principal ideal domains, unique factorization domains; the Gaussian integers; factorization techniques and irreducibility criteria. The final block of the semester will serve as an introduction to field theory, covering algebraic field extensions, symbolic adjunction of roots; construction with ruler and compass; and finite fields. Throughout the semester there will be an emphasis on examples, many of them coming from calculus, linear algebra, discrete math, and elementary number theory. There will also be a heavy emphasis on the reading and writing of mathematical proofs. Prerequisite: MATH 335. Offered every other spring. This course will consist largely of an independent project in which students, read several sources to learn about a mathematical topic that complements material studied in other courses, usually an already completed depth sequence. This study will culminate in an expository paper and a public or semi-public presentation before an audience consisting of at least several members of the mathematics faculty as well as an outside examiner. Prerequisites: At least one "depth sequence" completed and permission of the department.
A series of applets for teaching Fractal Geometry. Includes: L-Systems; Box-Counting Fractal Dimension; Cellular Automata;... see more A series of applets for teaching Fractal Geometry. Includes: L-Systems; Box-Counting Fractal Dimension; Cellular Automata; Iterated Function Systems (deterministic, random, data-driven, and with memory); Pascal's Triangle; Circle Inversion; Limit Sets of Circle Inversion. The online course materials that go with this applet series is at . This course is taught to high school math teachers as well as university students. This is a page of links to applets that can be used in courses below the level of calculus. Most of these applets have... see more This is a page of links to applets that can be used in courses below the level of calculus. Most of these applets have been constructed at Saint Louis University Department of Mathematics and Computer Science. Some applets are designed to explore triangle construction or to illustrate various theorems from geometry and trigonometry. Other applets deal with the construction of graphs of functions, conics, and vectors. Math Water Table is an online liquid simulator. (Former obbliq)To get the area of a limited number of shapes (rectangles and... see more Math Water Table is an online liquid simulator. (Former obbliq)To get the area of a limited number of shapes (rectangles and triangles)To verify the area formulas of some limited geometrical shapes.Video help at: Ideas: useful to explain multiplication and division. The old program is in the mirror link. NonEuclid is Java Software forinteractively creating ruler and compass constructions in both thePoincaré Disk and the Upper... see more NonEuclid is Java Software forinteractively creating ruler and compass constructions in both thePoincaré Disk and the Upper Half-Plane Models of Hyperbolic Geometryfor use in high school and undergraduate education.
Schaum's Outline of Theory and Problems of Matrix Operations 9780070079786 ISBN: 0070079781 Pub Date: 1988 Publisher: McGraw-Hill Summary: Master matrix operations with Schaum'sthe high-performance study guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Outlines because they produce results. Each year, hundreds of thousands of students improve their test scores and final grades with these indispensable study guides. Get the edge on your classmates. Use Schaum's!If you d...on't have a lot of time but want to excel in class, this book helps you: Brush up before tests Find answers fast Study quickly and more effectively Get the big picture without spending hours pouring over lengthy textbooksSchaum's Outlines give you the information teachers expect you to know in a handy and succinct formatwithout overwhelming you with unnecessary details. You get a complete overview of the subject. Plus, you get plenty of practice exercises to test your skill. Compatible with any classroom text, Schaum's lets you study at your own pace and reminds you of all the important facts you need to rememberfast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams.Inside, you will find: 363 detailed problems with step-by-step solutions Clear, concise explanations of matrix operations Help with Eigenvalues and the QR Algorithm A solved-problem approach that teaches you with hands-on help Exercises for improving your problem-solving skillsIf you want top grades and a thorough understanding of matrix operations, this powerful study tool is the best tutor you can have!Chapters include: Basic Operations Simultaneous Linear Equations Square Matrices Matrix Inversion Determinants Vectors Eigenvalues and Eigenvectors Functions of Matrices Canonical Bases Similarity Inner Products Norms Hermitian Matrices Positive Definite Matrices Unitary Transformations Quadratic Forms and Congruence Nonnegative Matrices Patterned Matrices Power Methods for Locating Real Eigenvalues The QR Algorithm Generalized Inverses Answers to Supplementary Problems Bronson, Richard is the author of Schaum's Outline of Theory and Problems of Matrix Operations, published 1988 under ISBN 9780070079786 and 0070079781. Six hundred sixty eight Schaum's Outline of Theory and Problems of Matrix Operations textbooks are available for sale on ValoreBooks.com, one hundred seventy one used from the cheapest price of $0.01, or buy new starting at $13.24 item is printed on demand. Confusing Textbooks? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's. More than 40 million students have trusted Schau [more] This item is printed on demand. Confusing Textbooks? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's. More than 40 million students have trusted Schaum's Outlines to help them succeed in the classroom and on exams. Schaum's is the
The student uses numerical and computational concepts and procedures in a variety of situations. 1.1 The student demonstrates number sense for real numbers and algebraic expressions in a variety of situations. 1.1.A1 generates and/or solves real-world problems using equivalent representations of real numbers and algebraic expressions (2.4.A1a) ($), e.g., a math classroom needs 30 books and 15 calculators. If B represents the cost of a book and C represents the cost of a calculator, generate two different expressions to represent the cost of books and calculators for 9 math classrooms. compares and orders real numbers and/or algebraic expressions and explains the relative magnitude between them (2.4.K1a) ($), e.g., will (5n)² always, sometimes, or never be larger than 5n? The student might respond with (5n)² is greater than 5n if n > 1 and (5n)² is smaller than 5 if o < n < 1. 1.1.A2 determines whether or not solutions to real-world problems using real numbers and algebraic expressions are reasonable (2.4.A1a) ($), e.g., in January, a business gave its employees a 10% raise. The following year, due to the sluggish economy, the employees decided to take a 10% reduction in their salary. Is it reasonable to say they are now making the same wage they made prior to the 10% raise? 1.1.K3 knows and explains what happens to the product or quotient when a real number is multiplied or divided by (2.4.K1a): 1.1.K3A a rational number greater than zero and less than one, 1.1.K3B a rational number greater than one, 1.1.K3C a rational number less than zero. 1.2 The student demonstrates an understanding of the real number system; recognizes, applies, and explains their properties, and extends these properties to algebraic expressions. 1.2.A1 generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning (2.4.A1a) ($): 1.2.A1A commutative, associative, distributive, and substitution properties, e.g., the chorus is sponsoring a trip to an amusement park. They need to purchase 15 adult tickets at $6 each and 15 student tickets at $4 each. How much money will the chorus need for tickets? Solve this problem two ways. 1.2.A1B identity and inverse properties of addition and multiplication, e.g., the purchase price (P) of a series EE Savings Bond is found by the formula ½ F = P where F is the face value of the bond. Use the formula to find the face value of a savings bond purchased for $500. 1.2.A1C symmetric property of equality, e.g., Sam took a $15 check to the bank and received a $10 bill and a $5 bill. Later Sam took a $10 bill and a $5 bill to the bank and received a check for $15. $ addition and multiplication properties of equality, e.g., the total price for the purchase of three shirts in $62.54 including tax. If the tax is 3.89, what is the cost of one shirt, if all shirts cost the same? 1.2.A1D addition and multiplication properties of equality, e.g., the total price for the purchase of three shirts is $62.54 including tax. If the tax if $3.89, what is the cost of one shirt? 1.2.A1E zero product property, e.g., Jenny was thinking of two numbers. Jenny said that the product of the two numbers was 0. What could you deduct from this statement? Explain your reasoning. 1.2.K1 explains and illustrates the relationship between the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] using mathematical models (2.4.K1a), e.g., number lines or Venn diagrams. 1.2.K2 identifies all the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] to which a given number belongs (2.4.K1m). 1.2.A2 Jenny said that the product of the two numbers was 0. What analyzes and evaluates the advantages and disadvantages of using integers, whole numbers, fractions (including mixed numbers), decimals or irrational numbers and their rational approximations in solving a given real-world problem (2.4.A1a) ($), e.g., a store sells CDs for $12.99 each. Knowing that the sales tax is 7%, Marie estimates the cost of a CD plus tax to be $14.30. She selects nine CDs. The clerk tells Marie her bill is $157.18. How can Marie explain to the clerk she has been overcharged? 1.2.K3 names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects (2.4.K1a) ($): addition and multiplication properties of equality (if a = b, then a + c = b + c and if a = b, then ac = bc) and inequalities (if a > b, then a + c > b + c and if a > b, and c > 0 then ac > bc); 1.2.K3E zero product property (if ab = 0, then a = 0 and/or b = 0). 1.2.K4 uses and describes these properties with the real number system (2.4.K1a) ($): 1.2.K4A transitive property (if a = b and b = c, then a = c), 1.2.K4B reflexive property (a = a). 1.3 The student uses computational estimation with real numbers in a variety of situations. 1.3.A1 adjusts original rational number estimate of a real-world problem based on additional information (a frame of reference) (2.4.A1a) ($), e.g., estimate how long it takes to walk from here to there; time how long it takes to take five steps and adjust your estimate. uses various estimation strategies and explains how they were used to estimate real number quantities and algebraic expressions (2.4.K1a) ($). 1.3.A2 estimates to check whether or not the result of a real-world problem using real numbers and/or algebraic expressions is reasonable and makes predictions based on the information (2.4.A1a) ($), e.g., if you have a $4,000 debt on a credit card and the minimum of $30 is paid per month, is it reasonable to pay off the debt in 10 years? 1.3.A3 determines if a real-world problem calls for an exact or approximate answer and performs the appropriate computation using various computational strategies including mental math, paper and pencil, concrete objects, and/or appropriate technology (2.4.A1a) ($), e.g., do you need an exact or an approximate answer in calculating the area of the walls to determine the number of rolls of wallpaper needed to paper a room? What would you do if you were wallpapering 2 rooms? 1.3.K3 knows and explains why a decimal representation of an irrational number is an approximate value (2.4.K1a). 1.3.K4 knows and explains between which two consecutive integers an irrational number lies (2.4.K1a). 1.3.A4 explains the impact of estimation on the result of a real-world problem (underestimate, overestimate, range of estimates) (2.4.A1a) ($), e.g., if the weight of 25 pieces of paper was measured as 530.6 grams, what would the weight of 2,000 pieces of paper equal to the nearest gram? If the student were to estimate the weight of one piece of paper as about 20 grams and then multiply this by 2,000 rather than multiply the weight of 25 pieces of paper by 80; the answer would differ by about 2,400 grams. In general, multiplying or dividing by a rounded number will cause greater discrepancies than rounding after multiplying or dividing. 1.4 The student models, performs, and explains computation with real numbers and polynomials in a variety of situations. applications from business, chemistry, and physics that involve addition, subtraction, multiplication, division, squares, and square roots when the formulae are given as part of the problem and variables are defined (2.4.A1a) ($), e.g., given F = ma, where F = force in newtons, m = mass in kilograms, a = acceleration in meters per second squared. Find the acceleration if a force of 20 newtons is applied to a mass of 3 kilograms. 1.4.A1B volume and surface area given the measurement formulas of rectangular solids and cylinders (2.4.A1f), e.g., a silo has a diameter of 8 feet and a height of 20 feet. How many cubic feet of grain can it store? 1.4.A1C probabilities (2.4.A1h), e.g., if the probability of getting a defective light bulb is 2%, and you buy 150 light bulbs, how many would you expect to be defective? 1.4.A1D application of percents (2.4.A1a), e.g., given the formula A = P(1+rdivided by n) to the nt, when A = amount, P= principal, r = annual interest, n = number of compounding periods per year, t= number of years. If $1,000 is placed in a savings account with a 6% annual interest rate and is compounded semiannually, how much money will be in the account at the end of 2 years? 1.4.A1E simple exponential growth and decay (excluding logarithms) and economics (2.4.A1a) ($), e.g., a population of cells doubles every 20 years. If there are 20 cells to start with, how long will it take for there to be more than 150 cells? or If the radiation level is now 400 and it decays by ½ or its half-life is 8 hours, how long will it take for the radiation level to be below an acceptable level of 5? 1.4.K1 computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology (2.4.K1a) ($). 1.4.K2 performs and explains these computational procedures (2.4.K1a): 1.4.K2A addition, subtraction, multiplication, and division using the order of operations 1.4.K2B multiplication or division to find ($): 1.4.K2Bi a percent of a number, e.g., what is 0.5% of 10? 1.4.K2Bii percent of increase and decrease, e.g., a college raises its tuition form $1,320 per year to $1,425 per year. What percent is the change in tuition? 1.4.K2Biii percent one number is of another number, e.g., 89 is what percent of 82? 1.4.K2Biv a number when a percent of the number is given, e.g., 80 is 32% of what number? 1.4.K2C manipulation of variable quantities within an equation or inequality (2.4.K1d), e.g., 5x – 3y = 20 could be written as 5x – 20 = 3y or 5x(2x + 3) = 8 could be written as 8/(5x) = 2x + 3; simplification or evaluation of real numbers and algebraic monomial expressions raised to a whole number power and algebraic binomial expressions squared or cubed; 1.4.K2F simplification of products and quotients of real number and algebraic monomial expressions using the properties of exponents; 1.4.K2G matrix addition ($), e.g., when computing (with one operation) a building's expenses (data) monthly, a matrix is created to include each of the different expenses; then at the end of the year, each type of expense for the building is totaled; 1.4.K2H scalar-matrix multiplication ($), e.g., if a matrix is created with everyone's salary in it, and everyone gets a 10% raise in pay; to find the new salary, the matrix would be multiplied by 1.1. 1.4.K3 finds prime factors, greatest common factor, multiples, and the least common multiple of algebraic expressions (2.4.K1b).
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).
More About This Textbook Overview Error Patterns in Computation: Using Error Patterns to Help Each Student Learn, Tenth Edition Robert B. Ashlock, Covenant College The only text of its kind to show teachers how to identify common error patterns in mathematics! As students learn about mathematical operations and methods of computation, they may adopt erroneous procedures and misconceptions. This engaging book was written to model how the instructor can make thoughtful analyses of their students' work and in so doing, discover patterns in errors made. This supplementary text guides teachers to consider reasons why students may have learned erroneous procedures in the first place and presents strategies for helping those students. Readers come away from the book with a clear vision of how to use student error patterns to gain more specific knowledge of students' understanding and to use that information to inform their future instruction. In addition to being substantially revised, the new edition offers greater emphasis on the following important topics: Use of diagnosis as a part of formative assessment, including open-ended assessment and problem writing as examples Application of Big Ideas--including compensation principles, relations between operations, and "There are many names for a number"--to form connections among facts, procedures, and concepts by applying big ideas Distinction between misconceptions and error patterns in computation Understanding of our system of numeration Understanding the meanings of operations of arithmetic so students will know when to use each operation when solving problems Related Subjects Meet the Author Robert Ashlock began his career in 1957 as a fourth and fifth grade teacher with a bachelor's degree in elementary education. He later received a master's degree in elementary school administration from Butler University and a doctorate in elementary education from Indiana University. He became a graduate assistant and teaching associate at Indiana University in 1964 and went on to teach at several institutions including the University of Maryland, Reformed Theological Seminary, Belhaven College, and finally, Covenant College in Lookout Mountain, Georgia. Ashlock came to Covenant in 1988 to fill the need for a specialist in elementary education who could also teach on the graduate level. He directed the Master of Education Program, taught both undergraduate and graduate education courses, and coordinated the process necessary for the teacher education program to be approved by the Georgia Professional Standards Commission. He is one of only two professors ever to receive the title Professor Emeritus at Covenant. He is known throughout the education community for his book, Error Patterns in Computation: Using Error Patterns to Improve Instruction , which is currently in its tenth edition. Although retired, Ashlock continues to teach a few classes. Part II: Diagnosis and Instruction 9. Diagnosing Misconception and Error Patters in Computation and in Other Mathematical Topics 10. Providing Data-Driven Instruction in Computation 11. Enriching Instruction in Computation and Other Mathematical Topics
Hello people, I am learning middle school math with pizzazz book b. I am in search of a resource that can give me answers to the problems. I need to pass this course with good marks. I can't give it time because I work part time as well. Any resource that can help me do my homework would really be appreciated. Algebrator is a useful program to solve middle school math with pizzazz book b problems. It gives you step by step solutions along with explanations. I however would warn you not to just copy the answers from the software. It will not aid you in understanding the subject. Use it as a reference and solve the problems yourself as well. Algebrator is one handy tool. I don't have much interest in math and have found it to be complicated all my life. Yet one cannot always drop math because it sometimes becomes a compulsory part of one's course work. My friend is a math wiz and I found this program in his laptop. It was only then I understood why he finds this subject to be so simple. I remember having often faced problems with scientific notation, perfect square trinomial and adding matrices. A really great piece of algebra program is Algebrator software. By simply typing in a problem homework a step by step solution would appear by a click on Solve. I have used it through many math classes – Algebra 2, College Algebra and Remedial Algebra. I greatly recommend the program.
Books on Computers > Mathematical & Statistical Software In Stock.Delivers in 60 seconds! "Mathematica Cookbook" helps you master the application's core principles by walking you through real-world problems. Ideal for browsing, this book includes recipes for working with numerics, data structures, algebraic equations, calculus, and statistics. You'll also venture into exotic territory with recipes for data visualization using 2D and 3D graphic tools,... more In Stock.Delivers in 60 seconds! Description: This... more In Stock.Delivers in 60 seconds! Description: Packed with fully explained examples, LaTeX Beginner's Guide is a hands-on introduction quickly leading a novice user to professional-quality results. If you are about to write mathematical or scientific papers, seminar handouts, or even plan to write a thesis, then this book offers you a fast-paced and practical introduction.... more In Stock.Delivers in 60 seconds! 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prepare readers to better understand the current literature in research journals, this book explains the basics of classical PDEs and a wide variety of more modern methods—especially the use of functional analysis—which has characterized much of the recent development of PDEs. It gives equal treatment to elliptic, hyperbolic, and parabolic theory, and features an abundance of applications to equations that are important in physics and engineering—both on the basic and more advanced level. Provides worked, figures and illustrations, and extensive references to other literature. First-Order Equations. Principles for Higher-Order Equations. The Wave Equation. The Laplace Equation. The Heat Equation. Linear Functional Analysis. Differential Calculus Methods. Linear Elliptic Theory. Two Additional Methods. Systems of Conservation Laws. Linear and Nonlinear Diffusion. Linear and Nonlinear Waves. Nonlinear Elliptic Equations. Appendix on Physics. For anyone using PDEs in physics and engineering applications.
Chalk Dust Math Courses (sixth grade through college) Courses like these are critical for many families who are deciding whether or not they can handle homeschooling through high school. The courses really do allow students to work independently, which means parents who never went beyond Algebra 1 can still provide their children with a solid math education. Professor Dana Mosely is your video instructor in this outstanding series of math courses for sixth grade through early college levels. High production quality and skillful presentation combine to make these top-notch video courses. Mosely's many years of teaching experience are obvious as he clarifies commonly confusing issues. He keeps the presentation moving at just the right pace, although students can always rewind and review if they don't catch it first time around. Parents with weak math backgrounds should love these courses since they really do the teaching for you. Even better, purchase of a course entitles students to free technical assistance from Professor Mosely. (Those who purchase complete used courses can pay a $50 fee for consultation service per student, per course, per year.) Courses start with Basic Math (6th grade level) and continue through Calculus I. (Chalk Dust also produces SAT Math Review which is not included in this review.) Each course has a number of DVDs which reflects both the size of textbooks and complexity of concepts taught. All courses include a textbook and solutions guide. Mosely follows the textbook lessons in order of presentation, with the exception of the geometry course. In that course, Mosely provides different approaches to some topics. In all the courses, he usually expands upon the textbook presentation, sometimes adding his own learning strategies to the lessons. He covers the main concepts then works out sample problems on a chalkboard with an occasional computer graphic or graphing calculator illustration. Students should watch a section on the video, then go to the text and work about 30 exercise problems in that particular section in the book. Each section requires about 2 days to complete. In most of the texts there are far more problems than most students will ever need to complete, so use discretion in assigning exercises. Chalk Dust includes a missive with each course explaining how to assign problems. The textbooks are from Houghton Mifflin, and the lead author on most of them is Ron Larson, one of the most respected and prolific math authors in the United States. The Basic Math text is authored by Aufmann, Barker, and Lockwood, and these authors are also responsible for the Prealgebra text. Some texts are identical to those used in schools, while some have been published as special editions for Chalk Dust. Algebra 1 and 2 texts are softbound standard with a hardbound option for an extra $20. The textbooks are designed for classroom teachers, so they do not function well on their own for home schooling students. However, the combination of video presentations and solutions guides with the texts results in excellent courses that work well for independent study. This series of texts is strong on real-life applications and word problems that enhance conceptual understanding. They include calculator use at all levels. In addition to lessons, examples and practice problems, textbooks also have reviews and tests. The softbound Solutions Guides for all courses include complete solutions to all problems with the exception of Guides for Trigonometry and College Algebra. Their Guides are student editions that have worked out solutions to only odd problems from student exercises, although they have all solutions for test questions. Solutions Guides are a valuable component in these courses. You can purchase components separately, but you really need all three components—text, DVDs, and solutions guide. Chalk Dust's website has short demos of programs available for free viewing so you can check it out before purchasing. Free demos are available at the publisher's website. Full-set orders include a 30-day money back guarantee. Also available on the Chalk Dust website ( is information about creating tests (if you need to re-test from time to time), grading tests, and assigning test and course grades Basic Math (2003) 2 DVDs, Text and Solutions Guide - $225 The text for this course is Houghton Mifflin's Basic Math, Second Edition, by Aufmann, Barker, and Lockwood, but it is a special edition published for Chalk Dust. The course functions well for remediation or reteaching of basic concepts students might not have mastered at earlier levels. While Chalk Dust lists it as a sixth grade course, it is not a complete course by some standards because topics such as geometry, area, volume, and integers are not included. The Chalk Dust course covers basic concepts and operations, including exponents and order of operations with whole numbers, fractions, and decimals. It also covers ratio and proportion, percents, and graphs. Also, new to this edition are the topics of statistics, probability, U.S. customary units of measurement, and the metric system of measurement. Many practical applications appear in examples and word problems, and an entire chapter is devoted to business and consumer math skills such as percent calculations in making purchases, computing interest, calculating the cost of buying a home or car, calculating wages, and balancing a checkbook. Although the course is not typical of 6 th grade math due to the omission of several topics mentioned above, those topics are covered in the next Chalk Dust course, Prealgebra, so Basic Math may be regarded as a foundation in the basics necessary for upper level work. I would use it with an average student at seventh grade or higher who needs remediation before going on to a grade level course. A four-function calculator might be used along with this course, but it's not absolutely essential. If you are looking ahead, you might want to go ahead and purchase a TI-83 Plus graphing calculator since it can be used with all courses. Prealgebra (2002) This prealgebra course is fairly similar in content to Saxon's Algebra 1/2. The text is Prealgebra, Second Edition by Aufmann, Barker, and Lockwood, published especially for Chalk Dust Company by Houghton Mifflin Company. This approximately 650-page, hardcover textbook includes instruction, examples, exercises, tests, and answers to odd-numbered problems in the exercises. It comes with a softcover Complete Student Solutions Manual that contains step-by-step solutions to both even and odd numbered problems. The text first reviews basic math skills and concepts, including exponents, and radicals, before moving on to topics such as polynomials, first-degree equations, the rectangular coordinate system, measurement, proportion, percent, geometry, statistics, and probability. Even though this level of math covers many algorithms with no immediate applications, this text still includes many word problems and practical applications. Periodically, lessons include mention of how to use a scientific calculator, with a few questions directing students to perform calculator operations. Calculator use is introduced at this level, and students should use a scientific or graphing calculator with the course. Courses such as this used to be considered eighth grade level, but the new math standards have advanced the math agenda so this is now considered seventh grade level in most states. For Prealgebra there is a second option called the Value Set. It substitutes three black-and-white books for the full-color text and omits the solutions manual. Lessons are taught on six DVDs rather than ten, but the full content is there. Students still get exercises and review problems, chapter tests, chapter solutions, an exercises and review Solutions CD, and technical support. Algebra 1 (2001) 10 DVDs, Text, and Solutions Guide - $394 The text for this course is Algebra 1 by Larson and Hostetler in a special edition published for Chalk Dust. This is a traditional course targeted toward the average student. Mosely's thorough presentations plus the combination of video instruction with textbook reinforcement should make it easy for most students to master algebra while working independently through the course. In addition the Complete Solutions Guide will help when both students and parents are stumped. While this text does not incorporate geometry instruction (as does Saxon) it does include algebraic applications in geometry. (Chalk Dust offers a separate Geometry course as do most publishers.) The Algebra 1 course has lessons and exercises for using a graphing calculator. In addition, the book's appendix adds sections on graphing calculators, geometry, and statistics, but the appendix sections are not included on video. Algebra 2 (2001) 13 DVDs, Textbook, and Solutions Guide - $429 The textbook for this course is Algebra 2 by Larson and Hostetler in a special second edition published for Chalk Dust Company. Mosely closely follows the lessons as presented in the textbook. Many first-year algebra concepts are reviewed at length, a boon for students who have taken geometry after one year of algebra and need a refresher. The Complete Solutions Guide covers all the problems. The scope and sequence is a bit different from some other Algebra 2 courses. While it covers functions at length along with radicals, inequalities, conic sections, systems of equations, matrices, and logarithms, it does not even introduce trigonometry. The inclusion of elementary trigonometry techniques is a relatively recent trend in Algebra 2 courses and Chalk Dust follows the more traditional approach in offering trigonometry as a separate and much more comprehensive course. Instructions for using a TI-83 graphing calculator are part of the video instruction and also appear in a separate section in the appendix. Additional calculator information appears as "technology tips" in sidebars throughout the book. Occasionally, video lessons actually show the calculator and its screen so that students can use their own calculators and follow along performing operations. In my opinion, this is the most practical solution for covering Algebra 2 unless parents are great at math and have time to teach it themselves. Even though the cost seems high, keep in mind that everything can be used with other children then resold when you are finished, or you could share a set of tapes with another family. College Algebra (2001) 13 DVDs, Textbook, and Solutions Guide - $409 The College Algebra textbook is by Larson and Hostetler. The text follows the same format as do Larson's other algebra books. As you might have guessed from the course title, College Algebra is really a college course rather than high school. However, you might use it after Algebra 2 or, in exceptional cases, instead of Algebra 2. The course reviews much of the material covered in Algebra 2 but takes it to a deeper level in most instances and at a more rapid pace. For example, in the section on graphing equations, we encounter new types of equations and graphs. In the study of functions, we encounter more complex functions than previously. It might be possible for outstanding Algebra 1 students to skip Algebra 2 and move directly into this text, but for most students it should follow an Algebra 2 course. Some students will be able to skip the first section of the course that reviews fundamental concepts of algebra. The solutions guide for this course is actually a student edition, so complete solutions are shown for only odd problems from student exercises—this is typical of college math textbooks. All test solutions are shown. Although the course is titled College Algebra, it is only a little more challenging than Algebra 2. In comparison to Saxon's math series, the content of College Algebra is somewhat equivalent to algebra coverage in Saxon's Advanced Math. However, Saxon also covers geometry and trigonometry, which this course does not. Chalk Dust offers separate Geometry and Trigonometry courses and also covers trigonometry within its Precalculus course. On the other hand, this course covers statistics and probability, which receive little attention in Saxon, and it also has more coverage on conic sections. The use of a graphing calculator is highly recommended, but the course can be completed without one. College-bound students who do not need calculus and trigonometry will have a very solid math background if they continue algebra studies through this course. Students completing the Chalk Dust College Algebra course should be able to test out of college algebra at the college of their choice. College-bound students interested in an engineering or science degree are advised to take the Chalk Dust Precalculus course that covers topics in both the Trigonometry and College Algebra courses plus other material. An additional benefit of taking Precalculus rather than Trigonometry and College Algebra separately is the cost: $534 for Precalculus versus $828 for the other two courses. Geometry This course has been totally revised to support an entirely new text, Geometry, by Daniel Alexander and Geralyn Koeberlein (Houghton Mifflin Company, 2007). I have not yet reviewed it. Trigonometry (2001) 9 DVDs, Textbook, and Solutions Guide - $419 The text for this course is Trigonometry, Fifth Edition, by Larson and Hostetler. This is a traditional course covering both trigonometry and some analytic geometry. Graphing calculators are referenced throughout the text and demonstrated throughout the video as well. Although these calculators can be somewhat expensive, they can be critical in demonstrating equations and the relationship between the algebraic form (the equation) and the geometric form (the graph). The TI-83 Plus is recommended. If students are not already familiar with the calculator, they should go through the user-friendly instructions that come with it and learn the calculator techniques on a need-to-know basis as they are encountered during the course. Keep in mind that Chalk Dust provides technical support by phone or email so calculator issues are not a big deal. The solutions guide is a student edition so complete solutions are shown for only odd problems from student exercises. All test solutions are shown. (Note: Precalculus covers the content of Trigonometry and College Algebra so students need not do either of those courses in addition to Precalculus.) Precalculus (2001) 18 DVDs, Textbook, and Solutions Guide - $534 There are more tapes or DVDs for this course than for other Chalk Dust courses because this course is really two courses in one, College Algebra and Trigonometry, with the addition of even more material not contained in either of the other two. There are over 40 hours of video presentation associated with this course. Dana Mosely follows lessons in the text, expanding explanations and working out sample problems. With this course, students really should stop the video occasionally and try to solve example problems so they can fully grasp the concepts. This would be a one-semester course at the college level, but high school students should definitely take a full school year or more to complete it. The text used in the 2004 version of this course is Precalculus With Limits, A Graphing Approach, Third Edition by Larson, Hostetler, and Edwards. Both content and presentation in the textbook help make the course more appealing. There are a number of fully-explained examples for each topic in the book. In addition, the text has some full-color illustrations; historical/biographical sidebars; and real life, business, and science applications within the chapter problems. With the combination of videos, textbook, and the complete solutions guide (with solutions to all problems), students really should be able to learn independently. After completing this course, students should be ready for college-level calculus so they should be able to test out of College Algebra and Trigonometry or out of Precalculus. A graphing calculator is standard equipment for this course. The TI-83 Plus is recommended. (See the review of Trigonometry for comments on the calculator.) Calculus I (2001) 12 Videos or 8 DVDs, Text and Solutions Guide - $409 The text for this course is Calculus of a Single Variable, Sixth Edition, by Larson, Roland, Hostetler, and Edwards. The text actually covers two courses--Calculus 1 and Calculus 2--but the videos and the solutions guide cover only Calculus 1. This is a true college level course. I suspect that most students tackling such a course will want to earn college credit if possible, so students should check with the college of their choice beforehand to make sure they will have the opportunity to test out of Calculus I once the course is completed. I would not be surprised if the college uses the same text since it is one of the most popular calculus texts in the country. Chalk Dust for the Elementary Grades CD-ROM plus Binder - $69 per course. I have to add a note about Chalk Dust's new CD-ROM math courses for the elementary grades, marketed under the trade name Math Matters. These courses for grade levels 3, 4, and 5 were developed under the direction of Dana Mosely of Chalk Dust. The courses include colorful illustrations and animations as well as voice instruction for a key topic in each lesson. The CD-ROM for each course comes with a three-ring binder that includes tests, answers, and other material. Each course has approximately 180 lessons and covers an entire year's math curriculum. All lessons include cumulative review. Some of the lessons allow the student to type answers in blanks provided while others call for written work from the student. Written mid-chapter and chapter tests are provided in the binder. Unlike other math courses offered by Chalk Dust, students are not expected to work independently. Parents will still have to monitor and control the learning experience due to the grade levels involved. Sample lessons and more course information are available at the math matters website, or by phone at 407-851-0444 .
Find a Maple Shade PrecalProceeding through course material in this way allows a student to understand the context and motivation behind key concepts and through this form of understanding, solving problems becomes a matter of specializing the broader idea (which is far easier than learning how to perform calculations by
: IntroductionNotes to Teachers and Students: When we teach complex numbers to beginning engineering students, we encourage a geometrical picture supported by an algebraic structure. Every algebraic manipulation carried out in a lecture is accompanied by a care-fully drawn picture in order to fix the idea that geometry and algebra go hand-in-glove to complete our understanding of complex numbers. We assign essentially every problem for homework. We use the MATLAB programs in this chapter to illustrate the theory of complex numbers and to develop skill with the MATLAB language. The numerical experiment introduces students to the basic quadratic equation of electrical and computer engineering and shows how the roots of this quadratic equation depend on the coefficients of the equation. Introduction It is hard to overestimate the value of complex numbers. They first arose in the study of roots for quadratic equations. But, as with so many other great discoveries, complex numbers have found widespread application well outside their original domain of discovery. They are now used throughout mathematics, applied science, and engineering to represent the harmonic nature of vibrating systems and oscillating fields. For example, complex numbers may be used to study traveling waves on a sea surface; standing waves on a violin string; the pure tone of a Kurzweil piano; the acoustic field in a concert hall; the light of a He-Ne laser; the electromagnetic field in a light show; the vibrations in a robot arm; the oscillations of a suspension system; the carrier signal used to transmit AM or FM radio; the carrier signal used to transmit digital data over telephone lines; and the 60 Hz signal used to deliver power to a home. In this chapter we develop the algebra and geometry of complex numbers. In Chapter 3 we will show how complex numbers are used to build phasor representations of power and communication signals
Mathematics This course introduces computer simulation as a research tool through its application to problems from calculus, differential equations, linear algebra, graph theory, dynamical systems, and physics. MS 451 Nonlinear Dynamics 3 CR.HR. MS258 MS 451 Nonlinear Dynamics 3 CR.HR. MS258 This course introduces methods by which information can be extracted from nonlinear differential equations that are often not exactly solvable. Graphical methods, fixed points and their stability, and bifurcations are examined with biological, physical, and chemical applications emphasized. Select topics from chaos theory may be included. MS 499 Topic/ 1-3 variable CR.HR. MS 499 Topic/ 1-3 variable CR.HR. This course is intended to provide the opportunity to offer advanced courses in mathematics that would not normally be a part of the Husson curriculum. As such the topics will depend upon the interests of students and faculty. MS 91 Fundamental Skills for College Mathematics 3 CR.HR. MS 91 Fundamental Skills for College Mathematics 3 CR.HR. This course is intended to prepare students having minimal mathematical backgrounds for college algebra and other quantitatively oriented courses. The emphasis is on building basic analytic reasoning skills. The course content includes numerical and algebraic expressions, solution of first degree equations, strategies for solving work problems, and the graphing of linear functions. Placement is determined by diagnostic testing. This course does not count towards a degree. A minimum grade of C is required. MS 92 Fundamentals of Mathematics 4 CR.HR. MS 92 Fundamentals of Mathematics 4 CR.HR. This course reviews fundamental principles and applications of arithmetic and serves as preparation for MS 093 Core Arithmetic and Algebra. The course does not satisfy degree requirements. Five contact hours per week. A minimum grade of C is required. MS 93 Core Arithmetic and Algebra 4 CR.HR. MS 93 Core Arithmetic and Algebra 4 CR.HR. Core Arithmetic and Algebra provides a review of necessary concepts and skills required for success in general education college mathematics, and serves as preparation for MS141 Contemporary College Algebra. The course does not count toward the degree. A minimum grade of C is required. MS 94 Core Mathematics Review 1 CR.HR. MS 94 Core Mathematics Review 1 CR.HR. Core Mathematics Review provides a review of necessary concepts and skills required for success in general education college mathematics. Normally offered during a two or three week period during the fall or spring semester or as part of the winter or summer term. Serves as preparation for MS141 Contemporary College Algebra. Does not satisfy degree requirements. Pass/Fail grading. One credit hour.
Support Us Development In the Summer of 2013 Channing will embark on its most ambitious development programme ever. Click here for more.... Mathematics ENTRY REQUIREMENTS: Grade A in GCSE Mathematics. Year 12 Mathematicians at the Royal Institute Course outline: AS Students study Pure Mathematics and Statistics and will be tested with and without a calculator, sitting modules C1, C2 and S1. There is no coursework. A2 Students go on to study more advanced Pure Mathematics and some Mechanics. The modules we sit are C3, C4 and M1. There is no coursework. FURTHER MATHEMATICS For some students, A level Mathematics does not provide sufficient challenge and so Further Maths offers the opportunity to get two A levels in Mathematics. We fast track the six modules of A level Mathematics into Year 12 and then study Further Pure Maths and Applied Maths in Year 13. There is no coursework. What could I go on to do at the end of my course? Mathematics is an excellent subject to have as part of any A level portfolio. It is an extremely valuable subject to have if going on to study Architecture, Science, Medicine, Finance, Social Science and Engineering. University admissions tutors in Arts subjects also value Mathematics A level as evidence of logical thought and an ability to handle the abstract.
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. Two hundred forty Introduction To Graph Theory textbooks are available for sale on ValoreBooks.com, eleven used from the cheapest price of $37.90, or buy new starting at $152.21 464 p. Contains: Illustrations. Walter Rudin Student Series in Advanced Mathematics. Audience: General/trade. BOX # 3812. (Media mail takes 5-14 days) Special note(Used book)I check each pages of this book it is in Very Good Condition. CDs is (not included): This book has Approximate(0)pages contains Answers of all Questions, Notes, Highlight, or Under-lines. This Hard Cover book: Jacket cover is (Good) Stem binding, and all 4 tips cover are (Good): Old(Ex library s Book contains marker s mark, library s logo and Jacket cover cutting ). Jacket cover is ( N/A). Email me before you Return it, If its not in better condition I described
Glencoe Secondary Mathematics to the Common Core State Standards, Geometry SE Supplement Math Triumphs--Foundations for Geometry Reading and Writing in the Mathematics Classroom Summary TheSpanish Homework Practice Workbookcontains two Spanish 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.
The Pearson Guide To Quantitative Aptitude For Competitive Examination475 Our Price:404 You Save: 71 (15%) This item is presently Out of Stock. The Pearson Guide To Quantitative Aptitude For Competitive Examination (Paperback) The Pearson Guide To Quantitative Aptitude For Competitive Examination Book Description The quantitative aptitude section occupies a very important place in any competitive examination today. The QA questions assess your basic computation skills and the ability to reason mathematically. The Pearson Guide to Quantitative Aptitude for Competitive Examinations is a unique self-help manual that familiarizes you with basic mathematical concepts and enables you to apply them to a range of calculation-based problems. This book is divided into 31 chapters and covers a wide variety of topics. Fundamental principles are explained with the help of easy-to-understand examples. Practice exercises at the end of the chapters further refine problem-solving skills. Quantitative Aptitude, thus, is a complete preparation tool you can t afford to miss. Features More than 5,000 solved problems to help you develop problem-solving skills Popular Searches The book The Pearson Guide To Quantitative Aptitude For Competitive Examination by Dinesh Khattar (author) is published or distributed by PEARSON EDUCATION LIMITED [, 9788131719565]. This particular edition was published on or around 2008 date. The Pearson Guide To Quantitative Aptitude For Competitive Examination is available for use in Paperback binding. This book by Dinesh Khatt

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