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Other Formats Product Description This Paradigm Accelerated Curriculum Independent Math Activity Book Chapter 1 provides the practice work and activities for the Independent Math Chapter 1 Student Text. Word problems and numerical problems are included, as well as room to copy the "life principle". 44 pages, saddle-stitched binding, paperback. Answers sold separately in the Teacher's Resource Kit
Beginning And Intermediate Algebra An Integrated Approach 9780495117933 ISBN: 0495117935 Edition: 5 Pub Date: 2007 Publisher: Thomson Learning Summary: Easy to understand, filled with relevant applications, and focused on helping students develop problem-solving skills, BEGINNING AND INTERMEDIATE ALGEBRA is unparalleled in its ability to engage students in mathematics and prepare them for higher-level courses. Gustafson and Frisk's accessible style combines with drill problems, detailed examples, and careful explanations to help students overcome any mathematics anx...iety. Their proven five-step problem-solving strategy helps break each problem down into manageable segments: analyze the problem, form an equation, solve the equation, state the conclusion, and check the result. Examples and problems use real-life data to make the text more relevant to students and to show how mathematics is used in a wide variety of vocations. Plus, the text features plentiful real-world application problems that help build the strong mathematical foundation necessary for students to feel confident in applying their newly acquired skills in further mathematics courses, at home or on the job. Gustafson, R. David is the author of Beginning And Intermediate Algebra An Integrated Approach, published 2007 under ISBN 9780495117933 and 0495117935. One hundred forty six Beginning And Intermediate Algebra An Integrated Approach textbooks are available for sale on ValoreBooks.com, one hundred forty one used from the cheapest price of $7.70, or buy new starting at $127.66 very good looking hardback textbook! A super tight spine! Signs of use on corners and edges of book...as it was a class textbook--a solid book. All pages are intact [more] This is a very good looking hardback textbook! A super tight spine! Signs of use on corners and edges of book...as it was a class textbook--a solid book. All pages are intact ... with none missing! SMOKE FREE HOME! Do not settle for worn, torn, throwaways. Pay a few pennies more for a beautiful copy! *PLEASE NOTE: BECAUSE OF THE WEIGHT AND SIZE OF THIS BOOK, IT WILL ONLY BE SHIPPED MEDIA MAIL--STANDARD SHIPPING! *[less]
Algebra for Students DVD Series In Algebra for Students, students will learn about the power of algebra as a tool for representing, analyzing and generalizing situations, and will explore several functions, including linear, quadratic and exponential. Real-world applications of algebra are shown in multiple forms through tables, graphs and equations, and common errors and misconceptions are highlighted. Students will also learn how to translate verbal expressions to algebraic expressions while considering the reasonableness of solutions within the context of the situation. Teacher's guides are included and available online
Problems With a Point is a site developed for mathematics students and teachers in grades 6-12. The site contains practice problems on various topics that designed to help students understand mathematical concepts and... This website provides a basic overview of Data Mining and some applications for the process. The site lists some typical tasks addressed by data mining, such as identifying cross-sell opportunities and predicting aA short article designed to provide an introduction to functional equations, those in which a function is sought which is to satisfy certain relations among its values at all points. For example, we may look for... Written by Leo Moser and presented by the Trillia Group, this virtual text introduces visitors to the theory of numbers. After agreeing to the terms and conditions of use, users will be able to download the full...
Algebra and Trigonometry with Modeling and Visualization - 4th edition Summary: Gary Rockswold teaches algebra in context, answering the question, ''Why am I learning this?'' By experiencing math through applications, students see how it fits into their lives, and they become motivated to succeed. Rockswold's focus on conceptual understanding helps students make connections between the concepts and as a result, students see the bigger picture of math and are prepared for future courses. Introduction to Functions and Graphs; Linear Functions and Equations; Quadra...show moretic Functions and Equations; More Nonlinear Functions and Equations; Exponential and Logarithmic Functions; Trigonometric Functions; Trigonometric Identities and Equations; Further Topics in Trigonometry; Systems of Equations and Inequalities; Conic Sections; Further Topics in Algebra For all readers interested in college algebra and trigonometry. ...show less Good This is a good book, and this is a great deal on it! I ship fast, because I know you need the book! If this title was suppossed to have an access code originally, it may or may not still have i...show moret unused. Save your money, and buy from The Deal Factory! The book may have some markings or highlights, but still a great book. We cannot guarantee supplemental materials such as CDs or access codes will be available or unused
free textbook offered by BookBoon.'The success of Group Theory is impressive and extraordinary. It is, perhaps, the... see more This is a free textbook offered by BookBoon.'The success of Group Theory is impressive and extraordinary. It is, perhaps, the most powerful and influential branch of all Mathematics. Its influence is strongly felt in almost all scientific and artistic disciplines (in Music, in particular) and in Mathematics itself. Group Theory extracts the essential characteristics of diverse situations in which some type of symmetry or transformation appears. Given a non-empty set, a binary operation is defined on it such that certain axioms hold, that is, it possesses a structure (the group structure). The concept of structure, and the concepts related to structure such as isomorphism, play a decisive role in modern Mathematics.The general theory of structures is a powerful tool. Whenever someone proves that his objects of study satisfy the axioms of a certain structure, he immediately obtains all the valid results of the theory for his objects. There is no need to prove each one of the results in particular. Indeed, it can be said that the structures allow the classification of the different branches of Mathematics (or even the different objects in Music (! )).The present text is based on the book in Spanish "Teoría de Grupos: un primer curso" by Emilio Lluis-Puebla, published by the Sociedad Matemática Mexicana This new text contains the material that corresponds to a course on the subject that is offered in the Mathematics Department of the Facultad de Ciencias of the Universidad Nacional Autónoma de México plus optional introductory material for a basic course on Mathematical Music Theory.This text follows the approach of other texts by Emilio Lluis-Puebla on Linear Algebra and Homological Algebra. A modern presentation is chosen, where the language of commutative diagrams and universal properties, so necessary in Modern Mathematics, in Physics and Computer Science, among other disciplines, is introduced.This work consists of four chapters. Each section contains a series of problems that can be solved with creativity by using the content that is presented there; these problems form a fundamental part of the text. They also are designed with the objective of reinforcing students' mathematical writing. Throughout the first three chapters, representative examples (that are not numbered) of applications of Group Theory to Mathematical Music Theory are included for students who already have some knowledge of Music Theory.In chapter 4, elaborated by Mariana Montiel, the application of Group Theory to Music Theory is presented in detail. Some basic aspects of Mathematical Music Theory are explained and, in the process, some essential elements of both areas are given to readers with different backgrounds. For this reason, the examples follow from some of the outstanding theoretical aspects of the previous chapters; the musical terms are introduced as they are needed so that a reader without musical background can understand the essence of how Group Theory is used to explain certain pre-established musical relations. On the other hand, for the reader with knowledge of Music Theory only, this chapter provides concrete elements, as well as motivation, to begin to understand Group Theory.' Movenote let's you record video alongside documents or pictures to create an integrated video presentation with... see more Movenote let's you record video alongside documents or pictures to create an integrated video presentation with slides. Creating presentations is easy and fast. Simply record video with your device and swipe to synchronize the slides to the video. Presentations are shared by sending a link to the recipient and can be viewed without the app.First add the material you want to present to form a slideshow. Add pictures from your photo albums or take them directly with your camera. Alternatively bring a document from your mailbox or cloud storage like Dropbox. Also you can combine material from all these different sources. Secondly, record the video and simultaneously change slides by swiping. The recorded presentation will play out with the exact same timing. This is a free textbook offered by BookBoon.'Electronics and Computing in Textiles connects the fields of electronics and... see more This is a free textbook offered by BookBoon.'Electronics and Computing in Textiles connects the fields of electronics and computing with the field of textiles presenting the principles of the disciplines of electronics and computing with examples and applications in textiles. This structure is very important, especially because of the expansion of textiles in the modern multifunctional materials and products world. Furthermore, the progress in the textile processes with the use of automation systems is based mainly on electronic and computing concepts. Thus, Electronics and Computing in Textiles is essential in the modern textile engineering curriculum.'
Addressing individual learning styles, Tom Carson presents targeted learning strategies and a complete study system to guide students to success. Carson's Study System, presented in the "To the Student" section at the front of the text, adapts to the way each student learns, and targeted learning strategies are presented throughout the book to guide students to success. Tom speaks to students in everyday language and walks them through the concepts, explaining not only how to do the math, but also where the concepts come from and why they work. Product Details ISBN-13: 9780321828163 Publisher: Pearson Publication date: 4/10/2012 Edition description: New Edition Edition number: 4 Pages: 720 Product dimensions: 8.40 (w) x 10.80 (h) x 0.40 (d) Meet the Author Tom Carson's first teaching experience was teaching guitar as an undergraduate student studying electrical engineering. That experience helped him to realize that his true gift and passion are for teaching. He earned his MAT in mathematics at the University of South Carolina. In addition to teaching at Midlands Technical College, Columbia State Community College, and Franklin Classical School, Tom has served on the faculty council and has been a board member of the South Carolina Association of Developmental Educators (SCADE). Ever the teacher, Tom teaches outside the classroom by presenting at conferences such as NADE, AMATYC, and ICTCM on topics such as Combating Innumeracy, Writing in Mathematics, and Implementing a Study
>Bob, Chandry, this is what I am getting at. > >It seems to me that calculus is placed on a pedestal as >something unachievable by the masses. But looking at it, >I see a lot of material in the calculus that could be >approached by students on a sixth or seventh grade >level. If they can graph a straight line and a parabola, >they are game for calculus, at least some calculus. In other words, you can get the kids to go through the motions (to some extent), but what you have actually accomplished remains in considerable doubt. Why do I feel this way? Because that is what actually goes on a lot of the time (maybe most of the time) in college. That is the reason for the Calculus Reform Movement. So, your hypothesis, Peter, must be that you can more easily accomplish with middle school kids than with college students. This seems unlikely. The problem you are having, Peter, is what I have called "Mathematician's Disease",
Instructor Class Description Introduction to Elementary Functions Covers college algebra with an emphasis on polynomial, rational, logarithmic, exponential, and trigonometric functions. Prerequisite: either a minimum grade of 2.5 in B CUSP 121 or a score of 147-150 on the MPT-GSA assessment test. Offered: AWSp. Class description The goal of this course is to show students that math can be understood and enjoyed. The emphsis of the course is to learn and improve the algebraic skills necessary to go on taking more math courses. Lots of fractions, exponents, radicals, factorization, linear functions, quadratic functions and some disscussion of polynomials and rational functions. Graphing of various functions. Recognize and be comfortable using polynomial, exponential, and rational functions. Able to graph and manipulate functions symbolically. Apply functions and concepts to solve real world problems. Learn to become problem solvers. General method of instruction Group discussion and discovery. Lots of additional worksheets to supplement the material from the text. Recommended preparation The Placement test and the desire to learn. Class assignments and grading Attendance Policy: Since participation is vital for a successful experience, please arrive on time for class. Late arrivals interrupt our in-progress activities and discussions. If you must miss a class session, let me know as soon as possible so that you can make up the work that you miss. Grading: HW and quizzes – 50 pts HW/Attendance/Quizzes – 5 points for each completed HW Participation and attendance- 10pts 1st Midterm – 40 pts. 2nd Midterm – 40 pts. Final Exams – 60 pts The course is not graded on a curve. Following is a rough grading scale: <104 points (52%) – 0.0 104 points (52%) – 0.7 110 points (55%) – 1.0 130 points (65%) – 2.0 160 points (80%) – 3.0 180 points (90%) – 4.0 I reserve the right to change this scale, most likely in your favor. Homework Details: There will be homework nearly every night – about two to three hours each night. Occasionally, there may be worksheets to turn in. Homework should be turned in with the following: - Your name - Date due - Assignment #, section number, and the problem# written neatly on the outside. - Homework must be neat. - Space the problems far enough apart so I can find them easily. - Homework must be done on graph paper, as much as possible. No Tear offs! - Much of the assignments require lots of accurate graphing, so this is a must for those assignments. Homework does count toward your course grade, but almost entirely on a basis of how seriously you tried. Homework will be graded as follows: - If every problem is given a strong effort, you will receive 5 point. - If the effort on the assignment is considerably lacking, you will receive 0 points. Homework is generally due on Wednesdays before the lecture. I will collect one problem at RANDOM. No late HW. Please circle the problem that is being collected. Quizzes: Expect pop quizzes! Stay on top of things! NO make up quizzes. The median score of each exam are calculated and used to determine the grade. Improvement is heavily considered when determining Barry Minai Date: 04/23/2012 Office of the Registrar For problems and questions about this web page contact icd@u.washington.edu, otherwise contact the instructor or department directly. Modified:March 8, 2014
Essentials: Enhanced with Graphing Utilities This is the number one, best selling graphing-required version of Mike Sullivan's precalculus series because, simply, "IT WORKS." Mike Sullivan, ...Show synopsisThis is the number one, best selling graphing-required version of Mike Sullivan's precalculus series because, simply, "IT WORKS." Mike Sullivan, after twenty-five years of teaching, knows exactly what readers need to do to succeed and he therefore emphasizes and organizes his text around the fundamentals; preparing, practicing, and reviewing. Readers who prepare (read the book, practice their skills learned in previous math classes), practice (work the math focusing on the fundamental and important mathematical concepts), and review (study key concepts and review for quizzes and tests) succeed. This dependable text retains its best features-accuracy, precision, depth, strong reader support, and abundant exercises, while substantially updating content and pedagogy. After completing the book, readers will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus. Graphs. Functions and Their Graphs. Polynomial and Rational Functions. Exponential and Logarithmic Functions. Trigonometric Functions. Analytic Trigonometry. Applications of Trigonometric Functions. Polar Coordinates; Vectors. Analytic Geometry. Systems of Equations and Inequalities. Sequences; Induction; The Binomial Theorem. Review. For all readers interested in precalculus1866683-5-0-3 Orders ship the same or next business day. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions. ISBN: 9780131866683. Description:Fair. Covers scuffed/scratched, marks on page edges, minimal...Fair. Covers scuffed/scratched, marks on page edges, minimal shelf wear, 4
Jumpstarters for Algebra Resource Book Printed eBook Make algebra equations easy for students in grades 7 and up using Jumpstarters for Algebra: Short Daily Warm-Ups for the Classroom. This 48-page resource covers real numbers, algebraic expressions, linear equations, polynomials, factoring, rational expressions, square roots, and quadratic equations. The book includes five warm-ups per reproducible page, answer keys, and suggestions for use.
Overview Calculus III is not really a continuation of Calculus I and II. It takes both of them to a whole new dimension - the third dimension. We will learn calculus that can be applied to the three dimensional world in which we live (but which we frequently ignore because it cannot be completely reproduced on paper or on screens). Reading I have intentionally chosen a very readable text. In addition to planning time to do homework, please take time to carefully read the sections in the book. Notice use of the words "time" and "carefully". Read the sections slowly and actively. If you do not understand some statement reread it, think of some potential meanings and see if they are consistent, and if all else fails, ask me. If you do not believe a statement, check it with your own examples. Finally, if you understand and believe the statements, consider how you would convince someone else that they are true, in other words, how would you prove them? Because the text is exceptionally accessible, we will structure classtime more as an interactive discussion of the reading than lecture. For each class day there is an assigned reading. Read the section before coming to class. After completing questions from the reading we will discuss problems not a part of the problem sets during the class discussion. Learning Outcomes Upon successful completion of Math 223 - Calculus III, a student will be able to: Represent vectors analytically and geometrically, and compute dot and cross products for presentations of lines and planes, Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of multivariable calculus concepts. Grading Your grade in this course will be based upon your performance on various aspects. The weight assigned to each is designated below: Exams: Assignments: (5% each, complete 10) Exam 1 13% Problem Sets (5) 25% Exam 2 13% More (2) 10% Final Exam 25% Lab Writeups (3) 15% More may include extra problem sets, papers, or lab writeups. Problem set 3 is rather long and therefore worth 7%. Problem set 5 is rather short and therefore worth 3%. Problem Sets There will be five pairs of problem sets distributed throughout the semester. You must complete one of each pair. Problem sets are due on the scheduled dates. You are encouraged to consult with me outside of class on any questions toward completing the homework. You are also encouraged to work together on homework assignments, but each must write up their own well-written solutions. A good rule for this is it is encouraged to speak to each other about the problem, but you should not read each other's solutions. A violation of this policy will result in a zero for the entire assignment and reporting to the Dean of Students for a violation of academic integrity. I strongly recommend reading the suggestions on working such problems before beginning the first set. Each question will be counted in the following manner: 0 – missing question or plagiarised work 1 – question copied 2 – partial question 3 – completed question (with some solution) 4 – completed question correctly and well-written Each entire problem set will then be graded on a 90-80-70-60% (decile) scale. Late items will not be accepted. Problem sets will be returned on the following class day along with solutions to the problems. Because solutions will be provided, comments will be somewhat limited on individual papers. Please feel free to discuss any homework with me outside of class or during review. *New: Points lost on problem sets may be reearned (or preearned) by finding errors in the textbook (there are a few - both mathematical and writing) as follows: The first student who notifies me via email of an error will receive one problem set point. I will keep the errors listed here for you to check. Solutions and Plagiarism There are plenty of places that one can find all kinds of solutions to problems in this class. Reading them and not referencing them in your work is plagiarism, and will be reported as an academic integrity violation. Reading them and referencing them is not quite plagiarism, but does undermine the intent of the problems. Therefore, if you reference solutions you will receive 0 points, but you will not* be reported for an academic integrity. Simply - please do not read any solutions for problems in this class. Laboratory Activities and Writeups We will regularly be spending parts of classes on maple activities. Activity files are in my outbox in a folder called "MultiMaple". You may access them via a browser here (after logging in with your Geneseo account). Please come to class prepared for the activity (i.e. with a maple-installed computer and the file loaded), but without having completed it before. We will not use class time to prepare. I strongly recommend reading the suggestions on writing lab writeups before submitting one. Follow-up questions are posted here and will be updated so as to include questions for each lab. Lab writeups may be turned in no more than three class days after the lab activity. Reports After attending a mathematics department colloquium (or other approved mathematics presentation) you may write a report. In your report, please explain the main point of the presentation and include a discussion of how this presentation affected your views on mathematics. A – Well written, answers the questions, and is interesting and insightful B – Well written and answers the questions C – Well written or answers the questions (convinces the reader that you were there) D – attempted Papers are due within a classweek of the colloquium presentation. I will gladly look at papers before they are due to provide comments. Exams There will be two exams during the semester and a final exam during finals week. If you must miss an exam, it is necessary that you contact me before the exam begins. Exams require that you show ability to solve unfamiliar problems and to understand and explain mathematical concepts clearly. The bulk of the exam questions will involve problem solving and written explanations of mathematical ideas. The first two exams will be an hour worth of material that I will two evening hours to complete. The final exam will be half an exam focused on the final third of the course, and half a cumulative exam. Exams will be graded on a scale approximately (to be precisely determined by the content of each individual exam) given by 100 – 80% A 79 – 60% B 59 – 40% C 39 – 20% D below 20% E For your interpretive convenience, I will also give you an exam grade converted into the decile scale. The exams will be challenging and will require thought and creativity (like the problems). They will not include filler questions (like the exercises) hence the full usage of the grading scale. Feedback Occasionally you will be given anonymous feedback forms. Please use them to share any thoughts or concerns for how the course is running. Remember, the sooner you tell me your concerns, the more I can do about them. I have also created a web-site which accepts anonymous comments. If we have not yet discussed this in class, please encourage me to create a class code. This site may also be accessed via our course page on a link entitled anonymous feedback. Of course, you are always welcome to approach me outside of class to discuss these issues as well. Social Psychology Wrong answers are important. We as individuals learn from mistakes, and as a class we learn from mistakes. You may not enjoy being wrong, but it is valuable to the class as a whole - and to you personally. We frequently will build correct answers through a sequence of mistakes. I am more impressed with wrong answers in class than with correct answers on paper. I may not say this often, but it is essential and true. Think at all times - do things for reasons. Your reasons are usually more interesting than your choices. Be prepared to share your thoughts and ideas. Perhaps most importantly "No, that's wrong." does not mean that your comment is not valuable or that you need to censor yourself. Learn from the experience, and always try again. Don't give up. Math Learning Center This center is located in South Hall 332 and is open during the day and some evenings. Hours for the center will be announced in class. The Math Learning Center provides free tutoring on a walk-in basis. Academic Dishonesty While working on assignments with one another is encouraged, all write-ups of solutions must be your own. You are expected to be able to explain any solution you give me if asked. Exams will be done individually unless otherwise directed. The Student Academic Dishonesty Policy and Procedures will be followed should incidents of academic dishonesty occur. Disability Accommodations SUNY Geneseo will make reasonable accommodations for persons with documented physical, emotional or learning disabilities. Students should consult with the Director in the Office of Disability Services (Tabitha Buggie-Hunt, 105D Erwin, tbuggieh@geneseo.edu) and their individual faculty regarding any needed accommodations as early as possible in the semester. Religious Holidays It is my policy to give students who miss class because of observance of religious holidays the opportunity to make up missed work. You are responsible for notifying me by September 10 of plans to observe a holiday.
TI-89 Calculus Calculator Programs TI-89 calculator programs for sale. Enter your variables and see answers worked out step by step: a and b vectors, acceleration, area of parallelogram, component of a direction u, cos(a and b), cross product, curl, derivative, divergence of vector field, ...more>> Tiling with Polyominoes - Ivars Peterson (MathTrek) "Mathematicians have proved that the general question of whether it's possible to cover the plane with identical copies of a given finite set of tiles is, in principle, computationally undecidable. In other words, there's no cookbook recipe or handbook ...more>> Totally Tessellated - Bhushan, Kay, & Williams A comprehensive introduction to tessellations and tilings - the basic underlying mathematics and examples of tessellations in real life. The highly illustrated, printer-friendly site includes history (tessellations in mathematics and science, decorative ...more>> Trigonometry - Technical Tutoring Site provides an introduction to trigonometry, includes illustrative examples and exercises in basic trigonometry as well as a summary of the important basic trig identities and formulae. ...more>> Turtle Tracks - Ivars Peterson (MathTrek) One way to describe a geometric figure is in terms of the path generated by a moving point. Using the computer language LOGO, children can produce a list of commands to govern the motion of a "turtle" and trace out a geometric track on the computer screen. ...more>> Vagn Lundsgaard Hansen A personal home page with links to: a mathematical story "I am the greatest," solving and proving/explaining the isoperimetric problem for quadrilaterals; Mathematics and the Public - some experiences with the popularization of mathematics; and Mathematics ...more>> Virtual Polyhedra - George W. Hart A growing collection of over 1000 virtual reality polyhedra to explore, complementing Hart's Pavilion of Polyhedreality. Includes instructions for building paper models of polyhedra including modular origami, with ideas for classroom use. Each of the ...more>> Visualizing An Infinite Series - Cynthia Lanius This lesson uses a trapezoid successively divided in 4ths as a visual representation of an infinite geometric series, a mathematical concept that is often only treated symbolically. Explorations are outlined for investigating a number of series, and links ...more>> The Web Wizard's Math Challenge - J. Mooser An ongoing Internet contest; register (free) to submit answers and score points. Problems are designed to be readily understood but not readily solved. Speed counts, because points are awarded based on the order in which contestants submit correct answers. ...more>> wrotniak.net - J. Andrzej Wrotniak Includes shareware and freeware programs for Windows written by Wrotniak: scientific and regular calculators, a spherical geometry calculator, a logic and strategy game, a statistics graphing program, and a simple program to compute the area of a polygon. ...more>>
Book summary 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. [via] Shipping prices may be approximate. Please verify cost before checkout. Click on the price to find out more about a book. New books: 1 - 5 of 40 # Bookseller Notes Price 1. marvelousbks via United States Hardcover, ISBN 1565770390 Publisher: Saxon Publishers Inc, 2003 2nd ed.. Hardcover. . Brand New, may or may not have a school inventory number on side pages or inside cover.100% money-back guarantee if not satisfied! 2nd ed.
First Course in Abstract Algebra Considered a classic by many, John Fraleigh's A First Course in Abstract Algebra is an in-depth introductory text for the Abstract Algebra course. ...Show synopsisConsidered a classic by many, John Fraleigh's A First Course in Abstract Algebra is an in-depth introductory text for the Abstract Algebra course. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. It is geared towards high level courses at schools with strong math programs. New exercises have been written, while past exercises have been revised and modifed. Classical approach to abstract algebra. Focus on applications of abstract algebra. Classic text for the high end of the market - known and loved in this discipline. It is geared towards high level courses at schools with strong maths programs Accessible pedagogy includes historical notes written by Victor Katz (author of another AWL book The History of Mathematics), an authority in this area By opening with a study of group theory, this text provides students with an easy transition to axiomatic mathematics 8178089971 Book is lightly used with little or no...Very Good. 8178089971
Symmetry We all encounter symmetry in our everyday lives, in both natural and man-made... We all encounter symmetry in our everyday lives, in both natural and man-made structures. The mathematical concepts surrounding symmetry can be a bit more difficult to grasp. This unit explains such concepts as direct and indirect symmetries, Cayley tables and groups through exercises, audio and video. By the end of this unit you should be able to: explain what is meant by a symmetry of a plane figure; specify symmetries of a bounded plane figure as rotations or reflections; describe some properties of the set of symmetries of a plane figure; explain the difference between direct and indirect symmetries; use a two-line symbol to represent a symmetry; describe geometrically the symmetry of a given figure which corresponds to a given two-line symbol; find the composite of two symmetries given as two-line symbols; find the inverse of a symmetry given as a two-line symbol; write down a Cayley table for the set of symmetries of a plane figure; appreciate how certain properties of the set of symmetries of a figure feature in a Cayley table; explain the meaning of the terms group, Abelian group and the order of a group; give examples of finite groups and infinite groups; determine whether a given set and binary operation form a group by checking the group axioms; deduce information from a given Cayley table; understand that the identity in a group is unique; understand that each element in a group has a unique inverse; recognise how the uniqueness properties can be proved from the group axioms; explain the connections between properties of a group table and the group axioms; describe the symmetries of some bounded three-dimensional figures; use two-line symbols to denote symmetries of three-dimensional figures, and to form composites and inverses of such symmetries;
no-nonsense, practical guide to help you improve your algebra II skills with solid instruction and plenty of practice, practice, practice Practice Makes Perfect: Algebra II presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations, as well as an introducing you to probability and trigonometry. Inside you will find the help you need for boosting your skills, preparing for an exam or re-introducing yourself to the subject. More than 500 exercises and answers covering all aspects of algebra will get you on your way to mastering algebra!
Mathematics for College Physics 9780131414273 ISBN: 0131414275 Pub Date: 2003 Publisher: Prentice Hall PTR Summary: Designed for concurrent self-study or remedial math work for students in introductory courses, this text is ideal for students who find themselves unable to keep pace because of a lack of familiarity with necessary mathematical tools. It not only shows them clearly how mathematics is directly applied to physics, but discusses math anxiety in general and how to overcome it. Instead of a rigorous development of the con...cepts of mathematics (as is found in a typical math book), the text describes the various mathematical concepts and tools (including algebra, trigonometry, geometry, vectors, and statistics) and their direct use in solving physics problems. Almost all sections end with worked-out examples and exercises directly from introductory physics.[read more]
Welcome to the Math Help Blog! The Math Help webblog is dedicated to bringing you free math help online resources. We are frequently updating our Math Help website topics. If you are looking for math help resources or math help answers and cannot find it on our Math Help website, feel free to contact us. Whether you are seeking free math homework help, or just looking for general math help, we want to have the answers for your math questions for you here on Math Help website. On Math Help website, math topics are laid out in form of math lessons. Our math lessons, which we aim to frequently add on to, include math lessons on integers, logic, quadratic formula, quadratic equation, polynomials, and integration. All resources on Math Help website are free. On Math Help website, we start our math lessons by introducing the definition of a math topic such as integers, logic, quadratic equations, polynomials, and integration. Once we have defined them clear enough, we then state theorems, math rules, math laws, math formulae associated with those math lessons. In some sections, we also give examples. More math examples and math worksheets will be collected and presented on a math website dedicated for math examples and math worksheets
Elementary Concepts of Topology by Paul Alexandroff Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures. Experiments in Topology by Stephen Barr Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit. From Geometry to Topology by H. Graham Flegg Introductory text for first-year math students uses intuitive approach, bridges the gap from familiar concepts of geometry to topology. Exercises and Problems. Includes 101 black-and-white illustrations. 1974 edition. General Topology by Stephen Willard Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures. A Geometric Introduction to Topology by C. T. C. Wall First course in algebraic topology for advanced undergraduates. Homotopy theory, the duality theorem, relation of topological ideas to other branches of pure mathematics. Exercises and problems. 1972 edition. Topology for Analysis by Albert Wilansky Three levels of examples and problems make this volume appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important topological concepts. 1970Product Description: Critically acclaimed text presents detailed theory of Fréchet (V) spaces and a comprehensive examination of their relevance to topological spaces, plus in-depth discussions of metric and complete spaces. Numerous exercises reinforce teachings of each chapter. "...an elegant piece of work suitable for the beginning student and the mature mathematician." — Scripta Mathematica. Second
Replies to: Best calculator?? Well if you're talking about a non graphical one I would strongly recommend a Casio. First I bought a Texas Instruments one (called TI-30X) which I personally did not like at all. My math teacher took one look at it and told me to throw it away and never use it again. He told me to buy a Casio FX 991MS and I did. I love it it has everything a non-graphical calculator would possibly have, it solves quadratics, matricies, vectors, eq'n with multiple variables and more. Seriously I'm so into this calculator I'm going to buy another one just in case my first one got lost and I couldn't find one near my university! On a side note I haven't gone to university this calculator has only been used for Calculus 1 but I'm pretty sure its one of the best. Enjoy! If you get into higher level mathematics, you may find TI-89's ability to do symbolic evalution helpful. Every engineering student I knew had one. I resisted for a very long time, since I had graphing calc software on my palm pilot that did most of what I needed. It wasn't until I took Complex Analysis (a senior level math course) I finally broke down and bought a used TI-89 because I couldn't do symbolic evaluation otherwise. I've used a TI-83+ for 5 years now and it's been pretty good to me. It is VERY helpful to have a graphing calculator rather than a scientific calculator for calculus. For physics, it won't matter as much. At some point in your engineering courses, you'll probably have to solve a large systems of equations, and the matrix feature of the TI-83+ will become very helpful. I have a TI-84 Silver Plus, and I love every square millimeter of it. I've had no problems with it. Granted, I've only used it for high school physics and calculus, but I love it. Of course, I think Texas Instruments rules the world, but I'm probably a little biased... It reallly depends on the instructors, because some don't allow graphing calculators. I would recommend a ti-89 and some regular non graphing calculator that can do sin,cos, tan for the those classes that have calculator restrictions. The best calculators for number-crunching are those with an RPN mode, like the HP-33S (scientific) or HP-50G (graphing). The 33S is the most powerful scientific on the market: it can be used in either RPN or algebraic mode, and it has programming capability (which Casio and TI scientifics lack). The 33S is not as powerful as a graphing calculator, but it can be used in many situations where graphing calcs are banned, such as engineering licensing exams. The best calculators for symbolic math are graphing calculators, particularly the TI-89 or HP-50G. The 89 is noted for its ease of use, and is very popular with students. The 50G is more powerful and flexible, but it has a significantly steeper learning curve, and is more commonly used by professionals. The 89 and 50G also support calculations with units, which is handy for engineers. The 50G has the broadest units support, but the 89 probably has all the units you would need as an undergraduate. Real engineers use Hp's. New interns and students use Ti. you can tell whos the new hire, by who is carrying a Ti. I use the Hp 50G and the 33S. I wont debate this subject here as I know im right, but HP makes the best calculators, the only reason Ti is popular is due to them buying out the market with bribes. There calculators actually do suck. If you are looking for the best graphing calculator its either the HP 48GX or the Hp 50G. For a scientific it is byfar the 33S. If you plan to take the FE and PE then buy the 33S as the Ti 36 is awful. HP 50g all the way, it is far more powerfull than a Ti-89. Someone who knows what they are doing can do complex mathmatics with an HP so much faster than with Ti. The only reason the school system in the U.S. uses TI calculators is because when they got new math curriculum in the 70s TI payed off people to only use TI for the text, even though they are no good. TI is only a player in the calculator market because of backdoor bribery.
Product description Algebra 2 covers all topics that are traditionally covered in second-year algebra as well as a considerable amount of geometry. In fact, students completing Algebra 2 will have studied the equivalent of one semester of informal geometry. Time is spent developing geometric concepts and writing proof outlines. Real-world problems are included along with applications to other subjects such as physics and chemistry. Type: Boxed Set ()Category: > Home SchoolingISBN / UPC: 9781600320163/1600320163Publish Date: 1/1/2000Item No: 132081Vendor: Saxon Publishers
MCV4U: The Derivatives of Functions - The Product and Quotient Rule Ontario Curriculum Expectation 3.5: solve problems, using the product and chain rules, involving the derivatives of polynomial functions, sinusoidal functions, exponential functions, rational functions, radical functions, and other simple combinations of functions. Learning Goal: students will be able to solve problems, using the product and quotient rule, involving the derivatives of polynomial functions. Success Criteria: Using different assessment strategies (clickers, think - pair - share, problem solving, Smart Board) check student's learning goals. Accommodation: There is extra work in the handout provided for students or peers who finish early.
This thorough and detailed exposition is the result of an intensive month-long course sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives. The material will be particularly useful for those wishing to advance their understanding by exploring mirror symmetry at the interface of mathematics and physics. This one-of-a-kind volume offers the first comprehensive exposition on this increasingly active area of study. It is carefully written by leading experts who explain the main concepts without assuming too much prerequisite knowledge. The book is an excellent resource for graduate students and research mathematicians interested in mathematical and theoretical physics. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA). Readership Graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics. Reviews "This book, a product of the collective efforts of the lecturers at the School organized ... by the Clay Mathematics Institute, is a valuable contribution to the continuing intensive collaboration of physicists and mathematicians. It will be of great value to young and mature researchers in both communities interested in this fascinating modern grand unification project."
Mathematica for Students Now Bundled with New Mathematica Site Licenses for High Schools June 21, 2005--Complimentary copies of Mathematica for Students are now available with all new annual Mathematica site licenses for high schools in the U.S. and Canada. These special one-year editions give students all the powerful functionality of Mathematica for use on their personal computers at home. Mathematica--the technical software used at thousands of high schools around the world--accelerates classroom curriculums in nearly all math and science subjects, including algebra, trigonometry, calculus, chemistry, physics, and computer science. Teachers use it every day to create courseware and colorful 3D demos that make difficult topics come alive for students. "These complimentary licenses will give teachers much more freedom and flexibility in developing their curriculums around Mathematica," said Paul Wellin, manager of Wolfram Education Group. "Classroom time shouldn't be wasted in a computer lab completing exercises that could be done at home." Students use Mathematica to tackle all of their technical projects and create professional-quality reports and presentations. In addition to freeing up time in the classroom, these home-use licenses will give students the opportunity to explore advanced subjects in greater detail and gain valuable experience using the same software used at almost every major university. "We want students to be confident and comfortable using Mathematica before they have to use it in college," said Valerie Smith, precollege programs manager at Wolfram Research. "Using it at home--whenever and however they want--will give these students a unique advantage. Now they can work more independently, finish their assignments outside of school, and virtually extend the classroom into their own homes." For this special program, Wolfram Research will match each new Mathematica license with a student home-use license at no extra charge. Additional student copies are also available for a discounted price. Interested schools can contact Wolfram Research at 1-800-WOLFRAM or sales@wolfram.com.
Soalan Matematik Tingkatan 4
Applications Other MATLAB Tutorial This is a group of easy step-by-step Matlab tutorials. See the descriptions and go to the topic of your interest. After these 'in-a-nutshell' lessons, you'll be almost ready to do your own Matlab programs! Tutorial Lesson 2:Vector Algebra (algebra with many numbers at once!). You'll learn to create arrays and vectors, and how to perform algebra and trigonometric operations on them. This is called 'Vector Algebra'... Working with Polynomials Polynomials are used so commonly in algebra, geometry and math in general that Matlab has special commands to deal with them. The polynomial 24 + 3x3 − 10x2 − 11x + 22 is represented by...
Book DescriptionProduct Description Review Praise for the First Edition: "Written to appeal to all mathematics teachers. Teachers who are struggling with introducing these topical ideas will find the book is written in such a way as to facilitate their understanding of the topics. The language is easy to understand and the book is very user friendly. In addition, those teachers who have a sound grasp of these key concepts can find fresh ideas for teaching old concepts presented in a manner that is intellectual in design." -- Journal of School Improvement, Volume 3, Issue 2, Fall 2002 20051116 "A 'must' for any who wish for more proven classroom practices. From geometry to algebra, teachers will find it packed with ideas." -- California Bookwatch, September 2006 20060920 --This text refers to an alternate Hardcover edition. About the Author Herbert A. Hauptman is a world-renowned mathematician who pioneered and developed a mathematical method that has changed the whole field of chemistry. For this work he was recipient of the 1985 Nobel Price in chemistry. With this book Dr. Hauptman brings his highly sophisticated knowledge of mathematics and his many years of exploration in higher mathematics to the advantage of secondary school audience. Alfred S. Posamentier is Professor of Mathematics Education and Dean of the School of Education at the City College of the City University of New York. He has authored and co-authored several resource books in mathematics education for Corwin Press. Inside This Book(Learn More) Browse and search another edition of this book. First Sentence Objective: To have students understand intuitively and abstractly why the product of two negatives is positive&nbspRead the first page have successfully used insights from this book to get my kids to discover why much of math works the way it does. It is great. One small caveat: this book is not particularly well organized in ready-to-use lesson plan format. Most of the ideas in this book need to be worked with to devlop full-blown lessons. But the ideas are good enough that this is not too hard to do. 5.0 out of 5 starsGreat resource for teaching the underlying logic of mathJan. 25 2004 By Paul P. Arnold - Published on Amazon.com Format:Paperback used insights from this book to get my kids to discover why math works the way it does. It is great. One small caveat: this book is not particularly well organized in ready-to-use lesson plan format. Most of the ideas in this book need to be worked with to develop full-blown lessons. But the ideas are good enough that this is not too hard to do. 9 of 9 people found the following review helpful 5.0 out of 5 starsPacked with ideas.Sept. 23 2006 By Midwest Book Review - Published on Amazon.com Format:Paperback The updated second edition of 101+ Great Ideas for Introducing Key Concepts in Mathematics: A Resource for Secondary school Teachers is a 'must' for any who wish more proven classroom practices. Over a hundred strategies for teaching math are arranged by subject matter, with each listing identifying objectives, materials, and procedures. Both hands-on and computer-based approaches are detailed, with plenty of lessons and examples throughout. This comes form a mathematician/professor and a math pioneer and Nobel Prize recipient: from geometry to algebra, teachers will find it packed with ideas. Diane C. Donovan California Bookwatch 4 of 4 people found the following review helpful 4.0 out of 5 starsGood InformationMay 29 2007 By Charity Gleason - Published on Amazon.com Format:Paperback\|Amazon Verified Purchase Some of the ideas in this book I found a tad confusing but there are quite a few great analogies and tricks to make remembering math concepts easier for students. I reccommend this book for any secondary math teacher.
Marden's Theorem concerns the relative positions of the roots of a cubic polynomial and those of its derivative. This article gives a proof of Marden's theorem, along with dynamic geometry animations and some of the history of the result. This applet encourages students to use the mathematics of the motion of a projectile to choose angle and velocity necessary to hit a roving target. The source code is available from the link within the Sharing Area of the Flash Forum. These applets provide interactive student activities to make connections between the graphical and analytical interpretation of "completing the square" and writing the equation of a parabola in general and standard form. This ESTEEM module in the Biometrics Category is a collection of workbooks has tools for linear regression, polynomial fit, and chi-square analysis to test whether a data set is in Hardy-Weinberg Equilibrium.
Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis. The text covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter. This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. Although the book is independent of a specific computer program, MATLAB® code is available on the authors' website to illustrate various concepts.
Basic Mathematics - 7th edition Summary: Patient and clear in his explanations and problems, Pat McKeague helps students develop a thorough understanding of the concepts essential to their success in mathematics. Each chapter opens with a real-world application. McKeague builds from the chapter-opening applications, such as the average amount of caffeine in different beverages, and uses the application as a common thread to introduce new concepts, making the material more accessible and engaging for student...show mores. Diagrams, charts, and graphs are emphasized to help students understand the material covered in visual form. McKeague's unique and successful EPAS system of Example, Practice, Answer, and Solution actively involves students with the material and thoroughly prepares them for working the Problem Sets. The Sixth Edition of BASIC MATHEMATICS also features a robust suite of online course management, testing, and tutorial resources for instructors and students. This includes iLrn Testing and Tutorial, vMentor live online tutoring, the Digital Video Companion CD-ROM with MathCue, a Book Companion Web Site featuring online graphing calculator resources, and The Learning Equation (TLE), powered by iLrn. TLE provides a complete courseware package, featuring a diagnostic tool that gives instructors the capability to create individualized study plans. With TLE, a cohesive, focused study plan can be put together to help each student succeed in math
What Can I Do With A Major In Mathematics? Mathematics is the study of measurement, properties, and relationships of quantities and sets, using numbers and symbols. Mathematics is both a discipline and a tool used extensively in the sciences, medicine, engineering, and industry. Math majors develop the ability to explore, conjecture, and reason logically, as well as use mathematical methods to solve problems. Theoretical mathematicians develop new principles or new relationships between existing math principles without consideration to practical uses. Applied mathematicians typically use theories and techniques in the application of mathematical knowledge to other domains. Is This Major For You? You might like this major if you also like: solving puzzles; intellectual challenges; art as it relates to shape, balance, and design; precise and succinct writing; philosophy Consider this major if you are good at: attention to detail; creativity; critical reading/thinking; observing; math; quantitative analysis; spatial reasoning Employment Settings Colleges and universities CPA, insurance, financial firms Manufacturing firms Wholesale and retail trade firms Federal agencies Banks and brokerage firms Computer hardware and software firms Sample Occupations Software Developer Engineer Statistician Computer Programmer Investment Analyst Cartographer Actuary Educator Academic Assistance Center Resources Great Jobs for Math Majors Careers for Number Crunchers and Other Quantitative Types Careers in Computers Opportunities in Engineering Careers Careers in Insurance Opportunities in Financial Careers 100 Jobs in Technology
I use a TI83+, not a voyager2000, but I found TICalc very helpful. They have all sorts of tutorials. Just download programs, look at them, and watch what they do. Also, read the manual so you know what format everything takes, that is the most useful knowledge, the format every instruction takes.
Formats Book Description Publication Date: Jan. 1 2010 \| Series: Algebra Survival GuideProduct Description About the Author Josh Rappaport is the author of the Parents' Choice award-winning Algebra Survival Guide, and co-author of the newly released Card Game Roundup books. Josh taught middle school and high school, and for the last 13 years has been president of the "Now I Get It!" Learning Center, where he teaches and tutors children of all ages. Trust me when I say this the best Alegbra guide on the market. I know because I tried them all(no joke.) As an adult, who never had Algebra in high school, I was not prepared for it in college. And there are few college courses that go all the way back to the beginning, mine expected that you already had basic algebra fundamentals. The guide along with the workbook, actually replaced my textbook. The textbook was simply put, confusing, and unrelatable. The guide, and workbook were lifesavers for me. The clear, precise and easy to understand examples clarified much of what confused me. And associating all of the properties and laws to analogies worked liked a charm. In fact, I soon learned I knew th properties and laws better than my classmates and began using the analogies to explain them so they to could remember all the little tricks this guide taught me. My teenage son, who has struggled with Algebra, now has his own copies and wonders why his teachers have never thought to make it so easy to learn. 48 of 51 people found the following review helpful 5.0 out of 5 starsHighly recommend the book and workbookAug. 27 2007 By T. Malnar - Published on Amazon.com Format:Paperback I purchased the Algebra Survival guide and the workbook for my sons who would be taking Algebra in 8th grade. They easily completed the entire book over the summer. The survival guide is easy to understand. The Emergency Fact sheet will be a great reference. They will sail through Algebra this year. I highly recommend these books as a prelude to classroom Algebra for all students. 53 of 62 people found the following review helpful 5.0 out of 5 starsA Classic Start!July 7 2004 By John D MacDonald - Published on Amazon.com Format:Paperback As in my review of the Algebra Survival Book itself, I have nothing but praise for this workbook and for the simplicity and clarity these books offer jointly. I would recommend this as a MUST have if you seriously want to begin understanding the fundamentals of Algebra.
Math Competition LinksAmerican Mathematics Contest 8 (Middle School) The AMC 8 is a 25 question, 40 minute multiple choice examination in junior high school (middle school) mathematics designed to promote the development and enhancement of problem solving skills. The examination provides an opportunity to apply the concepts taught at the junior high level to problems that not only range from easy to difficult but also cover a wide range of applications. American Mathematics Contest 10 (Secondary Grades) The AMC 10 is a 25-question, 75-minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Calculators are allowed. The main purpose of the AMC 10 is to spur interest in mathematics and to develop talent through the excitement of solving challenging problems in a timed multiple-choice format. The problems range from the very easy to the extremely difficult. American Mathematics Contest 12 (Secondary Grades) The AMC 12 is a 25-question, 75-minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Calculators are allowed. The main purpose of the AMC 12 is to spur interest in mathematics and to develop talent through solving challenging problems in a timed multiple-choice format. Because the AMC 12 covers such a broad spectrum of knowledge and ability there is a wide range of scores. The National Honor Roll cutoff score, 100 out of 150 possible points, is typically attained or surpassed by fewer than 3% of all participants. The AMC 12 is one in a series of examinations (followed in the United States by the American Invitational Examination and the USA Mathematical Olympiad) that culminate in participation in the International Mathematical Olympiad, the most prestigious and difficult secondary mathematics examination in the world. The Mandelbrot Competition (Secondary Grades) In those ten years the contest has grown to two divisions encompassing students from across the United States as well as from several foreign countries. Nearly half of the competitors in the USA Math Olympiad in the last couple of years have been Mandelbrot competitors. The Mandelbrot Competition is split into two divisions: Division A for more advanced problem solvers and Division B for less experienced students. Mathcounts (Grades 7-8) Each year, more than 500,000 students participate in MATHCOUNTS at the school level. Those who do tell us that their experience as a "mathlete" is often one of the most memorable and fun experiences of their middle school years. Math Problems of the Week (Grades K-12) The Problem of the Week is an educational web site that originates at the University of Mississippi. All the prizes are generously donated by CASIO electronics. All contest winners are chosen randomly from the pool of contestants that successfully solve that week's problem.
MathsCasts by MathsCasts To listen to an audio podcast, mouse over the title and click Play. Open iTunes to download and subscribe to iTunes U collections. Description These MathsCasts are produced by the mathematics support centres at Swinburne University, the University of Limerick and Loughborough University. They are part of an ongoing collaborative research project to develop high quality resources and investigate the effectiveness of MathsCasts to support mathematics learning. They are mostly targeted at prerequisite to first year level, in a range of subjects such as: Engineering, Sciences, Business, Computing and Technology. We have also commenced production of second year mathematics topics. MathsCasts are licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License The three mathematics support centres can be contacted the following way: MASH Centre (Swinburne, Australia) MLC (Limerick, Ireland) MLSC (Loughborough, UK) Name Description Released Price 1 VideoWhy do we need the absolute value when we integrate 1 over x? (MathsCasts) We look at the integral of 1 over x dx and explain the precise details that lead to the use of abs(x) in the log function obtained from antidifferentiation. The definition of the vector product is used to identify the cross products of the various basis vectors i, j and k with each-other, in preparation for unravelling a component form for the vector product. We explain the concept of an irrotational vector field and potential for such a field, then show how the potential is used to calculate a path integral of the vector filed given end-points for the path. A specified vector field shown to be irrotational. VideoVectors: Example of Expressing the Addition/Subtraction of Vectors as a Single Vector (MathsCasts) Worked example shows how to use the triangle law, the definition of equal vectors and the definition of negative vectors to express the addition and subtraction of two or more vectors as a single vector. Outline of formula for finding the cross product of two 3D vectors which are written in terms of i, j and k. Worked example of finding the cross product of two 3D vectors which are written in terms of i, j and k. Defines cross product of vectors and illustrates the geometrical representation of the cross product and use of the right hand rule. Outlines differences in results between dot product and cross product. Using the definition of the dot product to find formula for finding the angle between two vectors. Working through example to find the angle between two vectors which are expressed in terms of i and j. Proof of some basic properties of the dot product.(i) Dot product of perpendicular vectors,(ii) Dot product of parallel vectors, (iii) Dot product of a vector with itself, and (iv) Commutative property of the dot product Defines negative vector and shows why vector ba is equal to vector -ab. Defines position vector and states that a vector which starts at the origin can be expressed in terms of its end point only, i.e.as a single letter vector. Introduction to combined inequalities. Example of forming a combined inequality from a given word statement and worked example of solving a combined inequality consisting of the word 'or' and solutions checked. Explains the partial fraction expansion procedure when the denominator has repeated linear roots, and applies this technique to a simple example. Then applies this expansion to conduct the integration. Uses substitution in the resulting integrals. VideoTransposition with required letter in numerator and denominator - Part 1 (MathsCasts) This recording gives a demonstration of how to make a letter the subject of a formula in the case where the letter appears in both numerator and denominator of the original equation, but only to the power of 1 in each case. This recording demonstrates how to integrate rational functions where the numerator is a constant and the denominator is an irreducible quadratic function. We complete the square on the denominator, then we integrate by substitution to find the answer. Gives the general formula then applies this to an example. Cartesian form is convert to polar form, then the required power of the number is calculated, and finally the result is converted back into Cartesian form. We look at how to simplify algebraic fractions when there is a number and/ or power of a letter that is common to all terms on the numerator and denominator, thus allowing us to simplify the original fraction by cancelling out this common factor. We find the equation of the tangent to a curve at a specific point, by first finding the general expression for the derivative of the curve, then evaluating it at the point, and then using this information to find the equation of the tangent. Gives a basic example of implicit differentiation to find dy/dx, and compares this to the result from explicit differentiation for the same example. Second example is a circle, with graphical interpretation of dy/dx in two points. VideoTransposition with required variable in the denominator (MathsCasts) In this recording we look at how to rearrange a formula where the letter that we want to make the subject is in the denominator. That is, we look how to make f the subject when presented with an expression of the form a/b = c/d + e/f. We look at cases when we can add and subtract surds- namely when terms can be re-written with the same number under the square root sign. Two examples are given- in the second example the surds need to be simplified before adding/ subtracting them. We continue investigation of the RLC circuit, introducing complex versions of voltage and current. The complex impedance results naturally from these quantities and gives a clear picture of why the current and voltage differ by a phase, and by how much. We discuss integrals with a linear function of sin or cos in the denominator of the integrand. We address the question of existence then exhibit a substitution which allows for use of the residue theorem to evaluate the integral. VideoReversing the order of integration of a double integral 1 (MathsCasts) Part 1 of 3. We show how to swap the order of integration in a double integral depending on x and y. We use the same examples as for the region of integration for double integrals. We start with constant integration limits and progress to variable limits. We show how to find eigenvalues for an NxN matrix then do a 2x2 example. This MathsCast follows from an introductory MathsCast on eigenvalues and eigenvectors and it is also helpful to view the presentations on linear dependence and independence first. We introduce geometric series involving a combination of partial fractions derived from a quadratic denominator. It is shown how to develop series which converge for any value of x by treating the partial fractions in different ways before expansion. Two examples are given of rearranging an equation or formula to make a particular letter the subject. This is done by first considering each operation that was originally done to the required letter, and then reversing these operations. We look at how to simplify surds. This is done by finding the largest perfect square that is a factor of the number under the square root and hence bringing this part of the expression outside the square root. We expand the binomial series for the case n = 1/2 to evaluate an approximation for the square root of 2. Convergence is discussed briefly then we deal with the case when the first term in the binomial expression is a constant other than one. Gives the definition and conditions for the inverse of a function to exist, and then applies this to an example where the original function is not one-to-one and where the domain of f(x) hence needs to be restricted in order to define the inverse function Introduction to 'head to tail' vector subtraction in the geometric sense. This is then applied to an example of working out a boat's velocity relative to water given the velocity of the current and the velocity of the boat relative to land are both known Introduction to "head to tail" vector addition in the geometric sense. This is then applied to an example of working out a boat's velocity relative to land given the velocity of the current and the velocity of the boat relative to water are both known. We investigate inequalities involving quadratic expression and show how to use a combination of algebraic rearrangement and graph sketching to find solutions. The solutions are written as inequalities and as intervals. VideoLaplace transform of an integral using reversal of order of a double integral (MathsCasts) We use the known result for Laplace transform of a derivative sF(s) to speculate about the result for the transform of an integral. We guess that it might involve division by s. This result is proven using a double integration method. Examples are given of the visual interpretation of systems of 3 simultaneous linear equations in 3 unknowns for the case where there is a unique solution, an infinite number of solutions, and no solutions. After a brief review of circular polar coordinates, a double integral is written using Cartesian coordinates. We draw the region of integration and describe it in terms of polar coordinates in order to rewrite the integral in polar coordinates. Outlines the general process for setting up and solving a related rates problem (where related quantities change over time). This is then applied to an example involving a chemical being drained out of a cylindrical tank. Outlines the general process for setting up and solving a related rates problem (where related quantities change over time). This is then applied to an example involving the relative speed and distance apart of two bicycles at a specified time. We derive the formula for the Laplace transform of df/dt in terms of that for f(t) and f(0). It is then shown how to extrapolate the rule to write down the transforms for 2nd, 3rd and higher derivatives. VideoSketching the region of integration of double integrals (MathsCasts) We examine some double integrals with Cartesian variables x and y. We investigate the integration limits and relate them to the 2D region of integration in the x-y plane. This is preparatory to reversing the order of integration. The conditions for equality of complex numbers are given. An example of grouping and then equating real and inaginary parts of complex numbers on both sides of an equation to find unknown quantities is then given. Outlines the general formula for finding the determinant of a 2x2, then goes through one simple example. Note at the end regarding the fact that if the determinant equals zero then that matrix has no inverse. VideoEvaluating double integrals by reversing the order of integration (MathsCasts) We examine two double integrals in which the anti-differentiation is at first sight impossible. We then reverse the order of integration and sidestep the problem of seemingly impossible integration. The integrals are thus evaluated. VideoThe small element of area for circular polar coordinates (MathsCasts) We investigate a small piece of area in a 2D region. We justify pictorially, the factor of r in the form dA = r dr theta. The Jacobian determinant is given for circular polars, which is then shown to yield r as the appropriate factor in the area dA. We discuss combinations of even and odd functions involving sums, products etc and investigate their odd and even properties. We show the use of such properties in reducing the work needed to evaluate a certain kind of integral. We extend the expansion of the nth power of a binomial and investigate the power series for the nth power of (1+x). For all n, Infinite Maclaurin series are obtained and the coefficients identified. We revisit part 1 where n is positive integer. Positive integer powers of the binomial (a+b) are examined. It is shown how to expand the brackets to obtain a finite series using coefficients from the Pascal triangle. Later these coefficients are identified as the nCr coefficients. Example of solving a second-order linear ordinary differential equation with constant coefficients in the case where the auxiliary equation has a repeated root and the right hand side of the equation is a polynomial. This recording demonstrates use of the quadratic formula in relation to three examples: one with 2 distinct solutions, one with a repeated solution and one with no real solutions. The discrminant function is introduced in relation to this. We investigate the significance of differentiating a Laplace transform and relate the derivative to the inclusion of an extra factor of 't' in the original transform. The idea is extended to multiple derivatives and powers of t. We investigate the Laplace transform of a function when multiplied by the Heaviside step-function. The 2nd shift theorem is introduced. It is shown how to prepare a function for use with the 2nd shift theorem. Defines the Laplace transform. Briefly describes the uses of a Laplace transform then deals with technical issues such as what is meant by infinity integration limit. Concludes with explanation of the restrictions on the Laplace variable 's'. This screencast demonstrates how to solve a first-order separable differential equation in the case where the right hand side of the equation is a mixture of x and y terms that needs to be factorised so that the equation can be separated and solved. Explains graphically what it means to multiply a matrix and a vector. Then introduces eigenvectors as vectors belonging to the matrix with a special property in matrix vector multiplication. Eigenvalues are also explained in this context. We explain what is meant by an odd function in terms of symmetry, then give a rule satisfied by the function. We show how to test for oddness then discuss the area under the graph of an even function between points an equal distance of the y axis. We explain what is meant by an even function in terms of symmetry, then give a rule satisfied by the function. We show how to test for evenness then discuss the area under the graph of an even function between points an equal distance of the y axis. This recording shows how velocity and acceleration of a particle travelling through 3D space are calculated given we have a general vector expression for the position vector at time t - this is then illustrated with a specific example. Shows how to use known Laplace transforms to evaluate infinite integrals involving exponentials in product with other functions. We extend the idea to products of an exponential with another fctn and with t using the derivative of Laplace transform method An example of solving a degree four polynomial where all powers are even. The substitution w = z^2 is used to rewrite as quadratic, the quadratic formula is applied to find the two solutions and then the complex square roots of both values of w are found. Shows how to sketch a 3D curves which is given in vector form on 2D paper. The curve is rewritten in scalar parametric form, values for the parameter t are selected, and points on the curve calculated. These are then plotted and the curve is sketched. Defines the factorial function and shows examples where it is used: e.g. in the MacLaurin series for exp(x), for cos(x), but also in nCr (n choose r). It concludes with a proof that 0!=1, using the Gamma function. Starts with an introduction to the equation of a straight line in 3D in both Cartesian and vector form. An example is then given of converting the Cartesian equations of a straight line into its scalar parametric equations and hence its vector equation. We examine the integration involved in calculating some Fourier coefficients and discuss the approach to be taken when one has a formula sheet in comparison with having to calculate the integral on paper. We introduce geometric series in which the variable is a quantity other than x or the constant is not 1. Convergence is discussed and we show how to get a series that converges when the absolute value of x is greater than 1 or some other number. Covers the multiplication and division of complex numbers given in exponential and their equivalent formulas in polar form (deduced from the exponential ones) as an introduction to the deduction of De Moivre's Formula and its use to find complex roots. This screencast gives an example of a projectile in 2D space where gravity is the only force acting. Vector methods are hence used to find the velocity and position vector of the projectile, given that its initial velocity and position are known. An example of finding the cube roots of a complex number by first converting the number from Cartesian to polar form, then hence using De Moivre's Theorem to find the roots in polar form, and then converting the roots into Cartesian form The general principle is explained of how to divide one complex number by another when both numbers are written in Cartesian form, so that the denominator of the final answer is a real number. A specific example of using this process is then given. An example of first finding the vector and scalar parametric equations of two straight lines in 3D, given we know two points on each line. Gaussian Elimination then confirms that the lines intersect at a common point, whose coordinates are found. An explanation is given of the general visual interpretation of polar coordinates. An example of then given of choosing different angles, evaluating 'r' at each of these angles and then plotting and joining the resulting points by hand. Permission for limited re-use is provided under the terms of the Australian Creative Commons Attribution Non-commercial No Derivatives (by-nc-nd) licence 3.0 Customer Ratings We have not received enough ratings to display an average for this collection.
Also Available in: Vedic mathematics Made Easy (Paperback) Vedic mathematics Made Easy Book Description About the Book : A Simplified Approach For Beginners Can you multiply 231072 by 110649 and get the answer in just a single line? Can you find the cube root of 262144 or 704969 in two seconds? Can you predict the birth-date of a person without him telling you? Can you predict how much money a person has without him telling you? Can you check the final answer without solving the question? Or, in a special case, get the final answer without looking at the question? Can you solve squares, square roots, cube-roots and other problems mentally?All this and a lot more is possible with the techniques of Vedic Mathematics described in this book. The techniques are useful for students, professionals and businessmen. The techniques of Vedic Mathematics have helped millions of students all over the world get rid of their fear of numbers and improve their scores in quantitative subjects. Primary and secondary school students have found the Vedic mathematics approach very exciting. Those giving competitive exams like MBA, MCA, CET, UPSC, GRE, GMAT etc. have asserted that Vedic Mathematics has helped them crack the entrance tests of these exams. Popular Searches The book Vedic mathematics Made Easy by Dhaval Bathia (author) is published or distributed by Jaico Publishing House [8179924076, 9788179924075]. This particular edition was published on or around 2005-1-1 date. Vedic mathematics Made Easy has Paperback binding and this format has 256 number of pages of content for use. The printed edition number of this book is 1. This book by Dhaval Bathia
The History of Mathematics: An Introduction his...more historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social context behind mathematics' greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Sixth Edition a valuable resource that teachers and students will want as part of a permanent library.(less) Hardcover, 800 pages Published November 8th 2005 by McGraw-Hill Science/Engineering/Math (first published 1985) ...more to follow the discussion if one wasn't at least passably fluent with set theory, as just one example. Some of the terminology used in these cases without explanation was more than a touch impenetrable, and considering that the topics being discussed were topics that are rarely discussed until at least upper-level undergraduate courses and frequently beyond, it is not unreasonable to expect enough explanation to enable someone without much previous exposure to the concepts to at least understand what is being discussed; because there was not even that much explanation, I would not recommend the last couple of chapters to anyone without at least some graduate level math courses under their belt. Most of the book, though, did not suffer from this problem and was quite readable. (less) see...more seems fashionable in some fringe circles to suppose. (less)
books.google.com - This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective.... art and craft of problem solving The art and craft of problem solving This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective. From inside the book Page 330 Review: The Art and Craft of Problem Solving User Review - Goodreads Great problems, lack of solutions. If you want a challenge, this is it. Review: The Art and Craft of Problem Solving User Review - Goodreads This is a lovely book about sharpening your mind to tackle tougher and tougher problems. Unfortunately it is so focused on math that it doesn't lend itself readily to being adapted into my courses. It was still fun to try some of the problems, though. About the author (1999) About the Author Paul Zeitz studied history at Harvard and received a Ph.D. in mathematics from the University of California, Berkeley. He taught high school math in San Francisco and Colorado and. He has helped train several American IMO teams, most notably the 1994 "Dream Team" which, for the first time in history, achieved a perfect score.
Precalculus With Limits 9780073365800 ISBN: 0073365807 Pub Date: 2007 Publisher: McGraw-Hill College Summary: The Barnett, Ziegler, Byleen College Algebra series is designed to be user friendly and to maximize student comprehension, emphasizing computational skills, ideas, and problem solving as opposed to mathematical theory. Suitable for a one or two semester college algebra with trigonometry or precalculus course, Precalculus with Limits introduces a unit circle approach to trigonometry and includes a chapter on limits to... provide students with a solid foundation for calculus concepts.The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematical concepts. In each section, the worked examples are followed by matched problems that reinforce the concept being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. A MathZone site featuring algorithmic exercises, videos, and other resources accompanies the text. Barnett, Raymond A. is the author of Precalculus With Limits, published 2007 under ISBN 9780073365800 and 0073365807. Thirty five Precalculus With Limits textbooks are available for sale on ValoreBooks.com, thirty three used from the cheapest price of $19.89, or buy new starting at $83.35
4 3 2 2 0 1 2 Verry nice Needs english or language settings I can't understand it. It would be more use full if it had that. Cause I can't understand it and I'm uninstalling it till I can read it A Google User User reviews A Google User August 14, 2012 Verry nice Needs english or language settings I can't understand it. It would be more use full if it had that. Cause I can't understand it and I'm uninstalling it till I can read itHow to calculate the linear equation, area, volume, and more! All our application Formelsammlung Mathematik! Formelsammlung Mathematik and you will know the answer to any question! Formelsammlung Mathematik everything you need while studying. Install Formelsammlung Mathematik, enjoy pleasure mathThe application "math expert pro" is a collection of formulas out of mathematics and physics. The special feature is that the application can calculate the formulas. The calculation is based on the motto "Tell me what you know, and I will check which calculations are possible."This app will provide you a great tool if you want to plot a mathematic function. You only have to write formula, and curve will be displayed in a customizable chart. You can choose minimal and maximal
Student Solutions Manual for Larson/Hostetler/Edwards' Algebra and Trigonometry: A Graphing Approach and Precalculus: A Graphing Approach Summary This manual offers step-by-step solutions for odd-numbered text exercises and for all items in the Chapter and Cumulative Tests, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer. It also provides practice tests with answers.
Browse Results Modify Your Results An Introduction to Mathematics for Economics introduces quantitative methods to students of economics and finance in a succinct and accessible style. The introductory nature of this textbook means a background in economics is not essential, as it aims to help students appreciate that learning mathematics is relevant to their overall understanding of the subject. Economic and financial applications are explained in detail before students learn how mathematics can be used, enabling students to learn how to put mathematics into practice. Starting with a revision of basic mathematical principles the second half of the book introduces calculus, emphasising economic applications throughout. Appendices on matrix algebra and difference/differential equations are included for the benefit of more advanced students. Other features, including worked examples and exercises, help to underpin the readers' knowledge and learning. Akihito Asano has drawn upon his own extensive teaching experience to create an unintimidating yet rigorous textbook
Possibly the biggest challenge teachers face in the classroom is getting their pupils to think for themselves. When children learn to think independently, they are able to take control of their own learning. What's more, they become good at dealing with the many problems that life will inevitably throw their way – not only good at solving these problems, but at choosing the kind of thinking strategies that will help solve them. This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. It's amazing how many images the world's photographers produce! Professional or not, images surround us in our everyday lives. What makes successful photographers stand out? What drives us to revisit the same images over and over? Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space.
Introduction to Econometrics provides students with clear and simple mathematics notation and step-by step explanations of mathematical proofs to ...Show synopsisIntroduction to Econometrics provides students with clear and simple mathematics notation and step-by step explanations of mathematical proofs to give them a thorough understanding of the subject. Extensive exercises are incorporated throughout to encourage students to apply the techniques and build confidence. This new edition has been thoroughly revised in line with market feedback. Retaining its student-friendly approach, Introduction to Econometrics has a comprehensive revision guide to all the essential statistical concepts needed to study econometrics, more Monte Carlo simulations than before and new summaries and non-technical introductions to more advanced topics at the end of chapters. Online Resource Centre For lecturers: - Instructor manuals for the text and data sets, detailing the exercises and their solutions - PowerPoint slides For students: - Data sets - Study guide - Software manual - PowerPoint slides with explanations - Contact the author99567085 Brand New International edition. 100% Same...New. 019956708599567085 Brand New Paperback Overseas International...New. 0199567085
Book summary This introduction to the geometry of lines and conics in the Euclidean plane is example-based and self-contained, assuming only a basic grounding in linear algebra. Including numerous illustrations and several hundred worked examples and exercises, the book is ideal for use as a course text for undergraduates in mathematics, or for postgraduates in the engineering and physical sciences. [via]
JEE Main Mathematics Syllabus 2013 JEE Mathematics Syllabus Pdf-JEE Main Maths Syllabus 2013: JEE Main Syllabus 2013 contains Maths,Physics and Chemistry subjects and the pen and paper based exam will conduct on 7-4-2012 from 9 :30 am to 12:30 PM.The JEE Mains 2013 Online exam will conduct on 2 dates of 8th April and 25th April,2013.Here you can download the Topic/Unit wise Full Maths Syllabus for JEE Main exam 2013 by clicking on Pdf symbol in the left side. Download JEE Main Syllabus for Mathematics: UNIT 1 : Sets,Relations and Functions Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions;. one-one, into and onto functions, composition of functions. UNIT 2 : Complex Numbers and Quadratic equation Complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots. UNIT 3 : Matrices and Determinants Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices. UNIT 4 : Permutation and Combinations: Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications. UNIT 5 : Mathematical Indiction Principle of Mathematical Induction and its simple applications. UNIT 6 : Binomial Theorem and Simple Applications: Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications. Evaluation of simple integrals of the type Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form. UNIT 10: Differential Equations: Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type: dy/dx+p(x)y=q(x) UNIT 11: Co-ordinate Geometry: Cartesian system of rectangular co-ordinates 10 in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes. Straight lines Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines. Circles, conic sections Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency. UNIT 12: 3-D Geometry: Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines. UNIT 13: Vector Algebra: Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product. UNIT 14: Statistics and probability: Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
Elementary Linear Algebra 9780471669609 ISBN: 0471669601 Edition: 9 Pub Date: 2004 Publisher: Wiley Summary: This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. Clear, accessible, step-by-step explanati...ons make the material crystal clear. The authors spotlight the relationships between concepts to give a unified and complete picture. Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues. Howard Anton is the author of Elementary Linear Algebra, published 2004 under ISBN 9780471669609 and 0471669601. Four hundred fifty nine Elementary Linear Algebra textbooks are available for sale on ValoreBooks.com, one hundred thirty seven used from the cheapest price of $6.08, or buy new starting at $12.75.[read more] Ships From:Salem, ORShipping:Standard, ExpeditedComments:New Condition. SKU:9780471669609-1-0-3 Orders ship the same or next business day. Expedited shipp... [more]
basic mathematics and high school mathematics. Pre-algebra gives students the basic building blocks for algebra. Single variable equations and ratios are the biggest focus for pre-algebra students
an alphabetical dictionary and handbook that gives parents of elementary, middle school, and high school students what they need to know to help their children understand the math they're learning. The book can also be used by students themselves and is suitable for anybody who is reviewing math to take standardized tests or other exams. Foreign students, whose English-language mathematics vocabulary needs to be strengthened, will also benefit from this book.
Digital video from the Futures Channel. Synopsis: "To design buildings that don't fall down, you need to know how your materials will respond to forces such as gravity, wind, and earthquakes." Running time 3:02 minutes. Rating: Related Resources Usage Tip Use of Resource: How I use Structural Engineering - Video from the Futures Channel This video comes with three lesson plans for grades 6-12 with details: Weight on a String Subject: Mathematics Topics: Algebra--Equations and Expressions; Powers, Roots and Scientific Notation Grades: 9 - 12 Knowledge and Skills: - Can evaluate expressions by substituting values for variables - Can simplify expressions using correct order of operations - Understands the function of grouping symbols in an expression - Understands the concept "root" Cantilevers Subject: Mathematics Topics: Algebra--Patterns, Functions and Relations; Linear Equations and Functions; Polynomial Equations and Functions Grades: 6 - 12 Concepts: - Function Knowledge and Skills: - Can explain the reasoning used to solve a problem - Can plot a point in a two -dimensional coordinate system, given the coordinates, or determine the coordinates of a given point - Can determine the equation of a linear function that closely matches a set of points (optional) - Can determine the equation of a cubic function that closely matches a set of points (optional) SkyHighScrapers Subject: Mathematics Topics: Algebra?Quadratic Equations and Functions Grades: 8 - 12 Concepts: - Quadratic Knowledge and Skills: - Can determine the equation of a quadratic function that closely matches a set of points - Given the equation of a specific quadratic relation, can rapidly sketch its graph
new, revised edition of the bestselling Speed Mathematics features new chapters on memorising numbers and general information, calculating statistics and compound interest, square roots, logarithms and easy trig calculations. Written so anyone can understand, this book teaches simple strategies that will enable readers to make lightning-quick calculations. People who excel at mathematics use better strategies than the rest of us; they are not necessarily more intelligent. With Speed Mathematics you'll discover methods to make maths easy and fun. This book is perfect for students, parents, teachers and anyone who enjoys working with figures and even those who are terrified of numbers!
Math for the Automotive Trade, 5th Edition MATH FOR THE AUTOMOTIVE TRADE, 5E is an up-to-date, highly practical book that helps you develop a real-world understanding of math concepts and applications in the modern automotive repair trade. Written at a beginner's level, this book is a comprehensive instructional workbook that shows you how to solve the types of math problems faced regularly by automotive technicians. Unique to MATH FOR THE AUTOMOTIVE TRADE, 5E are realistic practice exercises that allow you to determine if your answers fall within manufacturers' specifications and repair orders that are completed by finding the appropriate information in the professional literature and reference material, included in the book's valuable appendices151.95 Purchase Options Paperback $121.49 $12149 from$37.49 Save up to $114.46! Rent thru 09/06/14 for $37.49 $37.49 Save $114.46! Rent thru 03/05/15 for $42.99 $42.99 Save $108.96! Rent thru 02/28/16 for $46.49 $46.49 Save $105.46! Rent thru 02/17/18 for $51.99 $51.99 Save $99 access
MATH 201 Calculus I (5). Introduction to the differential calculus of elementary functions (including logarithmic, exponential, and trigonometric functions). Emphasis on limits, continuity, and differentiation. Applications of differentiation (including curve sketching, optimization, and related rates; antiderivatives. Students may not use any Computer Algebra System (CAS) capability in this course. Prerequisite: (1) A grade of C- or better in MATH 192; or (2) Satisfaction of the Entry Level Mathematics requirement and an appropriate score on the UC/CSU MDTP Calculus Readiness Test or equivalent. It is recommended that students enroll concurrently in MATH 281. Note: Students without recent credit in MATH 192 are advised to consult the Department of Mathematics and to take the UC/CSU Pre-calculus Diagnostic Test before enrolling in MATH 201. Course Objectives: Math 201 is the first in a sequence of four courses of basic calculus. Students passing this class will be able to do the following: 1.Understand and apply the concept of a limit. Be able to use graphical and numerical methods to identify situations where limits may not exist. Be able to apply algebraic methods to evaluate limits. 2.Understand and apply the concept of continuity. 3.Understand and apply the concept of derivative from the limit definition. Understand the geometric meaning of the derivative. Interpret the derivative as a rate of change. 4.Understand and apply the derivatives of basic functions, including trigonometric, logarithmic and exponential functions. 5.Understand and apply the rules of differentiation, including chain rule and implicit differentiation. 6.Understand and make use of applications of the derivative in linear approximations, rates of change, graphing functions, optimization problems, and roots of functions through Newton's method, and L'Hôpital's Rule. Homework: Mathematics is not a spectator sport. You learn by doing. Solve all odd problems from the sections listed above. Although homework assignments will not be collected, it is assumed that you will do the homework necessary for success in this class. We will spend considerable time at the beginning of each lecture working out homework problems. Answers to most of the assigned problems are in the back of the book. If you are not able to solve a particular problem, do not hesitate to ask! Your classmates will be grateful. Readings: The student is responsible for reading at least twice each section of the book covered in class: Before and after the lecture. The student will be told in advance what sections of the book are to read. If you are not able to understand something in the book, do not hesitate to ask! Your classmates will be grateful. Quizzes: There will be seven quizzes, each of them administered most Tuesdays at 5:05 the latest; the student will be able to drop the lowest score. Quizzes may not be made-up. If you miss a quiz you will get a score of "0" (zero) recorded. You may take any quiz early with the instructor's permission. Problems will be similar to those in the homework. The primary purpose of these quizzesis to provide you with frequent evaluation of your content acquisition and to help you to reduce math anxiety. Quiz work is individual, see Note 2 below. Activities: Seven activity assignments will be collected; the student will be able to drop the lowest score. Activity attendance is required. The student should work in groups of at least 3 people and 4 at most. During activity sessions the student will work on an activity sheet and each member of his/her group should hand in a report at the beginning of most Thursdays at the latest. Late reports and reports from students absent from even one meeting will not be accepted. A report should be neat and readable; solutions should follow an increasing numerical sequence. Each member of a group will receive the same number of points, so it is your responsibility to write down in each report only the names of those who substantially contributed to the activity. Exams: There will be two Midterm exams and a cumulative final. Questions and problems will deal with concepts discussed in lectures, homework, textbook, and activities. Exchange of information, calculators, and supplies is absolutely prohibited during exams! To clarify a particular situation, the instructor reserves the right to a further examination, written or oral. Exam work is individual, see Note 2 below. Midterm exams may not be made-up. If you miss an exam you will get a score of "0" (zero) recorded. You may take any exam early with the instructor's permission. Partial Credit: Only substantial contributions to the solution of a problem will count for partial credit. Mere restating of a problem or the quoting of an incorrect fact, for example, will not make you eligible for it. Students must watch out for logical mistakes, and must make sure that all the hypotheses are met before recalling a particular theorem. Grades: Your final grade is a function of the total of points awarded on the activities indicated above. Group homework is very helpful and greatly promoted in this course. However, it is necessary for college graduates to demonstrate individual competency on the subject. Therefore, regardless of your total of points, in order to get a D- or better in this course all of the following should be fulfilled at least: (a) To have scored at least 200 points in the 2 Midterm exams combined. (b) To have scored at least 105 points in the final exam. Generally, the following guidelines for grades apply: 960 -1000 A 900 - 959 A- 870 - 899 B+ 840 - 869 B 800 - 839 B- 770 - 799 C+ 740 - 769 C 700 - 739 C- 670 - 699 D+ 640 - 669 D 600 - 639 D- 0 - 599 F In order to take Math 202, you must pass Math 201 with a C- or better. To satisfy Goal B4, you need to earn C, not C-. Notes: 1) It is the student's responsibility to find out what (s)he missed if (s)he did not attend class. Office hours are not meant for tutorial courses, but rather to clarify particular situations or problems occurring during lectures, homework, labs, assignments or readings. Students are encouraged to make use of the Office Hours. 3) The instructor will hold graded papers for one week at most. After this period, he will trash old papers. Contact him as soon as you foresee a problem picking up your paper(s). 4) All handouts (with solutions) will be in the internet (follow the link Math 201 in 5) Beepers, cell phones, i-pods, laptops and similar electronic devices must be turned off at all times during class or lab time. If not, the student will have to leave the room without being allowed to return. 6) Students can be at most 10 minutes late. Students cannot leave the room unless it is for medical reasons. 7) Students with Disabilities: For list of your duties and privileges: 8) Additional Resources: The Math Tutoring Center is the best source for free help on campus: For hours, check
56 minute basic algebra lesson is for the beginning algebra student or for anyone who has not recently studied algebra. It includes the language and symbols of algebra, (plus or minus ±, equal to =, not equal to ≠, approximately equal to, less than <, less than or equal to ≤, greater than >, greater than or equal to ≥) and introduces the polynomial. In this lesson you will be introduced to the variable "x", learn what a term, factor, exponent and degree of a term mean and be able to: - understand what a polynomial, binomial, trinomial, are - evaluate a polynomial with integers (numbers) - simplify polynomials by collecting like terms - simplify polynomials with brackets - simplify polynomials using the distributive property - do application problems such as by how much does 2x^2 -3x + 5 exceed 3 x^2 - 5x + 6 This lesson contains explanations of the concepts and 27 example questions with step by step solutions plus 5 review questions with solutions. About this Author Teacher Sydney is a certified teacher, B.A., B. Ed. (Math Major). She prepared a math help program consisting of 65 very comprehensive, plain and "no fluff" math video lessons. These lessons are a convenient and easy way to get math help. Pick and choose only the lesson(s) or packages (series) that you want. There are free previews. You might look at the Transcripts for a quick review of the lesson content. For a complete list of lessons available on MindBites (mathmadesimple.mindbites.com. To access free previews please see above or visit MathMadeSimple.com and click on the tab "LIST OF ALL LESSONS". Recent Reviews All the terms and concepts of Algebra are here. Was an excellent refresher for me and would probably have made my earlier math classes go by much smoother. No frills and no fluff but it gets the job done. All the terms and concepts of Algebra are here. Was an excellent refresher for me and would probably have made my earlier math classes go by much smoother. No frills and no fluff but it gets the job done.
AN INTRODUCTION TO QUADRILATERAL GEOMETRY February 16, 2013 - 15:36 — Anonymous Author(s): Ovidiu T. Pop, Nicusor Minculete, and Mihaly Bencze Publisher: Editura Didactica Si Pedagogica, R. A. Year: 2013 ISBN: 978-973-30-3324-0 Short description: The book consists of seven chapters written by three eminent mathematicians in the subject of Euclidean Geometry. It is especially useful for students and teachers who are preparing for National and International Mathematical Olympiads.
The Mathematics VSB Course will discuss topics in Algebra. The first lesson will lay the groundwork for all succeeding lessons, by familiarizing the user with definitions and notations that will be used throughout the course
for College Students: Early Graphing An emphasis on the practical applications of algebra motivates readers and encourages them to see algebra as an important part of their daily lives. ...Show synopsisAn emphasis on the practical applications of algebra motivates readers and encourages them to see algebra as an important part of their daily lives. Strongly emphasizes good problem-solving skills, uses real-world applications. For anyone interested in Algebra
Saxon Algebra ½ basic homestudy kit contains two books, the student book and also the tests and answers book. Additional items are available in other kits or even alone. The solutions manual helps teachers grade more easily, another is a CD-ROM to aid student understanding of the material. The basic format of these pre Algebra books is the same as the other Saxon texts. Each lesson explanation covers another small increment of a concept and gives example problems. Next the student practices several similar problems. Finally, the student works through a problem set of 30 or so review problems. The review is comprehensive; any previous problem type, even some from previous books may appear in the problem sets. Topics and Methodology The topics covered in Saxon Algebra ½ are all topics typically covered in pre Algebra books, as well as more advanced topics from geometry and discrete mathematics. Since Saxon Algebra ½ is the culmination of pre-algebraic studies, students are expected to be competent in a number of areas of mathematics. These include decimals, mixed numbers, signed numbers, and numbers in base 2; arithmetic operations involving all those forms of numbers; order of operations; persents, proportions, ratios, and divisibility; rounding and place value; unit conversions and scientific notation. Students are introduced to the simplification of algebraic expressions; the evaluation of algebraic expressions, and the solution of linear equations in one unknown. The methodology of the Saxon Algebra books is based on a teaching philosophy that says learning does not have to be hard, but it does take time. Concepts are broken down into small increments to increase understanding, and review is constant to ensure that over time the repetition will imprint so deeply into a student's memory that he or she will not forget how to do any of the problems. DIVE Into Math offers CD-ROMs that show a teacher who explains in greater detail and more in-depth the lesson for each day and how it relates to everything else they've learned. The teacher also works several example as well as practice problems to show how its done. Standardized Test Preparation Saxon has an excellent reputation for preparing students well on standardized tests. Teacher Requirements Saxon Algebra 1/2 is designed in a way that is perfect for the homeschool family. Each lesson's explanation is clear and easy to understand, perfect for independent study. The solutions manual contains complete worked out problems, not merely the answers, making grading a piece of cake for parents. And for those parents who are not mathematically inclined, but want to be able to give a little more explanation when their student needs it there are the DIVE CD's.
Since each lesson is stored separately, you can easily move about from lesson-to-lesson as well as maneuver within the lesson you're watching. Taught from a Christian worldview, Dr. David Shormann also provides a weekly syllabus to help students stay on track with lessons. Saxon Math 6/5 covers divisibility, prime numbers, roots, powers, probability, multiplication, division, fractions, decimals, percents, geometry and negative numbers. *The current edition of Saxon Math 6/5 is the 3rd Edition. The 2nd edition is offered for families using older versions of Saxon Algebra 1 covers functions, linear and quadratic equations, statistics, probability, geometry and more. 3rd Edition. Algebra 2 covers traditional second year algebra topics, as well as geometry, real world problems, linear and nonlinear equations, statistics and probability, graphing and basic trigonometry. A balanced, integrated mathematics program that has proven itself a leader in the math teaching field, Saxon Geometry covers triangle congruence, postulates and theorems, surface area and volume, two-column proofs, vector addition, slopes and equations of lines, and other high school geometry concepts Students taking Physics should have completed Algebra II and at least half of Advanced Mathematics. DIVE CLEP Professor CLEP Professor is a software series that prepares students for College Level Examination Program (CLEP) and Advanced Placement (AP) exams. Each title in the series provides a diagnostic test, interactive video lectures that teach each concept, practice problems with video solutions, and computer based practice exams. DIVE into college-prep science! Once you add a text, DIVE Chemistry may be used with any high school chemistry textbook, including Abeka or the textbooks listed above. DIVE into college-prep science! Once you add a text, DIVE Physical Science lays a solid foundation for chemistry and physics. Topics include atoms, chemical compounds and reactions as well as force, motion, thermodynamics, and electricity. Students need to have completed Algebra 1 or be taking it concurrently.
Find a KemahThese subjects use the same notations as do algebra, so once you master them you can move forward into more advanced topics. Algebra is not necessarily easy, but it is completely logical. There is nothing you learn early that will be contradicted by later lessons.
0903 - Prealgebra/Basic Mathematics - 3 credit hours A basic arithmetic course, it is a prerequisite to Elementary Algebra (MA 0913) for students who have not mastered middle school mathematics. Course content includes: whole numbers and their operations; fractions and decimals; ratio and proportion; percentages; signed numbers; basic geometry; and data interpretation. A minimum grade of B- is required prior to enrolling in Elementary Algebra. Grading: Pass/Fail. 0913 - Elementary Algebra - 3 credit hours A competency-based course, for students who have not had high school Algebra I or whose algebraic skills are weak. Course content includes: a review of signed numbers; a comprehensive study of real numbers; solving linear equations and inequalities; introduction to exponents; introduction to polynomials; factoring; and rational expressions. Prerequisites: MATH 0903 or a minimum ACT mathematics subscore of 13 or an Accuplacer arithmetic score of 63-120 or equivalent. Grading: Pass/Fail. 0923 - Intermediate Algebra - 1 credit hour An algebra course whose content parallels content commonly found in a second-year high school algebra course, namely high school Algebra II. For students who have had high school Algebra I, but haven't had high school Algebra II or whose algebraic skills at that level are weak. Course content includes: an introduction to graphing; graphing linear equations and inequalities; solving linear systems; rational expressions; rational exponents and radicals; quadratic equations, and an introduction to functions and their graphs. Prerequisites: MATH 0961 or MATH 0913 or a minimum ACT mathematics subscore of 16 or an Accuplacer algebra score of 33-120 or equivalent. Grading: Pass/Fail. 0941 - Elementary Algebra A - 1 credit hour A competency-based course for students who have not had a high school Algebra I course or whose algebraic skills are weak. The course is designed to strengthen skills in working with integers, the real numbers, simplifying algebraic expressions, and translating English phrases into algebraic expressions. Prerequisites: MATH 0903 or a minimum ACT mathematics subscore of 13 or an Accuplacer arithmetic score of 63-120 or equivalent. Grading: Pass/Fail. 0951 - Elementary Algebra B - 1 credit hour A competency-based course which is a continuation of MATH 0941. The course is designed to strengthen skills in working with linear equations and inequalities, common formulas, and translating problems stated in English into algebraic relationships and to give an introduction to linear equations in two variables. Prerequisite: MATH 0941. Grading: Pass/Fail. 0961 - Elementary Algebra C - 1 credit hour A competency-based course which is a continuation of MATH 0951. The course is designed to strengthen skills in working with integer exponents and translating English phrases into algebraic expressions, to introduce polynomials, operations on polynomials and factoring of polynomials. Prerequisite: MATH 0951. Grading: Pass/Fail. 0971 - Intermediate Algebra A - 1 credit hour A competency-based course for students who have not had a high school Algebra II course or whose algebraic skills are weak. The course is designed to strengthen skills in working with integer exponents, graphical and algebraic solutions to linear equations and inequalities, and function notation. Prerequisites: MATH 0961 or MATH 0913 or a minimum ACT mathematics subscore of 16 or an Accuplacer algebra score of 33-120 or equivalent. Grading: Pass/Fail. 0981 - Intermediate Algebra B - 1 credit hour A competency-based course which is a continuation of MATH 0971. The course is designed to strengthen skills in working with systems of linear equations, operations on and factoring of polynomials, and solution of polynomial equations by factoring, completing the square and the quadratic formula. Prerequisite: MATH 0971. Grading: Pass/Fail. 0991 - Intermediate Algebra C - 1 credit hour A competency-based course which is a continuation of MATH 0981. The course is designed to strengthen skills in working with rational expressions and expressions involving rational exponents and radicals. Prerequisite: MATH 0981. Grading: Pass/Fail. 1003 - Data Models - 3 credit hours Mathematical models are developed and utilized for data analysis and decision making. Data sets and problems are taken from a wide array of disciplines. The integration of Mathematics and Technology is emphasized. Mathematical topics include: the need for rigor; Cartesian coordinate systems and their use in geographical information systems, density plots, discriminant analysis and contour plots; time series data; dynamical systems; and modeling with straight lines. Prerequisites: MATH 0961 or MATH 0913 or a minimum ACT mathematics sub score of 16 or an Accuplacer algebra score of 33-120 or an Accuplacer college-level mathematics score of 0-43. 1113 - College Algebra - 3 credit hours Content is an extension of content commonly found in second-year high school algebra courses. It is a prerequisite for most other college-level mathematics courses. Course content includes: functions and their graphs, nonlinear equations and inequalities, conic sections, matrices and determinants. Prerequisites: MATH 0991 or MATH 0923 or a minimum ACT mathematics subscore of 20 or an Accuplacer college-level mathematics score of 44-85 or equivalent. Course rotation: All semesters. 2301 - Mathematics & Technology - 1 credit hour An array of current technologies is utilized to solve mathematical problems at the level of calculus and below. Exposure to the appropriate use and limits of technology is the main objective. The course is conducted in a laboratory format and is intended for prospective math majors. Grading: Credit/No Credit. Corequisite: MATH 2315. Course Rotation: Fall. 2303 - Calculus for Business and Social Sciences - 3 credit hours Course covers selected topics in elementary calculus and analytic geometry for students in business and social sciences. Credit will be allowed for only one course of MATH 2315 or MATH 2303. Prerequisite: MATH 1113 or equivalent. Course Rotation: Spring in odd years. 2503 - Discrete Mathematics - 3 credit hours An introduction of the applications of mathematics to problem situations with an emphasis on the development of problem-solving skills (using Pólya's four-step process). Current technology (graphics calculators and computer software) will be used whenever possible. Conjectures will be posed and informal/formal proofs will be discussed with content including set theory, mappings, mathematical induction, and equivalence relations. Prerequisite: MATH 1124 or equivalent. Course Rotation: Fall. 3121 - History's Great Problems - 1 credit hour A study of selected topics from the history and nature of mathematics from ancient to modern times, with an emphasis on important mathematical concepts and problems. Prerequisite: MATH 2503. Course Rotation: Spring odd years. 3131 - History's Great Mathematicians - 1 credit hour A study of selected topics from the history and nature of mathematics from ancient to modern times, with an emphasis on the biographies and mathematical interests of prominent mathematicians. Prerequisite: MATH 2503. Course Rotation: Spring even years. 3151 - Mathematics Education I - 1 credit hour Historical and current perspectives of mathematics education; an introduction to mathematics education organizations and their resources; and exposure to technologies used in mathematics. Prerequisites: MATH 2315 and EDUC 1103. Course Rotation: Fall even years. 3161 - Mathematics Education II - 1 credit hour An introduction to place-based mathematics, ethnomathematics, and the integration of mathematics and social justice issues; and an emphasis on demonstrative mathematics in the school mathematics curriculum. Prerequisites: MATH 2315 and EDUC 1103. Course Rotation: Fall odd years. 3203 - Probability and Statistics - 3 credit hours Concepts and topics explored in this class include: a review of elementary properties of probabilities events, statistical densities and distributions; properties of random variables; expected values; law of large numbers; and sampling. Emphasis is on use of integrated statistical packages (or graphics calculator) to complement the statistical methodology. Corequisite: MATH 3314. Course Rotation: Fall. 4003 - History of Mathematics - 3 credit hours This course is a study of selected topics from the history and nature of mathematics from ancient to modern times, with an emphasis on the historical development of mathematics through a study of biographies of prominent mathematicians and the evolution of important mathematical concepts. The fundamental role of mathematics in the rise, maintenance, and extension of modern civilization will also be considered. Prerequisites: MATH 2325 and MATH 3113. Course Rotation: Varies. 4403 - Mathematical Modeling - 3 credit hours An introduction to the application and modeling processes of mathematics. This course emphasizes continuous models to include deterministic and stochastic models. The use of computer packages and algorithms will be incorporated into the solution process. An individual project is required. Prerequisite: MATH 3314 or MATH 3323. Course Rotation: Varies.
Facilitative Role of Graphing Calculators in Learning Col Algebr Description: The purpose of this paper was to explore (1) the facilitative effect of the use of a graphing calculator (gc) on mathematical problem solving in the context of an adult (18]) college algebra class; (2) the connection between mathematicsMore... List price: $62.00 Buy it from: $68.44 Customers Also Bought The purpose of this paper was to explore (1) the facilitative effect of the use of a graphing calculator (gc) on mathematical problem solving in the context of an adult (18]) college algebra class; (2) the connection between mathematics self-efficacy (mse) and college students' academic performance by using the gc as a tool in the college algebra class, (3) the effects of 6-week interventions designed to increase mse; and (4) the relationship between mse and individuals' learning styles. The results show that gc practice does benefit problem solving, particularly when the problem requires understanding of graphic representation. Higher accuracy and mse results showed that the use of gc successfully and positively promotes individuals' mse, and, specifically, algebra classes. On individuals' learning styles, visual learners do obtain a significant benefit from the use of gc's and higher mse when compared to balanced learners
This comprehensive textbook is designed to take undergraduate and beginning graduate students of mathematics, science, and engineering from the rudimentary beginnings to the exciting frontiers of dynamical systems and their applications. It is a masterful exposition of the foundations of ordinary differential and difference equations from the contemporary viewpoint of dynamical systems and bifurcations. In both conception and execution, the authors implemented a fresh approach to mathematical narration. Fundamental ideas are explained in simple settings, the ramifications of theorems are explored for specific equations, and above all, the subject is related in the guise of a mathematical epic. With its insightful and engaging style, as well as its numerous computer-drawn illustrations of notable equations of theoretical and practical importance, this unique book will simply captivate the attention of students and instructors alike. 345 illustrations.80387971414 Book Description:Springer-Verlag New York Inc., New York, NY, 1996. Book Condition: New. Language: english. Focuses on the subject of dynamical systems. The fundamental ideas of dynamics and bifurcations are explained. Print On Demand. Bookseller Inventory # 5595454 InIn
12th Grade Math Help This is a representative list of topics covered in our Grade 12 Math program - however all programs will be customized for the individual student. Instructions To Master -12th Grade Math Step 1 Monitoring to your progress and ask questions from the start of your 12th Grade Math semester. If you have problems with this homework, write down the specific numbers. Ask for help as soon as you have trouble and do not wait until the day before to a test. Teachers are a set more likely to help you if you have the material ready at hand and try to prepare ahead of time. Take the time to read the objects in the textbook even if you think that you understand it. Many students rely severely on the teachers lecture, but math textbooks now often contain color-coded examples, suitable charts and tricks for remembering formulas. The writers gear to the text books toward various learning styles, so you might pick something up that you missed from the teacher. Step 4 Figure out how concepts are mutually similar and different from each other. For example compare the concepts we learnt on Algebra 1, 2 when compared with 12th Grade Curriculum. Then, determine the differences between the two skills. This will help you remember formulas in addition to graphs so that you retain the information in a "big-picture" way as you enter 12th grade. Step 5 When a test draws near, use this chapter reviews and chapter tests of the book to practice quizzing yourself. Assigned to homework problems alone are almost never enough practice to do well on a test. In addition, tackle problems that are harder than ones your teacher assigned or that you expect to be on the test. 12th Grade Math 12th grade math, cover all topics covered in earlier grades, but in advanced level. It is very important to be well prepared and comfortable with concepts in this grade to get ready for Higher studies. You need to have a good knowledge of topics like: Algebra, Calculus, Geometry, Probability and Statistics.
Online Math Applications 1998 We designed our web page to meet three educational objectives: To apply math to real-life situations; To make math interesting and stimulating; To share interactive math experiences over the Internet. We show that math is part of our daily life by applying it to driving a car, listening to music, using a computer and saving and investing for college funds. The mathematical concepts in each of our topics are defined with simple equations at elementary and junior high math levels. When students realize that they can use simple math to understand and solve problems relevant to their lives, they will discover that math is stimulating. We take away fear of learning math by using simple equations for complicated real-life application. We ask users to submit a quiz to share in the hope of stimulating their imagination in the real world. As more users submit their quizzes, we will build up a database of interesting real-world math applications
A Java applet that introduces Riemann sums based on the midpoint and trapezoid methods, with questions to answer using the applet. Includes a re-scalable presentation version with large fonts. More: lessons, discussions, ratings, reviews,... A discovery worksheet that allows students to find the formal definition for Riemann sums. It ends with practice questions that students can do on their own. Included in the teacher sheets is an art... More: lessons, discussions, ratings, reviews,... This activity builds on the previous activity, One Type of Integral, by suggesting two more efficient ways of estimating the area under a curve (definite integral) than counting squares: adding the ar... More: lessons, discussions, ratings, reviews,... Graphical illustration of the Riemann sums of a function defined by its graph. The tool allows selecting the point inside the subintervals in several ways which helps show the dependence of the approx
Homework is due at the beginning of the following class meeting (it must be on the table before class begins). Homework may be turned in early (place it in my mail box, my hand, or gently slide it under my door). Late homework will be reduced in value by 50% for each day, or fraction thereof, it is late. Some of the homework will be easy, some difficult and some may be impossible (because that is the way problems are in real life)! Part of what you are to learn is what you can and cannot do. Comments: Number theory is the study of the integers which includes such things as cryptology, divisibility rules, finding massive primes... It is a great course for secondary education students because of its many simple and curious problems. Yes, number theory has proofs, though it is nowhere as proof intensive as Abstract Algebra or Real Analysis. Departmental Objectives: The student will: Identify and apply various properties of and relating to the integers including the Well-Ordering Principle, primes, unique factorization, the division algorithm, and greatest common divisors. Identify certain number theoretic functions and their properties. Understand the concept of a congruence and use various results related to congruences including the Chinese Remainder Theorem.
Precalculus228.49 FREE None(1 Copy): Owls Books OH, USA $81.33114.4767 FREE Used Good(1 Copy): Good 0840068077128.96132.13141.67 FREE Used Good(55 Copies): Good May NOT include supplemental materials such as CDs and access codes. May include some highlighting or writing. This Old Firehouse WA, USA $159.19 FREE New: New 0840068077171.99 FREE None(15 Copies): USED BOOK Book Emporium IN, USA $177.93 FREE Used Good(61224.62 FREE About the Book This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, providing students with a solid foundation in the principles of mathematical thinking. Comprehensive and evenly paced, the book provides complete coverage of the function concept, and integrates a significant amount of graphing calculator material to help students develop insight into mathematical ideas. The authors' attention to detail and clarity, the same as found in James Stewart's market-leading Calculus text, is what makes this text the market leader.
23 4 4 3 1 2 1 1 1 Adverts OK expression calculator but the interface is clunky and adverts make it worse. Calc Etc is much better and is free (no ads either) A Google User Well designed calculator. Best to me comparing to others. A Google User Expect to see graph support. A Google User Good tool for students A Google User Great tool. Like it A Google User Good but can be improved Says it does complex numbers - but although exp(i) works, log(i) sin(i) etc do not. I have moved to using addi instead. A Google User User reviews A Google User June 22, 2012 Adverts OK expression calculator but the interface is clunky and adverts make it worse. Calc Etc is much better and is free (no ads either) More from developerSmart Math Calculator is a powerful tool to calculate mathematical expression and/or solve unknown variables from the expressions. It supports complex number, array (matrix), higher order integral, unit conversion and chart plotting. It is a powerful tool for students and/or professionals to analyze mathematical problems. Because it also support normal calculation, it can also be used as normal calculator for all Android users. This calculator has provided more than 40 diffused mathematical functions covering trigonometric calculation, complex number, matrix, integration, polynomial and chart plotting. It is also able to handle mathematical operators like +, -, , /, , ', %, etc. And these operators fully support matrix and complex numbers. In this way user is able to evaluate complicated expressions, which are either not supported or hard to input in most traditional calculators. Moreover, the calculator is also able to 4x*2 + x == 3, or a group of expressions like y13+4y2-3y3==7 y2/2-3y3+y1==9 y3/3-6An input expression is made up of operands, operators, variables, functions and parameters. An operand or a parameter may not be a number, it can be an expression. Blank characters between expression elements do not affect calculation result. Capitalized and uncapitalized characters are both supported. Examples of expression includes pow(4.01,3.1) (0.0731 + 9i) + sin(toRAD(sum(17, 21, avg(3.71, log(198.2), -9.99,112.7)))), abs(-11.2)/(2!) + exp(i+0.7) + x1 2 == 12 - 6 x1 ** 3 or [[2, 3+7i], [3-4.07i, 4.11i], [2, 6]]' * [[2],[7-3i],[6.88 * stdev(2, 3, 4)]]. This calculator provides a calculator assistant tool which has two functions. One is inserting a constant into input. The other is converting value from one unit to another unit. If text in the input box is a valid real value, units conversion tab will use the value in the input box as initial value to-be-converted. Otherwise, units conversion tab does not place an initial value. If conversion is successful, user is able to insert the converted value into input. In order to help user input and evaluate (higher level) integration and plot 2D charts, this calculator includes built-in integration and chart-plotting utilities. User needs not
Algebra Reports I consistently hear from parents are that their children really understand algebra when they go through this course. It may not be exciting or colorful, but it really works. This set of videos with accompanying work sheets and answer keys comprises a complete first year algebra course and then some. Presentation is definitely not exciting, but it moves along at a steady pace without wasting time. Firebaugh uses a white board to demonstrate problem solving, explaining concepts clearly as he goes. Each video lesson presentation (145 in all) takes about fifteen minutes, then students practice on work sheets for about 30 to 45 minutes. Answer keys showing full solutions are included as well as tests. About 800 pages of work sheets, solutions, and tests come with the course. No parent preparation or participation is necessary. Students can work independently through all course work. The complete course consists of three groups of DVDs, listed on the order form as Phase One, Phase Two, and Phase Three. There are eight DVDs per Phase. One benefit of the "phase arrangement" is that you can purchase Phase One, try it out, then decide whether to invest in the complete program. A more important benefit is that you can use only Phases One and Two for a slower student who does not intend to pursue algebra any further. The material covered in the first two parts will still be sufficient for a first year algebra course. Students who complete all three Phases will have covered some coordinate geometry along with many Algebra 2 concepts. When you think about the cost, keep in mind that the DVD's are not consumable and you can reuse or resell them. Overall, this is a time and cost effective solution even though it lacks polish. Firebaugh also has an Algebra II course but I have not reviewed it. Pricing $79.95 per Phase
Mathematics Olympiad is a Problem solving Competition held in order to test and assess the innate problem solveing skills .. The Problems are restricted to those levels that requires minimal Back ground and high Ingenuity.. The Students are allowed to participate and not yet the candidates belonging to Under graduate Curriculum have been admitted into the programme.. The Mathematics Maths Olympiad India is conducted in three different stages.. Those have been mentioned in this web page.. Stage 1 - Regional Mathematical Olympiad (RMO) Stage 2 - Indian National Mathematical Olympiad (INMO) Stage 3 – International Mathematical Olympiad Training Camp (IMOTC) Stage 4: International Mathematical Olympiad (IMO) Homi Bhabha Centre for Science Education (HBCSE) is a National Centre of the Tata Institute of Fundamental Research (TIFR), Mumbai, India. The broad goals of the Centre are to promote equity and excellence in science and mathematics education from primary school to undergraduate college level, and encourage the growth of scientific literacy in the country. This web page Keeps You updated and enables you to have access and be fed up with the info about the Regional Indian International Mathematics Maths Olympiad India 2013-2014 .. We would provide the authentic info in this web page and if we are not certain we would mention that the updates are tentative .. Through the close sources we have , we would try and deliver you the right kind of stuffs at the right time which is more important and significant above all of those For more updates Visit the Face book page of this website and also follow the links given here in this web page.. Any queries don't hesitate to ask us and we are here to help and assist you in every possible manner, SaB Admin is an IT Engineer and full time blogger who wanna share his knowledge about the University, Recruitment, School Board & Entrance Exam Result, Time Table, Admit Card, Form, Date Sheet information.
Mathematical Ideas, Expanded Edition - Text Only - 10th edition Summary: The tenth edition of Mathematical Ideas is the best ever! We have continued with the features and pedagogy that have made this book so successful over the years and at the same time, we've spent a considerable amount of time to incorporate fresh data, new photos, and new content (by way of a new chapter on trigonometry). We have tried to reflect the needs of our users--both long-time readers and those new to the Math Ideas way of teaching liberal arts math. We hope y...show moreou'll be pleased with the results. Like its predecessors, this edition has been designed with a variety of students in mind. It is well-suited for several courses, including the aforementioned liberal arts audience, survey courses in mathematics, and mathematics for prospective and in-service elementary and middle school teachers. Ample topics are included for a two-term course, yet the variety of topics and flexibility of sequence make the text suitable for shorter courses as well. Our main objectives continue to be to provide comprehensive coverage of topics, appropriate organization, clear exposition, an abundance of examples, and well-planned exercise sets with numerous applications. Features : Chapter Openers Each chapter opens with an application related to the chapter topic. These help students see the relevance of mathematics they are about to learn. Margin Notes This popular feature has become a hallmark of this text and has been retained, updated, and added to where appropriate. Interspersed throughout the text, they deal with various subjects such as lives of mathematicians, historical vignettes, stamp and coin reproductions, anecdotes, newspaper and magazine articles, and current research in mathematics. They are designed to show students that math can be fun and interesting. We hope that users continue to enjoy the margin notes as much as we enjoy researching and composing them. Varied Exercise Sets We continue to present a variety of exercises including drill, conceptual, and applied problems. We continue to use graphs, tables, and charts when appropriate. Most sections include a few challenging exercises that require students to extend the ideas presented in the section. To address the issue of writing across the curriculum, most exercise sets include some exercises that require the student to answer by writing a few sentences. For Further Thought These entries encourage students to discuss among themselves their reasoning processes to gain a deeper understanding of key mathematical concepts by taking what they've just learned one step further. Examples Numerous, carefully written examples illustrate the concepts and skills introduced and give students step-by-step directions to help solve similar problems. Problem Solving Special paragraphs labeled "problem solving" relate the discussion of problem-solving strategies to techniques learned earlier in the chapter. Collaborative Investigations In response to instructor requests, we continue to address the issue of cooperative learning in the end-of-chapter feature "Collaborative Investigation." These exercises can be done in small groups or with the whole class and are designed to promote communication about mathematics topics. Chapter Tests Each chapter concludes with a chapter test so students can check their mastery of the material. The answers are provided at the back ofSusies Books Garner, NC 2003 Hardcover Fair This book is in acceptable conditon. It is a good reading copy for personal use if you want to save some money but do not try and give as a gift
Functions and Their Graphs. Using Technology: Graphing a Function. The Algebra of Functions. Portfolio. Functions and Mathematical Models. Using Technology: Finding the Points of Intersection of Two Graphs and Modeling. Limits. Using Technology: Finding the Limit of a Function. One-Sided Limits and Continuity. Using Technology: Finding the Points of Discontinuity of a Function. The Derivative. Using Technology: Graphing a Function and Its Tangent Line. Summary of Principal Formulas and Terms. Review Exercises. 3. DIFFERENTIATION. Basic Rules of Differentiation. Using Technology: Finding the Rate of Change of a Function. The Product and Quotient Rules. Using Technology: The Product and Quotient Rules. The Chain Rule. Using Technology: Finding the Derivative of a Composite Function. Marginal Functions in Economics. Higher-Order Derivatives. Using Technology: Finding the Second Derivative of a Function at a Given Point. Implicit Differentiation and Related Rates. Differentials. Portfolio. Using Technology: Finding the Differential of a Function. Summary of Principal Formulas and Terms. Review Exercises. 4. APPLICATIONS OF THE DERIVATIVE. Applications of the First Derivative. Using Technology: Using the First Derivative to Analyze a Function. Applications of the Second Derivative. Using Technology: Finding the Inflection Points of a Function. Curve Sketching. Using Technology: Analyzing the Properties of a Function. Optimization I. Using Technology: Finding the Absolute Extrema of a Function. Optimization II. Summary of Principal Terms. Review Exercises. Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Using Technology: Evaluating Definite Integrals. Evaluating Definite Integrals. Using Technology: Evaluating Definite Integrals for Piecewise-Defined Functions. Area between Two Curves. Using Technology: Finding the Area between Two Curves. Applications of the Definite Integral to Business and Economics. Using Technology: Consumers' Surplus and Producers' Surplus. Summary of Principal Formulas and Terms. Review Exercises. Functions of Several Variables. Partial Derivatives. Using Technology: Finding Partial Derivatives at a Given Point. Maxima and Minima of Functions of Several Variables. The Method of Least Squares. Using Technology: Finding an Equation of a Least-Squares Line. Constrained Maxima and Minima and the Method of Lagrange Multipliers. Double Integrals. Summary of Principal Terms. Review Exercises. Answers to Odd-Numbered Exercises. Index. Other Editions of Calculus for the Managerial, Life, and Social Sciences - With CD:
A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a... see more A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form.PDF versions are available to download for printing or on-screen viewing, an online version is available, and physical copies may be purchased from the print-on-demand service at Lulu.com. GNU Free Documentation License The American system of government, begun as an experiment in liberty and democracy in 1776, has proven to be remarkably... see more The American system of government, begun as an experiment in liberty and democracy in 1776, has proven to be remarkably resilient and adaptable. While often categorized as a democracy, the United States is more accurately defined as a constitutional federal republic. What does this mean? "Constitutional" refers to the fact that government in the United States is based on a Constitution which is the supreme law of the United States. The Constitution not only provides the framework for how the federal and state governments are structured, but also places significant limits on their powers. "Federal" means that there is both a national government and governments of the 50 states. A "republic" is a form of government in which the people hold power, but elect representatives to exercise that power. The book provides a thorough introduction to "modern'' or "abstract'' algebra at a level suitable for upper-level... see more The book provides a thorough introduction to "modern'' or "abstract'' algebra at a level suitable for upper-level undergraduates and beginning graduate students. The book addresses the conventional topics: groups, rings, fields, and linear algebra, with symmetry as a unifying theme. Finally, the best history has at its foundation a story. A printer challenges a King and so is laid the foundation of the... see more Finally, the best history has at its foundation a story. A printer challenges a King and so is laid the foundation of the first amendment; a New Jersey miner finds gold in California and sets off a torrent of movement westward; a woman going home from work does not relinquish her seat and a Civil Rights movement explodes.These stories all help to ask the question, "What is an American?" You'll help to answer that questionCollaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino,... see more and four year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind itPDF documentThis exciting new text provides a strategic marketing and managerial perspective of electronic commerce. The... see more PDF documentThis exciting new text provides a strategic marketing and managerial perspective of electronic commerce. The research of the four highly-qualified authors provides the basis for the book, allowing for first-hand experience, varied viewpoints, and relevance
The Math Center is a resource center that provides individual and group assistance in mathematics. The Math Center also facilitates Directed Learning Activities. Faculty instructors, instructional assistants, and Student tutors are available to assist students with challenging topics, answer questions, encourage understanding, and provide support for all math students. Students also have access to textbooks, graphing calculators, instructional videos, and computer programs. Math Center's Goals To help some students further develop basic skills in mathematics and keep them coming to school. To assist other students to further sharpen their pre-existing math skills and advance through math courses. To guide all students toward success in math and encourage them to excel through their scholastic endeavors and beyond.
Actions 9-10.1 Number and Operations 9-10.1.1 Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems. 9-10.1.1.PO 1 Justify with examples the relation between the number system being used (natural numbers, whole numbers, integers, rational numbers and irrational numbers) and the question of whether or not an equation has a solution in that number system. 9-10.5.1.PO 2 Analyze algorithms for validity and equivalence recognizing the purpose of the algorithm. 9-10.5.2.PO 1 Analyze a problem situation, determine the question(s) to be answered, organize given information, determine how to represent the problem, and identify implicit and explicit assumptions that have been made. 9-10.5.2.PO 4 Generalize a solution strategy for a single problem to a class of related problems; explain the role of generalizations in inductive and deductive reasoning. 9-10.5.2.PO 6 Synthesize mathematical information from multiple sources to draw a conclusion, make inferences based on mathematical information, evaluate the conclusions of others, analyze a mathematical argument, and recognize flaws or gaps in reasoning.
Practical Algebra Lessons, Hints, Examples, and common mistakes to avoid. Begins with topics such as absolute number and fractions, moves on through beginning, intermediate, and advanced algebra topics, and ends with a section on solving word problems. Elizabeth Stapel, Western International University. Learning Styles Inventory This learning style inventory was created by a learning specialist at Diablo Community College. It provides effective study strategies related to specific learning preferences.
Mathematical Thinking Problem-Solving and Proofs 9780130144126 ISBN: 0130144126 Edition: 2 Pub Date: 1999 Publisher: Prentice Hall Summary: For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematicsskills vital for success throughout the upperclass mathematics curriculum. The text offers both discrete an...d continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality. D'Angelo, John P. is the author of Mathematical Thinking Problem-Solving and Proofs, published 1999 under ISBN 9780130144126 and 0130144126. Four hundred thirty Mathematical Thinking Problem-Solving and Proofs textbooks are available for sale on ValoreBooks.com, one hundred forty one used from the cheapest price of $41.71, or buy new starting at $108.48edited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less]
More About This Textbook Overview Fundamentals of Mathematics represents a new kind of mathematical publication. While excellent technical treatises have been written about specialized fields, they provide little help for the nonspecialist; and other books, some of them semipopular in nature, give an overview of mathematics while omitting some necessary details. Fundamentals of Mathematics strikes a unique balance, presenting an irreproachable treatment of specialized fields and at the same time providing a very clear view of their interrelations, a feature of great value to students, instructors, and those who use mathematics in applied and scientific endeavors. Moreover, as noted in a review of the German edition in Mathematical Reviews, the work is "designed to acquaint [the student] with modern viewpoints and developments. The articles are well illustrated and supplied with references to the literature, both current and 'classical.'"The outstanding pedagogical quality of this work was made possible only by the unique method by which it was written. There are, in general, two authors for each chapter: one a university researcher, the other a teacher of long experience in the German educational system. (In a few cases, more than two authors have collaborated.) And the whole book has been coordinated in repeated conferences, involving altogether about 150 authors and coordinators.Volume I opens with a section on mathematical foundations. It covers such topics as axiomatization, the concept of an algorithm, proofs, the theory of sets, the theory of relations, Boolean algebra, and antinomies. The closing section, on the real number system and algebra, takes up natural numbers, groups, linear algebra, polynomials, rings and ideals, the theory of numbers, algebraic extensions of a fields, complex numbers and quaternions, lattices, the theory of structure, and Zorn's lemma.Volume II begins with eight chapters on the foundations of geometry, followed by eight others on its analytic treatment. The latter include discussions of affine and Euclidean geometry, algebraic geometry, the Erlanger Program and higher geometry, group theory approaches, differential geometry, convex figures, and aspects of topology.Volume III, on analysis, covers convergence, functions, integral and measure, fundamental concepts of probability theory, alternating differential forms, complex numbers and variables, points at infinity, ordinary and partial differential equations, difference equations and definite integrals, functional analysis, real functions, and analytic number theory. An important concluding chapter examines "The Changing Structure of Modern Mathematics
AGraphical Approach to Algebra and Trigonometry text covers all of the topics typically caught in a college algebra course, but with an organization that fosters students' understanding of the interrelationships among graphs, equations, and inequalities. With AGraphical Approach to Algebra and Trigonometry continues to incorporate an open design, with helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids to provide new and relevant opportunities for learning and teaching. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
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
Field 7: Mathematical Sciences Designated courses that enable students to reason quantitatively, abstractly, or computationally about the world using the symbol systems rooted in quantitative measures, logical analysis, and/or algorithms to solve practical problems. Goals & Objectives To reason quantitatively, abstractly, or computationally about the world using the symbol systems rooted in quantitative measures, logical analysis, and/or algorithms to solve practical problems.
See What's Inside Product Description This book demonstrates how some fundamental ideas about data analysis and probability can be introduced to build a strong foundation in young students. Activities designed to introduce and promote familiarity with essential concepts develop and extend students' ideas about data analysis and simple probability through the use of bar graphs, tallies, frequency tables, and Venn diagrams. Helpful margin notes provide teaching tips, anticipated student responses to questions, samples of students' work, and ways to modify the activities for students experiencing difficulty or needing enrichment. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers. This book focuses on algebra as a language of process, expands the notion of variable, develops ideas about the representation of functions, and extends students' understanding of algebraic equivalence and change. This book examines the study of geometry in the middle grades as a pivotal point in the mathematical learning of students and emphasizes the geometric thinking that can develop in grades 6–8 as a result of hands-on exploration. Customers Who Bought This Also Bought... investigations for prekindergarten and kindergarten contained in this book engage students in activities where they apply mathematical ideas from the five main content areas–number, algebra, geometry, measurement, and data analysis. The explorations in this book include such tasks as supplying missing numbers in story problems, using clues to identify locations on a map, and placing shapes inside or outside a circle according to a rule. 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.
All recent mathematics reform documents have called for improved and increased use of technology in mathematics instruction, both in school mathematics and in teacher preparation programs. The University of Illinois at Urbana-Champaign has redesigned one of its mathematics courses for elementary teachers to teach concepts of the calculus using Mathematica. This course, "Experimental Mathematics," is experimental in two senses: it encourages students to perform mathematical experiments using Mathematica, and the course itself is new and, hence, experimental.
Precalculus: Graphs and Models - 5th edition Summary: The Graphs and Models series by Bittinger, Beecher, Ellenbogen, and Penna is known for helping students ''see the math'' through its focus on visualization and technology. These texts continue to maintain the features that have helped students succeed for years: focus on functions, visual emphasis, side-by-side algebraic and graphical solutions, and real-data applications. With the Fifth Edition, visualization is taken to a new level with technology. The authors also in...show moretegrate smartphone apps, encouraging readers to visualize the math. In addition, ongoing review has been added with new Mid-Chapter Mixed Review exercise sets and new Study Guide summaries to help students new instructors edition. May contain answers and/or notes in margins. Includes CD-ROM! Ships same day or next business day. Free USPS Tracking Number. Excellent Customer Service. Ships from TN $74.50 +$3.99 s/h New Mccool Books Denham Springs, LA Please read before purchase>> annotated teacher edition with publisher notation review copy on cover New Book no writing or marks includes all Students content and all answers. text INCLUDES Graphing ...show moreCalculator Manual >>No access code or other supplements. ship immediately - Expedited shipping available ...show less $174.95 +$3.99 s/h New newtextstogo Manvel, TX Absolutely BRAND NEW ORIGINAL US HARDCOVER STUDENT 5th Edition / Mint condition / Never been read / ISBN-13: 9780321783967 / Shipped out in one business day with free tracking. $177.45 +$3.99 s/h New Textbookcenter.com Columbia, MO Ships same day or next business day! UPS(AK/HI Priority Mail)/ NEW book 100% BRAND NEW ORIGINAL US HARDCOVER STUDENT 5th Edition / Mint condition / Never been read / ISBN-13: 9780321783967 / Shipped out in one business day with free tracking. $202.28 +$3.99 s/h New PaperbackshopUS Secaucus, NJ New Book. Shipped from US within 4 to 14 business days. Established seller since 2000 $247.05 +$3.99 s/h New Supreme Bookstore San Jose, CA 1-19-12 Hardback 5
Precalculus, the authors encourage graphical, numerical, and algebraic modeling of functions as well as a focus on problem solving, conceptual understanding, and facility with technology. They have created a book that is designed for instructors and written for students making this the most effective precalculus text available today. Contents: P. Prerequisites 1. Functions and Graphs 2. Polynomial, Power, and Rational Functions 3. Exponential, Logistic, and Logarithmic Functions 4. Trigonometric Functions 5. Analytic Trigonometry 6. Applications of Trigonometry 7. Systems and Matrices 8. Analytic Geometry in Two and Three Dimensions 9. Discrete Mathematics 10. An Introduction to Calculus: Limits, Derivatives, and Integrals Appendix A: Algebra Review Appendix B: Key Formulas Appendix C: Logic
Edmonds Statistics...Are you motivated to learn? Discrete mathematics is a blend of many different elements of logic, combinatorics and graph theory. I hold a Master's in Math Education and have coached many students through various Discrete math courses
Background and Goals: Math 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete 105 are fully prepared for Math 115. Content: This course presents the concepts of precalculus from four points of view: geometric (graphs), numeric (tables), symbolic (formulas), and written (verbal descriptions). The emphasis is on the mathematical modeling of real-life problems using linear, polynomial, exponential, logarithmic, and trigonometric functions. Students develop their reading, writing, and questioning skills in an interactive classroom setting. Alternatives: Math 107, offered only in the winter term, is a course designed for students no necessarily planning to take calculus. Student Body: First-year students (non-mathematics concentrators) who are not necessarily required to take calculus. Credit: 3 Credits. Recent Texts: Background and Goals: The course will investigate topics relevant to the information age in which we live. An investigation of cryptography and coding methods, including prime numbers, randomness, and data compression will lead to the mathematics of the web. Use of interactive web sites and web data are an integral part of the course. The course will emphasize the representation of mathematical data in graphical , tabular, and symbolic forms and investigate the inferences that can be drawn from these models. Emphasis will be placed on the development of estimation skills, the ability to determine reasonableness of answers, and the ability to find alternative approaches to a problem. Content: Typical topics include cryptography, coding, politics, biological data, populations, chaos, and game theory. Topics will be presented as modules, generally a week or two in length. Alternatives: None. Subsequent Courses: Math 128 or Math 127 could be taken after Math 107. functions and graphs, derivatives and their applications to real-life problems in various fields, and an introduction to integration. The classroom atmosphere is interactive and cooperative. Both individual and team homework is assigned. Alternatives: Math 185 (Honors Calculus I ) is a more theoretical course which covers some of the same material. Math 175 (Intro to Cryptology) is a non-calculus alternative for students with a good command of first-semester calculus. Math 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for Math 115 should take Math 105 (Data, Functions and Graphs). Subsequent Courses: Math 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking Math 186 (Honors Calculus II). techniques of integration, applications of integration, Taylor series, an introduction to differential equations, and infinite series. The classroom atmosphere is interactive and cooperative. Both individual and team homework is assigned. Alternatives: Math 186 (Honors Calculus II) is a more theoretical course which covers much of the same material. Math 156 (Applied Honors Calculus II) also covers much of the same material using MAPLE and emphasizing applications to science and engineering. Subsequent Courses: Math 215 (Calculus III) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking Math 255 (Applied Honors Calculus III) or Math 285 (Honors Calculus III). Background and Goals: This course introduces students to the ideas and some of the basic results in Euclidean and non-Euclidean geometry. Beginning with geometry in ancient Greece, the course includes the construction of new geometric objects from old ones by projecting and by taking slices. The course is intended for students who want an introduction to mathematical ideas and culture. Emphasis is on conceptual thinking — students will do hands-on experimentation with geometric shapes, patterns and ideas. Content: The course begins with the independence of Euclid's Fifth Postulate and with the construction of spherical and hyperbolic geometries in which the Fifth Postulate fails; how spherical and hyperbolic geometry differs from Euclidean geometry. We then study the geometry of higher dimensions: coordinization — the mathematician's tool for studying higher dimensions; construction of higher-dimension analogues of some familiar objects like spheres and cubes; discussion of the proper higher-dimensional analogues of some geometric notions (length, angle, orthogonality, etc.). Alternatives: none Subsequent Courses: This course does not provide preparation for any further study of mathematics. Background and Goals:This course is intended for students who want to engage in mathematical reasoning without having to take calculus first. It is particularly well-suited for non-science concentrators or those who are thoroughly undecided. Students will make use of software to conduct numerical experiments and to make empirical discoveries. Students will formulate precise conjectures and in many cases prove them. Thus the students will, as a group, generate a logical development of the subject. Content: After studying the factorizations and greatest common divisors, emphasis will shift to the patterns that emerge when the integers are classified according to the remainder produced upon division by some fixed number (congruences). Once some basic tools have been established, applications will be made in several directions. For example, students may derive a precise parameterization of Pythagorean triples. Alternatives: none Subsequent Courses: This course does not provide preparation for any further study of mathematics. Background and Goals: This course is designed for students who seek an introduction to the mathematical concepts and techniques employed by financial institutions such as banks, insurance companies, and pension funds. Actuarial students, and other mathematics concentrators, should elect Math 424 which covers the same topics but on a more rigorous basis requiring considerable use of calculus. The course is not part of a sequence. Students should possess financial calculators. Content: Topics covered include: various rates of simple and compound interest, present and accumulated values based on these; annuity functions and their application to amortization, sinking funds, and bond values; depreciation methods; introduction to life tables, life annuity, and life insurance values. Alternatives: Math 424 (Compound Interest and Life Ins) covers the same material in greater depth and with a higher level of mathematical content. Background and Goals: Math 156 is part of the applied honors calculus sequence for engineering and science concentrators. The course is an alternative to Math 116 for students with strong mathematics ability and science. Background and Goals: The course will be very interactive, eliciting suggestions towards proof from the students so that all the problems are eventually solved by a joint effort between the students and the instructor. The format has worked well in the past for honors courses. To enhance the visualization, we plan to develop software for two-dimensional geometric constructions. This software will be able to produce multi-color pictures of geometric configurations. In the long run, such software will save us time in creating problem sets, handouts and perhaps slides. Additional topics may be added depending on the interest and abilities of the students. Content: A good text for the course is already available: the classic "Geometry Revisited" by Coxter and Greitzer, which contains a wonderful exposition of the material and has suitable exercises. As a precursor to the mathematics, the course will use familiar games such as the old game Mastermind where player A has a code which player B has to use. Students will pair off and play the game, with the important additional feature that the guesser must write down what(s) he knows and can deduce after each guess, and therefore motivate his/her next guess. This should help set the mood and instill the idea of analyzing the facts at hand and making logical deductions. After this the course will develop some basic theorems of Euclidean geometry. An example of such a theorem is that the angle bisectors (or medians, or altitudes, or perpendicular bisectors) of a triangle are concurrent. These results are fairly straightforward but exemplify the spirit of the course by providing a good introduction to rigorous proofs, Then we move to some more difficult but beautiful theorems from geometry such as Ceva's theorem, the Euler line, the nine-point circle theorem, Ptolemy's theorem and Morley's theorem. Background and Goals: This course is an alternative to Math 185 as an entry to the honors calculus sequence. The course stresses discovery as a vehicle for learning. Content: This course gives a historical introduction to Cryptology, from ancient times up to modern public key encryption, particularly RSA, and introduces a number of mathematical ideas involved in the development and analysis of codes. Mathematical topics include some enumeration, probability, and statistics, but the bulk of the course is devoted to elementary number theory. Students also work throughout the course on effectively communicating mathematics, both written and orally. Moreover, students will develop rigorous mathematical proof writing skills, and a primary goal of the course is to not only understand how various cryptosystems work, but why. Structure: The course has two components, classroom and computer lab. The classroom component meets three days each week, and is driven by in-class worksheets students complete in small groups. Each worksheet consists of definitions, examples, problems, and mathematical results that students attempt to understand through discussion with their peers and the instructor. As students solve problems from the worksheet, they present their solutions to the rest of the class. In the computer lab, various discovery-based projects allow the students to explore the ideas developed in the classroom and cryptosystems not covered in the worksheets. No previous experience with computer programming is necessary. Background and Goals: Students are expected to have some previous experience with the basic concepts and techniques of calculus. The course stresses discovery as a vehicle for learning. Students will be required to experiment throughout the course on a range of problems and will participate each semester in a group project. Content: The general theme of the course will be discrete-time and continuous-time dynamical systems. Examples of dynamical systems arising in the sciences are used as motivation. Topics include: iterates of functions, simple ordinary differential equations, fixed points, attracting and repelling fixed points and periodic orbits, ordered and chaotic motion, self-similarity, and fractals. Tools such as limits and continuity, Taylor expansions of functions, exponentials, logarithms, eigenvalues, and eigenvectors are reviewed or introduced as needed. There is a weekly computer work-station lab. Background and Goals: Most Alternatives: Math 115 (Calculus I) is a less theoretical course which covers much of the same material. Math 295 (Honors Mathematics I) gives a much more theoretical treatment of much of the same material. Background and Goals:Most This course is a continuation of Math 185. Content: Topics include integral calculus, transcendental functions, infinite sequences and series (including Taylor's series), and - time permitting - some simple applications to elementary differential equations. Tuesdays are mostly devoted to an introduction to linear algebra. Alternatives: Math 116 (Calculus II) is a somewhat less theoretical course which covers much of the same material. Math 156 (Applied Honors Calculus II) is more application based, but covers much of the same material. Background and Goals:An introduction to matrices and linear algebra. This course covers the basics needed to understand a wide variety of applications that use the ideas of linear algebra, from linear programming to mathematical economics. The emphasis is on concepts and problem solving. The courses 214&215 are designed as an alternative to Math 215&216 for students who need more linear algebra and less differential equations background. Alternatives: Math 419 (Linear Spaces and Matrix Theory) has a somewhat more theoretical emphasis. Math 217 is a more theoretical course which covers much of the material of Math 214 at a deeper level. Math 513 (Intro. to Linear Algebra) is an honors version of this course. Mathematics concentrators are required to take Math 217 or Math 513. Credit: 4 Credits. Credit is granted for only one course among Math 215, 255, and 285. Recent Texts:Multivariable Calculus (6th edition) by Stewart Background and Goals: The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to concentrate in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. Content: Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; line, surface, and volume integrals and applications; vector fields and integration; Green's Theorem and Stokes' Theorem. There is a weekly computer lab using MAPLE. Alternatives: Math 285 (Honors Calculus III) is a somewhat more theoretical course which covers the same material. Math 255 (Applied Honors Calculus III) is also an alternative. Subsequent Courses: For students intending to concentrate in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217 (Linear Algebra). Students who intend to take only one further mathematics course and need differential equations (respectively, linear algebra) should take Math 216 (respectively, Math 214). Content: Math 216 is a basic course on differential equations, intended for engineers and other scientists who need to apply the techniques in their work. The lectures are accompanied by a computer lab and recitation section where students have the opportunity to discuss problems and work through computer experiments to further develop their understanding of the concepts of the class. Topics covered include some material on complex numbers and matrix algebra, first and second order linear and non-linear systems with applications, introductory numerical methods, and elementary Laplace transform techniques. Alternatives: Math 286 (Honors Differential Equations) covers much of the same material. The sequence Math 217&316 covers all of this material and substantially more at greater depth and with greater emphasis on the theory. Math 256 (Applied Honors Calculus IV) is also an alternative. These courses are explicitly designed to introduce the student to both the concepts and applications of their subjects and to the methods by which the results are proved. Content: The topics covered include: systems of linear equations; matrix algebra; vectors, vector spaces, and subspaces; geometry of Rn; linear dependence, bases, and dimension; linear transformations; Eigenvalues and Eigenvectors; diagonalization; inner products. Throughout there will be emphasis on the concepts, logic, and methods of theoretical mathematics. Alternatives: Math 214, 417 and 419 cover similar material with more emphasis on computation and applications and less emphasis on proofs. Math 513 covers more in a much more sophisticated way. Subsequent Courses: The intended course to follow Math 217 is Math 316 (Differential Equations). Math 217 is also prerequisite for Math 312 (Applied Modern Algebra), Math 412 (Introduction to Modern Algebra) and all more advanced courses in mathematics. Credit: 4 Credits. Credit is granted for only one course among Math 215, 255, and 285. Recent Texts:Multivariable Calculus (6th edition) by Stewart Background and Goals: Math 255 is part of the applied honors calculus sequence for engineering andBackground and Goals: Math 256 is part of the applied honors calculus sequence for engineeringStudent Body: Sophomores and first-year students with suitable background Credit: 4 Credits. Credit is granted for only one course among Math 215, 255, and 285. Recent Texts:Multivariable Calculus (6th edition) by Stewart vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation, maximum-minimum problems; line, surface, and volume integrals and applications; vector fields and integration; curl, divergence, and gradient; Green's Theorem and Stokes' Theorem. Additional topics may be added at the discretion of the instructor. Alternatives: Math 215 (Calculus III) is a less theoretical course which covers the same material. Math 255 (Applied Honors Calc. III) is an applications-oriented honors course which covers much of the same material. first-order differential equations, higher-order linear differential equations with constant coefficients, an introduction to linear algebra, linear systems, the Laplace Transform, series solutions and other numerical methods (Euler, Runge-Kutta). If time permits, Picard's Theorem will be proved. Alternatives: Math 216 (Intro. to Differential Equations) and Math 316 (Differential Equations) cover much of the same material. Math 256 (Applied Honors Calculus IV) is also an alternative. Subsequent Courses: Math 471 (Intro. to Numerical Methods) and/or Math 572 (Numer. Meth. for Sci. Comput. II) are natural sequels in the area of differential equations, but Math 286 is also preparation for more theoretical courses such as Math 451 (Advanced Calculus I). Background and Goals: One of the best ways to develop mathematical abilities is by solving problems using a variety of methods. Familiarity with numerous methods is a great asset to the developing student of mathematics. Methods learned in attacking a specific problem frequently find application in many other areas of mathematics. In many instances an interest in and appreciation of mathematics is better developed by solving problems than by hearing formal lectures on specific topics. The student has an opportunity to participate more actively in his/her education and development. This course is intended for superior students who have exhibited both ability and interest in doing mathematics, but it is not restricted to honors students. This course is excellent preparation for the Putnam competition. Content: Students and one or more faculty and graduate student assistants will meet in small groups to explore problems in many different areas of mathematics. Problems will be selected according to the interests and background of the students Math 295 and 296 may be substituted for any Math 451 requirement. Math 296 and 395 may be substituted for any Math 217 requirement. Content: Axioms of the real numbers, completeness and connectedness in the real line. Functions of a real variable, limits and continuity, uniform continuity, extreme and intermediate value theorems, differentiation, integration, the fundamental theorem of calculus, Taylor's theorem with remainder Prerequisites: Sophomore standing and one previous university math course Frequency: Winter (II) Student Body: Credit: 3 Credits. Recent Texts: None Background and Goals: The Elementary Topics course may focus on any one of several topics. The material is presented at a level appropriate for sophomores and juniors without extensive coursework in math. This will be an inquiry based learning class which does not stress lecturing. Instead, the current offering of the course is a hands-on exploration of probability. Students will experiment throughout the course by working on a range of problems in peer groups inside of class. Content: The notions of probability and randomness are essential aspects of everyday life. In this course, we will uncover a number of mathematical surprises and structures that arise from these seemingly unstructured notions. Topics include basic probability, random walks, conditional probability, expectations, randomized strategies in games, Poisson distribution, and branching processes. Background and Goals: One of the main goals of the course (along with every course in the algebra sequence) is to expose students to rigorous, proof-oriented mathematics. Students are required to have taken Math 217, which should provide a first exposure to this style of mathematics. A distinguishing feature of this course is that the abstract concepts are not studied in isolation. Instead, each topic is studied with the ultimate goal being a real-world application. Content: Sets and functions, relations and graphs, rings, Boolean algebras, semigroups, groups, and lattices. Applications from areas such as switching, automata, and coding theory, and may include finite and minimal state machines, algebraic decompositions of logic circuits, semigroup machines, binary codes, and series and parallel decomposition of machines. Alternatives: Math 412 (Introduction to Modern Algebra) is a more abstract and proof-oriented course with less emphasis on applications and is better preparation for most pure mathematics courses. EECS 203 (Discrete Structures) covers some of the same topics with a more applied approach. Subsequent Courses: Math 312 is one of the alternative prerequisites for Math 416 (Theory of Algorithms), and several advanced EECS courses make substantial use of the material of Math 312. Another good follow-up course is Math 475 (Elementary Number Theory). Background and Goals: This is an introduction to differential equations for students who have studied linear algebra (Math 217). It treats techniques of solution (exact and approximate), existence and uniqueness theorems, some qualitative theory, and many applications. Proofs are given in class; homework problems include both computational and more conceptually oriented problems. Alternatives: Math 216 covers somewhat less material without presupposing linear algebra and with less emphasis on theory. Math 286 (Honors Differential Equations) is the honors version of Math 316. Subsequent Courses: Math 471 (Intro. to Numerical Methods) and/or Math 572 (Numer. Meth. For Sci. Comput. III) are natural sequels in the area of differential equations, but Math 316 is also preparation for more theoretical courses such as Math 451 (Advanced Calculus I). Student Body: Juniors and seniors interested in mathematics and the history of science Credit: 3 Credits. Recent Texts: None Background and Goals: This course examines the evolution of major mathematical concepts from mathematical and historical points of view. The course's goal is to throw light on contemporary mathematics by retracing the history of some of the major mathematical discoveries. Content: This course follows the evolution of three mathematical ideas in geometry, analysis and algebra. Typical choices of subject are: Euclid's parallel postulate and the development of non-Euclidean geometries, the notions of limit and infinitesimals, and the development of the theory of equations culminating with Galois theory. Background and Goals: The course content is similar to that of Math 451, but Math 351 assumes less background. This course covers topics that might be of greater use to students considering a Mathematical Sciences concentration or a minor in Mathematics. Background and Goals: This course is an introduction to Fourier analysis with emphasis on applications. The course also can be viewed as a way of deepening one's understanding of the 100-and 200-level material by applying it in interesting ways. Content: This is an introduction to Fourier analysis at an elementary level, emphasizing applications. The main topics are Fourier series, discrete Fourier transforms, and continuous Fourier transforms. A substantial portion of the time is spent on both scientific/technological applications (e.g. signal processing, Fourier optics), and applications in other branches of mathematics (e.g. partial differential equations, probability theory, number theory). Students will do some computer work, using MATLAB, an interactive programming tool that is easy to use, but no previous experience with computers is necessary. Alternatives: Math 454 (Bound Val. Probs. for Part. Diff. Eq.) covers some of the same material with more emphasis on partial differential equations. Subsequent Courses: This course is good preparation for Math 451 (Advanced Calculus I), which covers the theory of calculus in a mathematically rigorous way. Background and Goals: This is a survey course of the basic numerical methods which are used to solve practical scientific problems. Important concepts such as accuracy, stability, and efficiency are discussed. The course provides an introduction to MATLAB, an interactive program for numerical linear algebra, and may provide practice in FORTRAN programming and the use of software library subroutines. Convergence theorems are discussed and applied, but the proofs are not emphasized. Alternatives: Math 471 (Numerical Analysis) provides a more in-depth study of the same topics, with a greater emphasis on analyzing the accuracy and stability of the numerical methods. Math 571 (Numerical Linear Algebra) is a detailed study of the solution of systems of linear equations and eigenvalue problems, with some emphasis on large-scale problems. Math 572 (Numerical Methods for Differential Equations) covers numerical methods for both ordinary and partial differential equations. (Math 571 and 572 can be taken in either order). Subsequent Courses: This course is basic for many later courses in science and engineering. It is good background for 571-572. Background and Goals: This course, together with its sequel Math 489, provides a coherent overview of the mathematics underlying the elementary and middle school curriculum. It is required of all students intending to earn an elementary teaching certificate and is taken almost exclusively by such students. Concepts are heavily emphasized with some attention given to calculation and proof. The course is conducted using a discussion format. Class participation is expected and constitutes a significant part of the course grade. Enrollment is limited to 30 students per section. Although only two years of high school mathematics are required, a more complete background including pre-calculus or calculus is desirable. Content: Topics covered include problem solving, sets and functions, numeration systems, whole numbers (including some number theory) and integers. Each number system is examined in terms of its algorithms, its applications, and its mathematical structure. Background and Goals: The course is designed to show you how new mathematics is actually created: how to take a problem, make models and experiment with them, and search for underlying structure. The format involves little formal lecturing, much laboratory work, and student presentation of partial results and approaches. Please see the course website for more information. Content: Problems for projects are drawn from a wide variety of mathematical areas, pure and applied. Problems are chosen to be accessible to undergraduates. Alternatives: None Subsequent Courses: After this course students should be ready for a variety of courses and research experiences. Subsequent Courses: Students who have successfully completed the sequence Math 295-396 are generally prepared to take a range of advanced undergraduate and graduate courses such as Math 512 (Algebraic Structures), Math 513 (Intro. to Linear Algebra), Math 525 (Probability Theory), Math 590 (Intro. to Topology), and many others. Student Body: Undergraduate and graduate students from engineering and LS&A Credit: 3 Credits. Recent Texts:Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering by Strogatz Area: Applied/NA Background and Goals: This course is an introduction to the modern qualitative theory of ordinary differential equations with emphasis on geometric techniques and visualization. Much of the motivation for this approach comes from applications. Examples of applications of differential equations to science and engineering are a significant part of the course. There are relatively few proofs. Background and Goals: This course is designed to serve as an introduction to the methods and concepts of abstract mathematics. A typical student entering this course has substantial experience in using complex mathematical (calculus) calculations to solve physical or geometrical problems, but is unused to analyzing carefully the content of definitions and the logical flow of ideas which underlie and justify these calculations. Although the topics discussed here are quite distinct from those of calculus, an important goal of the course is to introduce the student to this type of analysis. Much of the reading, homework exercises, and exams consists of theorems (propositions, lemmas, etc.) and their proofs. Math 217 or equivalent required as background. Content: The initial topics include ones common to every branch of mathematics: sets, functions (mappings), relations, and the common number systems (integers, rational numbers, real numbers, complex numbers). These are then applied to the study of particular types of mathematical structures: groups, rings and fields. These structures are presented as abstractions from many examples such as the common number systems together with the operations of addition or multiplication, permutations of finite and infinite sets with function composition, sets of motions of geometric figures, and polynomials. Notions such as generator, subgroup, direct product, isomorphism, and homomorphism are defined and studied. Alternatives: Math 312 (Applied Modern Algebra) is a somewhat less abstract course which replaces some of the material on rings and fields of Math 412 with additional applications to areas such as switching and coding theory. Subsequent Courses: A student who successfully completes this course will be prepared to take a number of other courses in abstract mathematics : Math 416 (Theory of Algorithms), Math 451 (Advanced Calculus I), Math 475 (Elementary Number Theory), Math 575 (Intro. to Theory of Numbers), Math 513 (Introduction to Linear Algebra), Math 481 (Intro. to Mathematical Logic), and Math 582 (Intro. to Set Theory). All of these courses will extend and deepen the student's grasp of modern abstract mathematics. Prerequisites:MATH 312, 412, or EECS 280 and Math 465, or permission of instructor Frequency: Sporadically Student Body: Largely computer science concentrators with a few graduate students from other fields Credit: 3 Credits. Recent Texts:Algorithm Design by Kleinberg and Tardos Background and Goals: Many common problems from mathematics and computer science may be solved by applying one or more algorithms- well-defined procedures that accept input data specifying a particular instance of the problem and produce a solution. Students entering Math 416 typically have encountered some of these problems and their algorithmic solutions in a programming course. The goal here is to develop the mathematical tools necessary to analyze such algorithms with respect to their efficiency (running time) and correctness. Different instructors will put varying degrees of emphasis on mathematical proofs and computer implementation of these ideas. Content: Typical problems considered are: sorting, searching, matrix multiplication, graph problems (flows, travelling salesman), and primality and pseudo-primality testing (in connection with coding questions). Algorithm types such as divide-and-conquer, backtracking, greedy, and dynamic programming are analyzed using mathematical tools such as generating functions, recurrence relations, induction and recursion, graphs and trees, and permutations. The course often includes a section on abstract complexity theory including NP completeness. Alternatives: This course has substantial overlap with EECS 586 (Design and Analysis of Algorithms)- more or less depending on the instructors. In general, Math 416 will put more emphasis on the analysis aspect in contrast to design of algorithms. Subsequent Courses: EECS 574 (Computational Complexity) and 575 (Advanced Cryptography) include some topcis which follow those of this course. Background and Goals: Many problems in science, engineering, and mathematics are best formulated in terms of matrices - rectangular arrays of numbers. This course is an introduction to the properties of and operations on matrices with a wide variety of applications. The main emphasis is on concepts and problem-solving, but students are responsible for some of the underlying theory. Diversity rather than depth of applications is stressed. This course is not intended for mathematics concentrators, who should elect Math 217, or 513 if pursuing the honors concentration. Alternatives: Math 419 (Lin. Spaces and Matrix Thy.) is an enriched version of Math 417 with a somewhat more theoretical emphasis. Math 217 (Linear Algebra) is also a more theoretical course which covers much of the material of 417 at a deeper level (despite its lower number). Math 513 (Introduction to Linear Algebra) should be elected if pursuing honors and is also taken by some mathematics graduate students. Credit: 3 Credits. Credit is granted for only one course among Math 214, 217, 417, and 419. No credit granted to those who have completed or are enrolled in Math 513. Recent Texts:Linear Algebra and its Applications (4th Edition) by Strang Area: Algebra Background and Goals: Math 419 covers much of the same ground as Math 417 (Matrix Algebra I) but presents the material in a somewhat more abstract way in terms of vector spaces and linear transformations instead of matrices. There is a mix of proofs, calculations, and applications with the emphasis depending somewhat on the instructor. A previous proof-oriented course is helpful but by no means necessary. Alternatives: Math 417 (Matrix Algebra I) is less rigorous and theoretical and more oriented to applications. Math 217 (Linear Algebra) is similar to Math 419 but slightly more proof-oriented. Math 513 (Introduction to Linear Algebra) is much more abstract and sophisticated. Background and Goals: This is an introduction to the formal theory of abstract vector spaces and linear transformations. It is expected that students have complete at least one prior linear algebra course. The emphasis is on concepts and proofs with some calculations to illustrate the theory. Students should have significant mathematical maturity, at the level of Math 412 or 451. In particular, students should expect to work with and be tested on formal proofs. Background and Goals: This course is designed to allow students to explore the insurance mechanism as a means of replacing uncertainty with certainty. A main goal of the course is to explain, using mathematical models from the theory of interest, risk theory, credibility theory and ruin theory, how mathematics underlies many important individual and societal problems. Content: We will explore how much insurance affects the lives of students (automobile insurance, social security, health insurance, theft insurance) as well as the lives of other family members (retirements, life insurance, group insurance). While the mathematical models are important, an ability to articulate why the insurance options exist and how they satisfy the consumer's needs are equally important. In addition, there are different options available (e.g. in social insurance programs) that offer the opportunity of discussing alternative approaches. This course may be used to satisfy the LS&A upper-level writing requirement. Student Body: Junior and Senior mathematics concentrators; some business undergraduates Credit: 3 Credits. Recent Texts:Mathematics for Finance: An Introduction to Financial Engineering by Capinksi and Zastawniak Area: Actuarial & Financial Background and Goals: This course is an introduction to the mathematical models used in finance and economics with particular emphasis on models for pricing derivative instruments such as options and futures. The goal is to understand how the models derive from basic principles of economics, and to provide the necessary mathematical tools for their analysis. A solid background in basic probability theory is necessary. Background and Goals: This course explores the concepts underlying the theory of interest and then applies them to concrete problems. The course also includes applications of spreadsheet software. The course is a prerequisite to advanced actuarial courses. It also helps students prepare for some of the professional actuarial exams. Content: The course covers compound interest (growth) theory and its application to valuation of monetary deposits, annuities, and bonds. Problems are approached both analytically (using algebra) and geometrically (using pictorial representations). Techniques are applied to real-life situations: bank accounts, bond prices, etc. The text is used as a guide because it is prescribed for the professional examinations; the material covered will depend somewhat on the instructor. Alternatives: Math 424 is required for students concentrating in actuarial mathematics; others may take Math 147 (Introduction to Interest Theory), which deals with the same techniques but with less emphasis on continuous growth situations. Subsequent Courses: Math 520 (Life Contingencies I) applies the concepts of Math 424 and probability theory to the valuation of life contingencies (death benefits and pensions). Student Body: About 80% undergraduate mathematics, engineering, and computer science concentrators with a few graduate students Credit: 3 Credits. Recent Texts:A First Course in Probability (8th edition) by Ross Area: Analysis Background and Goals: This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of Math 116 and 215. Content: Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, joint distributions, expectations, variances, covariances. The culminating results are the Law of Large Numbers and the Central Limit Theorem. Beyond this, different instructors may add additional topics of interest. Alternatives: Math 525 (Probability Theory) is a similar course at a faster pace and with deeper coverage. A stronger mathematical background is helpful for Math 525. Subsequent Courses: Stats 426 (Introduction to Theoretical Statistics) is a natural sequel for students. Math 423 (Mathematics of Finance) and Math 523 (Risk Theory) include many applications of probability theory. Background and Goals: An overview of the range of employee benefit plans, the considerations (actuarial and others) which influence plan design and implementation practices, and the role of actuaries and other benefit plan professionals and their relation to decision makers in management and unions. This course is certified for satisfaction of the upper-level writing requirement. Content: Particular attention will be given to government programs which provide the framework, and establish requirements, for privately operated benefit plans. Relevant mathematical techniques will be reviewed, but are not the exclusive focus of the course. Alternatives: None Subsequent Courses: Math 521 (Life Contingencies II) and/or Math 522 (Act. Theory of Pensions and Soc. Sec.) (which can be taken independently of each other) provide more in-depth examination of the actuarial techniques used in employee benefit plans. Background and Goals: This course is a study of the axiomatic foundations of Euclidean and non-Euclidean geometry. Concepts and proofs are emphasized; students must be able to follow as well as construct clear logical arguments. For most students this is an introduction to proofs. A subsidiary goal is the development of enrichment and problem materials suitable for secondary geometry classes. Background and Goals: This course is about the analysis of curves and surfaces in 2- and 3-space using the tools of calculus and linear algebra. There will be many examples discussed, including some which arise in engineering and physics applications. Emphasis will be placed on developing intuitions and learning to use calculations to verify and prove theorems. Students need a good background in multivariable calculus (215) and linear algebra (preferably 217). Some exposure to differential equations (216 or 316) is helpful but not absolutely necessary. Alternatives: Math 437 is a substantially more advanced course which requires a strong background in topology (590), linear algebra (513) and advanced multivariable calculus (452). It treats some of the same material from a more abstract and topological perspective and introduces more general notions of curvature and covariant derivative for spaces of any dimension. Subsequent Courses: Math 635 (Differential Geometry) and Math 636 (Topics in Differential Geometry) further study Riemannian manifolds and their topological and analytic properties. Physics courses in general relativity and gauge theory will use some of the material of this course. Background and Goals: This course in intended for students with a strong background in topology, linear algebra, and multivariable advanced calculus equivalent to the courses 513 and 590. Its goal is to introduce the basic concepts and results of differential topology and differential geometry. Background and Goals: This course is an introduction to some of the main mathematical techniques in engineering and physics. It is intended to provide some background for courses in those disciplines with a mathematical requirement that goes beyond calculus. Model problems in mathematical physics are studied in detail. Applications are emphasized throughout. Content: Topics covered include: Fourier series and integrals; the classical partial differential equations (the heat, wave and Laplace's equations) solved by separation of variables; an introduction to complex variables and conformal mapping with applications to potential theory. A review of series and series solutions of ODEs will be included as needed. A variety of basic diffusion, oscillation and fluid flow problems will be discussed. Alternatives: This course overlaps with 454 and, to a much lesser extent, with 555. The coverage of PDEs in 450 is not as in-depth as 454; for example, in 450 coverage of special functions is reduced to the simplest Bessel functions. Those students needing a more thorough discussion of PDEs and boundary-value problems should take 454. On the other hand, 450 should provide a broader introduction to applied methods. Subsequent Courses: Math 555 (Complex Variables) and Math 556 (Methods of Applied Math I) are graduate-level courses that further develops both the theory and applications covered in 450. Background and Goals: This course has two complementary goals: (1) a rigorous development of the fundamental ideas of Calculus, and (2) a further development of the student's ability to deal with abstract mathematics and mathematical proofs. The key words here are "rigor" and "proof"; almost all of the material of the course consists in understanding and constructing definitions, theorems (propositions, lemmas, etc.), and proofs. This is considered one of the more difficult among the undergraduate mathematics courses, and students should be prepared to make a strong commitment to the course. In particular, it is strongly recommended that some course which requires proofs (such as Math 412) be taken before Math 451. Content: Topics include: logic and techniques of proof; sets, functions, and relations; cardinality; the real number system and its topology; infinite sequences, limits and continuity; differentiation; integration, the Fundamental Theorem of Calculus; infinite series; sequences and series of functions. Alternatives: There is really no other course which covers the material of Math 451. Although Math 450 is an alternative prerequisite for some later courses, the emphasis of the two courses is quite distinct. Math 351 covers similar topics with much less rigor. Subsequent Courses: The natural sequel to Math 451 is 452, which extends the ideas considered here to functions of several variables. In a sense, Math 451 treats the theory behind Math 115-116, while Math 452 does the same for Math 215 and a part of Math 216. Math 451 is also a prerequisite for several other courses: Math 575, Math 590, Math 596, and Math 597. Student Body: A majority of mathematics undergraduates with some non-mathematics graduate students Credit: 3 Credits. Recent Texts: Advanced Calculus of Several Variables by Edwards Area: Analysis Background and Goals: This course does a rigorous development of multivariable calculus and elementary function theory with some view towards generalizations. Concepts and proofs are stressed. This is a relatively difficult course, but the stated prerequisites provide adequate preparation. Student Body: Some mathematics undergraduates, but more non-mathematics graduate students Credit: 3 Credits. 1 credit after Math 354. No credit after Math 450. Recent Texts:Partial Differential Equations for Scientists by Farlow Area: Applied/Numerical Analysis Background and Goals: This course is devoted to the use of Fourier series and other orthogonal expansions in the solution of initial-value and boundary-value problems for second-order linear partial differential equations. Emphasis is on concepts and calculation. The official prerequisite is ample preparation. Subsequent Courses: Math 454 is prerequisite to Math 571 (Numer. Meth. for Sci. Comput. I) and Math 572 (Numer. Meth. for Sci. Comput. II). Although it is not a formal prerequisite, it is good background for Math 556 (Methods of Applied Math I). Background and Goals: The focus of this course is the application of a variety of mathematical techniques to solve real-world problems. Students will learn how to model a problem in mathematical terms and use mathematics to gain insight and eventually solve the problem. Concepts and calculations, using applied analysis and numerical simulations, are emphasized. Content: Construction and analysis of mathematical models in physics, engineering, economics, biology, medicine, and social sciences. Content varies considerably with instructor. Recent versions: Use and theory of dynamical systems (chaotic dynamics, ecological and biological models, classical mechanics), and mathematical models in physiology and population biology. Alternatives: Students who are particularly interested in biology should considered Math 463 (Math Modeling in Biology). Background and Goals:It is widely anticipated that Biology and Medicine will be the premier sciences of the 21st century. The complexities of the biological sciences make interdisciplinary involvement essential and the increasing use of mathematics in biology is inevitable as biology becomes more quantitative. Mathematical biology is a fast growing and exciting modern application of mathematics that has gained worldwide recognition. In this course, mathematical models that suggest possible mechanisms that may underlie specific biological processes are developed and analyzed. Another major emphasis of the course is illustrating how these models can be used to predict what may follow under currently untested conditions. The course moves from classical to contemporary models at the population, organ, cellular, and molecular levels. The goals of this course are: (1) Critical understanding of the use of differential equation methods in mathematical biology and (2) Exposure to specialized mathematical and computations techniques which are required to study ordinary differential equations that arise in mathematical biology. By the end of this course students will be able to derive, interpret, solve, understand, discuss, and critique discrete and differential equation models of biological systems. Content: This course provides an introduction to the use of continuous and discrete differential equations in the biological sciences. Biological topics may include single species and interacting population dynamics, modeling infectious and dynamic diseases, regulation of cell function, molecular interactions and receptor-ligand binding, biological oscillators, and an introduction to biological pattern formation. There will also be discussions of current topics of interest such as Tumor Growth and Angiogenesis, HIV and AIDS, and Control of the Mitotic Clock. Mathematical tools such as phase portraits, bifurcation diagrams, perturbation theory, and parameter estimation techniques that are necessary to analyze and interpret biological models will also be covered. Approximately one class period each week will be held in the mathematics computer laboratory where numerical techniques for finding and visualizing solutions of differential and discrete systems will be discussed. Student Body: Upper-level undergraduates and graduate students in mathematics, science, and engineering Credit: 3 Credits. Recent Texts: None Area: Applied/Numerical Analysis Background and Goals: Solution of an inverse problem is a central component of fields such as medical tomography, geophysics, non-destructive testing, and control theory. The solution of any practical inverse problem is an interdisciplinary task. Each such problem requires a blending of mathematical constructs and physical realities. Thus, each problem has its own unique components; on the other hand, there is a common mathematical framework for these problems and their solutions. This framework is the primary content of the course. This course will allow students interested in the above-named fields to have an opportunity to study mathematical tools related to the mathematical foundations. Content: The course content is motivated by a particular inverse problem from a field such as medical tomography (transmission, emission), geophysics (remote sensing, inverse scattering, tomography), or non-destructive testing. Mathematical topics include ill-posedness (existence, uniqueness, stability), regularization (e.g. Tikhonov, least squares, modified least squares, variation, mollification), pseudoinverses, transforms (e.g. k-plane, Radon, X-ray, Hilbert), special functions, and singular-value decomposition. Physical aspects of particular inverse problems will be introduced as needed, but the emphasis of the course is investigation of the mathematical concepts related to analysis and solution of inverse problems. Student Body: Upper-level undergraduates and graduate students in mathematics, science, and engineering Credit: 3 Credits. No credit granted to those who have completed or are enrolled in MATH 565 or 566. Recent Texts:Introductory Combinatorics (4th edition) by R. Brualdi Area: Discrete Mathematics Background and Goals: Combinatorics is the study of finite mathematical objects, including their enumeration, structural properties, design, and optimization. Combinatorics plays an increasingly important role in various branches of mathematics and in numerous applications, including computer science, statistics and statistical physics, operations research, bioinformatics, and electrical engineering. This course provides an elementary introduction to the fundamental notions, techniques, and theorems of enumerative combinatorics and graph theory. Student Body: The course is intended for graduate students and advanced undergraduates interested in the mathematical analysis of model of ecological systems. Credit: 3 Credits. Recent Texts: None Area: Applied Background and Goals: This course gives an overview of mathematical approaches to questions in the science of ecology. Topics include: formulation of deterministic and stochastic population models; dynamics of single-species populations; and dynamics of interacting populations (predation, competition, and mutualism), structured populations, and epidemiology. Emphasis is placed on model formulation and techniques of analysis. Content: Why do some diseases become pandemic? Why do certain species introductions result in widespread invasions? Why do some populations grow while others decline and still others cycle rhythmically? How are all of these phenomena influenced by climate change? These and many other fundamental questions in the science of ecology are intrinsically quantitative and concern highly complex systems. To answer them, ecologists formulate and study mathematical models. This course is intended to provide an overview of the principal ecological models and the mathematical techniques available for their analysis. Emphasis is placed on model formulation and techniques of analysis. Although the focus is on ecological dynamics, the methods we discuss are readily applicable across the sciences. The course presumes mathematical maturity at the level of advanced calculus with prior exposure to ordinary differential equations, linear algebra, and probability. Background and Goals: This is a survey of the basic numerical methods which are used to solve scientific problems. The emphasis is evenly divided between the analysis of the methods and their practical applications. Some convergence theorems and error bounds are proved. The course also provides an introduction to MATLAB, an interactive program for numerical linear algebra, as well as practice in computer programming. One goal of the course is to show how calculus and linear algebra are used in numerical analysis. Alternatives: Math 371/Engin. 303 (Numerical Methods) is a less sophisticated version intended principally for Sophomore and Junior engineering students; the sequence Math 571-572 (Numer. Meth. for Sci. Comput. I & II) is mainly taken by graduate students, but should be considered by strong undergraduates. Subsequent Courses: Math 471 is good preparation for Math 571 (Numer. Meth. for Sci. Comput. I) and Math 572 (Numer. Meth. for Sci. Comput. II), although it is not prerequisite to these Background and Goals: This is a survey of the basic numerical methods which are used to solve scientific problems. The goals of the course are similar to those of Math 471 but the applications are chosen to be of interest to students in the Actuarial Mathematics and Financial Mathematics programs. Recent Texts:An Introduction to the Theory of Numbers (Niven, Zuckerman and Montgomery) Area: Number Theory Background and Goals: This is an elementary introduction to number theory, especially congruence arithmetic. Number Theory is one of the few areas of mathematics in which problems easily describable to a layman (is every even number the sum of two primes?) have remained unsolved for centuries. Recently some of these fascinating but seemingly useless questions have come to be of central importance in the design of codes and ciphers. The methods of number theory are often elementary in requiring little formal background. In addition to strictly number-theoretic questions, concrete examples of structures such as rings and fields from abstract algebra are discussed. Concepts and proofs are emphasized, but there is some discussion of algorithms which permit efficient calculation. Students are expected to do simple proofs and may be asked to perform computer experiments. Although there are no special prerequisites and the course is essentially self-contained, most students have some experience in abstract mathematics and problem solving and are interested in learning proofs. At least three semesters of college mathematics are recommended. A Computational Laboratory (Math 476, 1 credit) will usually be offered as an optional supplement to this course. Alternatives: Math 575 (Intro. to Theory of Numbers) moves much faster, covers more material, and requires more difficult exercises. There is some overlap with Math 412 (Introduction to Modern Algebra) which stresses the algebraic content. Subsequent Courses: Math 475 may be followed by Math 575 (Intro. to Theory of Numbers) and is good preparation for Math 412 (Introduction to Modern Algebra). All of the advanced number theory courses, Math 675, 676, 677, 678, and 679, presuppose the material of Math 575, although a good student may get by with Math 475. Background and Goals: Intended as a companion course to Math 475 or 575. Participation should boost the student's performance in either of those classes. Students in the Lab will see mathematics as an exploratory science (as mathematicians do). Content: Students will be provided with software with which to conduct numerical explorations. No programming necessary, but students interested in programming will have the opportunity to embark on their own projects. Students will gain a knowledge of algorithms which have been developed for number theoretic purposes, e.g. for factoring. Background and Goals: All of modern mathematics involves logical relationships among mathematical concepts. In this course we focus on these relationships themselves rather than the ideas they relate. Inevitably this leads to a study of the (formal) languages suitable for expressing mathematical ideas. The explicit goal of the course is the study of propositional and first-order logic; the implicit goal is an improved understanding of the logical structure of mathematics. Students should have some previous experience with abstract mathematics and proofs, both because the course is largely concerned with theorems and proofs and because the formal logical concepts will be much more meaningful to a student who has already encountered these concepts informally. No previous course in logic is prerequisite. Content: In the first third of the course the notion of a formal language is introduced and propositional connectives ('and', 'or', 'not', 'implies'), tautologies and tautological consequence are studied. The heart of the course is the study of first-order predicate languages and their models. The new elements here are quantifiers ('there exists' and 'for all'). The study of the notions of truth, logical consequence, and provability leads to the completeness and compactness theorems. The final topics include some applications of these theorems, usually including non-standard analysis. This material corresponds to Chapter 1 and sections 2.0-2.5 and 2.8 of Enderton. Alternatives: Math 681, the graduate introductory logic course, also has no specific logic prerequisite but does presuppose a much higher general level of mathematical sophistication. Philosophy 414 may cover much of the same material with a less mathematical orientation. Subsequent Courses: Math 481 is not explicitly prerequisite for any later course, but the ideas developed have application to every branch of mathematics. Student Body: undergraduate concentrators in the Teaching Certificate Program and "minors" in other teaching programs Credit: 3 Credits. Recent Texts:Mathematics for High School Teachers: An Advanced Perspective (Peressini, Usiskin, Marchisotto and Stanley) Area: Teaching Background and Goals: This course is designed for students who intend to teach junior high or high school mathematics. It is advised that the course be taken relatively early in the program to help the student decide whether or not this is an appropriate goal. Concepts and proofs are emphasized over calculation. The course is conducted in a discussion format. Class participation is expected and constitutes a significant part of the course grade. Content: Topics covered have included problem solving; sets, relations and functions; the real number system and its subsystems; number theory; probability and statistics; difference sequences and equations; interest and annuities; algebra; and logic. Alternatives: There is no real alternative, but the requirement of Math 486 may be waived for strong students who intend to do graduate work in mathematics. Subsequent Courses: Prior completion of Math 486 may be of use for some students planning to take Math 312, 412, or 425. Background and Goals: This course, together with its predecessor Math 385, provides a coherent overview of the mathematics underlying the elementary and middle school curriculum. It is required of all students intending to earn an elementary teaching certificate and is taken almost exclusively by such students. Concepts are heavily emphasized with some attention given to calculation and proof. The course is conducted using a discussion format. Class participation is expected and constitutes a significant part of the course grade. Enrollment is limited to 30 students per section. Although only two years of high school mathematics are required, a more complete background including pre-calculus or calculus is desirable. Content: Topics covered include fractions and rational numbers, decimals and real numbers, probability and statistics, geometric figures, and measurement. Algebraic techniques and problem-solving strategies are used throughout the course. Background and Goals: Topology is the study of a class of interesting spaces, geometric examples of which are knots and surfaces. We focus on those properties of such spaces which don't change if the space is deformed. Much of the course is devoted to understanding particular spaces, such as Moebius strips and Klein bottles. The material in this course has a wide range of applications. Most of the material is theoretical, but it is well-suited for developing intuition and giving convincing proofs which are pictorial or geometric rather than completely rigorous. Content: Knots, orientable and non-orientable surfaces, Euler characteristic, open sets, connectedness, compactness, metric spaces. The topics covered are fairly constant but the presentation and emphasis will vary significantly with the instructor. Alternatives: Math 590 (Intro. to Topology) is a deeper and more difficult presentation of much of the same material. Math 433 (Intro. to Differential Geometry) is a related course at about the same level. Subsequent Courses: Math 490 is not prerequisite for any later course but provides good background for Math 591 (General and Differential Topology) or any of the other courses in geometry or topology. Student Body: undergraduates in the Elementary Teaching Certificate Program Credit: 3 Credits. Recent Texts: coursepack Area: Teaching Background and Goals: This is a required course for elementary teaching certificate candidates that extends and deepens the coverage of mathematics begun in the required two-course sequence Math 385-489. Topics are chosen from geometry, algebra, computer programming, logic, and combinatorics. Applications and problem-solving are emphasized. The class usually meets three times per week in recitation sections. Grades are based on class participation, two one-hour exams, and a final exam. Content: Selected topics in geometry, algebra, computer programming, logic, and combinatorics for prospective and in-service elementary, middle, or junior-high school teachers. Content will vary from term to term. Background and Goals: As a topics course, this course will vary greatly from term to term. In one recent offering, the aim of the course was to introduce at an elementary level the basic concepts of the theory of dynamical systems. Student Body: Mainly undergraduate mathematics concentrators with a few graduate students from other fields Background and Goals:MathAlternatives: Math 412 (Introduction to Modern Algebra) is a substantially lower level course which covers about half of the material of Math 512. The sequence Math 593-594 covers about twice as much Group and Field Theory as well as several other topics and presupposes that students have had a previous introduction to these concepts at least at the level of Math 412. Student Body: Mainly undergraduate mathematics concentrators with a few graduate students from other fields Background and Goals: MathContent: This course is a continuation of Math 512. It covers basic definitions and properties of rings and modules including quotients, ideals, factorization, and field extensions. Further topics are selected from: representation theory; structure theory of modules over a PID; Jordan canonical form; Galois theory, Nullstellensatz; finite fields; Euclidean, Principal ideal, and unique factorization domains; polynomial rings in one and several variables; and algebraic varieties. Background and Goals: The goal of this course is to teach the basic actuarial theory of mathematical models for financial uncertainties, mainly the time of death. In addition to actuarial students, this course is appropriate for anyone interested in mathematical modeling outside of the physical sciences. Concepts and calculation are emphasized over proof. Content: The main topics are the development of (1) probability distributions for the future lifetime random variable, (2) probabilistic methods for financial payments depending on death or survival, and (3) mathematical models of actuarial reserving. This corresponds to Chapters 3--6 and part of 7 of Bowers. Subsequent Courses: Math 520 is prerequisite to all succeeding actuarial courses. Math 521 (Life Contingencies II) extends the single decrement and single life ideas of 520 to multi-decrement and multiple-life applications directly related to life insurance and pensions. The sequence 520--521 covers the Part 4A examination of the Casualty Actuarial Society and covers the syllabus of the Course 150 examination of the Society of Actuaries. Math 522 (Act. Theory of Pensions and Soc. Sec) applies the models of 520 to funding concepts of retirement benefits such as social insurance, private pensions, retiree medical costs, etc. Background and Goals: This course extends the single decrement and single life ideas of Math 520 to multi-decrement and multiple-life applications directly related to life insurance. The sequence 520--521 covers covers the Part 4A examination of the Casualty Actuarial Society and covers the syllabus of the Course 150 examination of the Society of Actuaries. Concepts and calculation are emphasized over proof. Background and Goals: This course develops the mathematical models for pre-funded retirement benefit plans. Concepts and calculation are much more important than proofs. Content: Mathematical models for (1) retirement income, (2) retiree medical benefits, (3) disability benefits, and (4) survivor benefits. There is some coverage of how accounting theory and practice can be explained by these models and of the U.S. laws and regulations that give rise to the models used in practice. Student Body: Undergraduate students of financial and actuarial mathematics Background and Goals: Risk management is of major concern to all financial institutions and is an active area of modern finance. This course is relevant for students with interests in finance, risk management, or insurance, and provides background for the professional examinations in Risk Theory offered by the Society of Actuaries and the Casualty Actuary Society. Students should have a basic knowledge of common probability distributions (Poisson, exponential, gamma, binomial, etc.) and have at least Junior standing. Two major problems will be considered: (1) modeling of payouts of a financial intermediary when the amount and timing vary stochastically over time, and (2) modeling of the ongoing solvency of a financial intermediary subject to stochastically varying capital flow. These topics will be treated historically beginning with classical approaches and proceeding to more dynamic models. Student Body: A mix of undergraduate and graduate students, drawn largely from mathematics, statistics, and engineering, and graduate students in the Applied and Interdisciplinary Mathematics (AIM) program Background and Goals: This course is a thorough and fairly rigorous study of the mathematical theory of probability. There is substantial overlap with Math 425 (Intro. to Probability), but here more sophisticated mathematical tools are used and there is greater emphasis on proofs of major results. Math 451 is the required prerequisite. This course is a core course for the Applied and Interdisciplinary Mathematics (AIM) graduate program. Content: Topics include the basic results and methods of both discrete and continuous probability theory. Different instructors will vary the emphasis between these two theories. Alternatives: EECS 501 also covers some of the same material at a lower level of mathematical rigor. Math 425 (Intro. to Probability) is a course for students with substantially weaker background and ability. Recommended: Good understanding of advanced calculus covering limits, series, the notion of continuity, differentiation and the Riemann integral ; Linear algebra including eigenvalues and eigenfunctions. Background and Goals: The theory of stochastic processes is concerned with systems which change in accordance with probability laws. It can be regarded as the 'dynamic' part of statistic theory. Many applications occur in physics, engineering, computer sciences, economics, financial mathematics and biological sciences, as well as in other branches of mathematical analysis such as partial differential equations. The purpose of this course is to provide an introduction to the many specialized treatise on stochastic processes. Most of this course is on discrete state spaces. It is a second course in probability which should be of interest to students of mathematics and statistics as well as students from other disciplines in which stochastic processes have found significant applications. Special efforts will be made to attract and interest students in the rich diversity of applications of stochastic processes and to make them aware of the relevance and importance of the mathematical subtleties underlying stochastic processes. Content: The material is divided between discrete and continuous time processes. In both, a general theory is developed and detailed study is made of some special classes of processes and their applications. Some specific topics include generating functions; recurrent events and the renewal theorem; random walks; Markov chains; limit theorems; Markov chains in continuous time with emphasis on birth and death processes and queueing theory; an introduction to Brownian motion; stationary processes and martingales. Significant applications will be an important feature of the course. Coursework: weekly or biweekly problem sets and a midterm exam will each count for 30% of the grade. The final will count for 40%. Additional information: Those wishing to discuss the course should contact taoluo@umich.edu. Student Body: Undergraduate students of actuarial mathematics and insurance majors in Business Background and Goals: Historically the Actuarial Program has emphasized life, health, and pension topics. This course will provide background in casualty topics for the many students who take employment in this field. Guest lecturers from the industry will provide some of the instruction. Students are encouraged to take the Casualty Actuarial Society's Part 3B examination at the completion of the course. Content: The insurance policy is a contract describing the services and protection which the insurance company provides to the insured. This course will develop an understanding of the nature of the coverages provided, the bases of exposure and principles of the underwriting function, how products are designed and modified, and the different marketing systems. It will also look at how claims are settled, since this determines losses which are key components for insurance ratemaking and reserving. Finally, the course will explore basic ratemaking principles and concepts of loss reserving. Student Body: graduate and undergraduate students from many disciplines Background and Goals: This course centers on the construction and use of agent-based adaptive models study phenomena which are prototypical in the social, biological and decision sciences. These models are "agent-based" or "bottom-up" in that t he structure placed at the level of the individuals as basic components; they are "adaptive" in that individuals often adapt to their environment through evolution or learning. The goal of these models is to understand how the structure at the individual or micro level leads to emergent behavior at the macro or aggregate level. Often the individuals are grouped into subpopulations or interesting hierarchies, and the researcher may want to understand how the structure of development of these populations affects macroscopic outcomes. Content: The course will start with classical differential equation and game theory approaches. It will then focus on the theory and application of particular models of adaptive systems such as models of neural systems, genetic algorithms, classifier system and cellular automata. Time permitting, we will discuss more recent developments such as sugarscape and echo. Student Body: largely engineering and physics graduate students with some math and engineering undergrads, and graduate students in the Applied and Interdisciplinary Mathematics (AIM) program Background and Goals: This course is an introduction to the theory of complex valued functions of a complex variable with substantial attention to applications in science and engineering. Concepts, calculations, and the ability to apply princip les to physical problems are emphasized over proofs, but arguments are rigorous. The prerequisite of a course in advanced calculus is essential. This course is a core course for the Applied and Intersciplinary Mathematics (AIM) graduate program. Student Body: Graduate students in matehematics, science, and engineering, and graduate students in the Applied and Interdisciplinary Mathematics (AIM) program Background and Goals: This is an introduction to methods of applied functional analysis. Students are expected to master both the proofs and applications of major results. The prerequisites include linear algebra, undergraduate analysis, advanced calculus and complex variables. This course is a core course for the Applied and Intersciplinary Mathematics (AIM) graduate program. Student Body: Graduate students in mathematics, science and engineering, and graduate students in the Applied and Interdisciplinary Mathematics (AIM) program Background and Goals: This is an introduction to methods of asymptotic analysis including asymptotic expansions for integrals and solutions of ordinary and partial differential equations. The prerequisites include linear algebra, advanced calculus and complex variables. Math 556 is not a prerequisite. This course is a core course for the Applied and Intersciplinary Mathematics (AIM) graduate program. Student Body: grad students in math, science, and engineering, and graduate students in the Applied and Interdisciplinary Mathematics (AIM) program Background and Goals: This course is an introduction to dynamical systems (differential equations and iterated maps). The aim is to survey a broad range of topics in the theory of dynamical systems with emphasis on techniques and results that are useful in applications. Chaotic dynamics will be discussed. This course is a core course for the Applied and Intersciplinary Mathematics (AIM) graduate program. Student Body: undergraduate and graduate students in mathematics or science Background and Goals: This course in intended for students with a fairly strong background in pure mathematics, but not necessarily any experience with applied mathematics. Proofs and concepts, as will as intuitions arising from the field of application will be stressed. Content: This course will focus on a particular area of applied mathematics in which the mathematical ideas have been strongly influenced by the application. It is intended for students with a background in pure mathematics, and the course will develop the intuitions of the field of application as well as the mathematical proofs. The applications considered will vary with the instructor and may come from physics, biology, economics, electrical engineering, and other fields. Recent examples have been: Dynamical Systems, Statistical Mechanics, Solitons, and Nonlinear Waves. Background and Goals: A fundamental problem is the allocation of constrained resources such as funds among investment possibilities or personnel among production facilities. Each such problem has as it's goal the maximization of some positive objective such as investment return or the minimization of some negative objective such as cost or risk. Such problems are called Optimization Problems. Linear Programming deals with optimization problems in which both the objective and constraint functions are linear (the word "programming" is historical and means "planning" rather that necessarily computer programming). In practice, such problems involve thousands of decision variables and constraints, so a primary focus is the development and implementation of efficient algorithms. However, the subject also has deep connections with higher-dimensional convex geometry. A recent survey showed that most Fortune 500 companies regularly use linear programming in their decision making. This course will present both the classical and modern approaches to the subject and discuss numerous applications of current interest. Content: Formulation of problems from the private and public sectors using the mathematical model of linear programming. Development of the simplex algorithm; duality theory and economic interpretations. Postoptimality (sensitivity) analysis; a lgorithmic complexity; the elipsoid method; scaling algorithms; applications and interpretations. Introduction to transportation and assignment problems; special purpose algorithms and advanced computational techniques. Students have opportunities to form ulate and solve models developed from more complex case studies and use various computer programs. Prerequisites: Math 217, 417, or 419 and Math 216, 286, or 316 and to have a basic familiarity with partial differential equations as would be gained by the completion of Math 450 or 454 or to have permission of the instructor. Frequency: Winter (II) Student Body: Graduate Students, Math, Science, Engineering and Medical School. (Both the Department of Mathematics and the Program in Bioinformatics have approved this course for cross-listing. Further approval is in process). Credit: 3 Credits. Recent Texts: Math Biology, J. D. Murray Past Instructors: T. Jackson Background and Goals: Mathematical biology is a fast growing and exciting modem application which has gained worldwide recognition. This course will focus on the devrivation, analysis, and simulation of partial differential equations (PDEs) which model specific phenomena in molecular, cellular, and population biology. A goal of this course is to understand how the underlying spatial variability in natural systems influences motion and behavior. Content: Mathematical topics covered include derivation of relevant PDEs from first principle; reduction of PDEs to ODEs under steady state, quasi-state and traveling wave assumptions; solution techniques for PDEs and concepts of spatial stability and instability. These concepts will be introduced within the setting of classical and current problems in biology and the biomedical sciences such as cell motion, transport of biological substances and, biological pattern formation. Above all, this course aims to enhance the interdisciplinary training of advanced undergraduate and graduate students from mathematics and other disciplines by introducing fundamental properties of partial differential equations in the context of interesting biological phenomena. Prerequisites: Math 217, 216 and EECS 183 or equivalent, or permission of instructor Frequency: Winter (II) Credit: 3 credits Recent Texts: none Past instructors: D. Forger Student Body: Background and Goals: Numerical methods have become an essential part of modern biological and medical research. This course will survey many of these methods and provide students with tools necessary to meet the next generation of challenges in biological research. Unlike many other courses in numerical methods, we will focus on solving specific problems rather than analysis of techniques. Content: Will vary, but a recent topics offering included: methods to extract parameters from data, stochastic methods to simulate biochemical networks within cells and neural networks, principal component analysis in large data sets, techniques for simulating biological fluids, time series analysis, model reduction techniques, and optimal perturbations of biological systems. Student Body: Largely math and EECS grad students with a few math undergrads, and graduate students in the Applied and Interdisciplinary Mathematics (AIM) program. Background and Goals: This course has two somewhat distinct halves devoted to Graph Theory and Combinatorics. Proofs, concepts, and applications play about an equal role. Students should have taken at least one proof-oriented course. This course is a core course for the Applied and Interdisciplinary Mathematics (AIM) graduate program. Alternatives: There are small overlaps with Math 566 (Introduction to Algebraic Combinatorics) and Math 416 (Theory of Algorithms). Math 465 has similar content but is significantly less demanding than Math 565. Background and Goals: This course is designed to introduce math majors to an important area of applications in the communications industry. From a background in linear algebra it will cover the foundations of the theory of error-correcting codes and prepare a student to take further EECS courses or gain employment in this area. For EECS students it will provide a mathematical setting for their study of communications technology. Content: Introduction to coding theory focusing on the mathematical background for error-correcting codes. Shannon's Theorem and channel capacity. Review of tools from linear algebra and an introduction to abstract algebra and finite fields. Basic examples of codes such and Hamming, BCH, cyclic, Melas, Reed-Muller, and Reed-Solomon. Introduction to decoding starting with syndrome decoding and covering weight enumerator polynomials and the Mac-Williams Sloane identity. Further topics range from asymptotic parameters and bounds to a discussion of algebraic geometric codes in their simplest form. Student Body: math and engineering grads, strong undergrads, and graduate students in the Applied and Interdisciplinary Mathematics (AIM) program Background and Goals: This course is a rigorous introduction to numerical linear algebra with applications to 2-point boundary value problems and the Laplace equation in two dimensions. Both theoretical and computational aspects of the subject are discussed. Some of the homework problems require computer programming. Students should have a strong background in linear algebra and calculus, and some programming experience. This course is a core course for the Applied and Intersciplinary Mathematics (AIM) graduate program. Content: The topics covered usually include direct and iterative methods for solving systems of linear equations: Gaussian elimination, Cholesky decomposition, Jacobi iteration, Gauss-Seidel iteration, the SOR method, an introduction to the multigrid method, conjugate gradient method; finite element and difference discretizations of boundary value problems for the Poisson equation in one and two dimensions; numerical methods for computing eigenvalues and eigenvectors. Alternatives: Math 471 (Intro to Numerical Methods) is a survey course in numerical methods at a more elementary level. Subsequent Courses: Math 572 (Numer Meth for Sci Comput II) covers initial value problems for ordinary and partial differential equations. Math 571 and 572 may be taken in either order. Math 671 (Analysis of Numerical Methods I) is an advanced course in numerical analysis with varying topics chosen by the instructor. Prerequisites: Math 217, 417, 419, or 513 and one of Math 450, 451, or 454 or permission Frequency: Winter (II) Credit: 3 credits Recent Texts: Numerical Solutions of PDE's (Morton and Mayer) Past instructors: S. Karni, P. Smereka Student Body: math and engineering grads, strong undergrads, and graduate students in the Applied and Interdisciplinary Mathematics (AIM) program Background and Goals: This is one of the basic courses for students beginning study towards the Ph.D. degree in mathematics. Graduate students from engineering and science departments and strong undergraduates are also welcome. The course is an introduction to numerical methods for solving ordinary differential equations and hyperbolic and parabolic partial differential equations. Fundamental concepts and methods of analysis are emphasized. Students should have a strong background in linear algebra and analysis, and some experience with computer programming. This course is a core course for the Applied and Intersciplinary Mathematics (AIM) graduate program. Background and Goals: Many of the results of algebra and analysis were invented to solve problems in number theory. This field has long been admired for its beauty and elegance and recently has turned out to be extremely applicable to coding problems. This course is a survey of the basic techniques and results of elementary number theory. Students should have significant experience in writing proofs at the level of Math 451 and should have a basic understanding of groups, rings, and fields, at least at the level of Math 412 and preferably Math 512. Proofs are emphasized, but they are often pleasantly short. Content: Standard topics which are usually covered include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Diophantine equations, primitive roots, quadratic reciprocity and quadratic fields, application of these ideas to the solution of classical problems such as Fermat's last `theorem'(proved recently by A. Wiles). Other topics will depend on the instructor and may include continued fractions, p-adic numbers, elliptic curves, Diophantine approximation, fast multiplication and factorization, Public Key Cryptography, and transcendence. This material corresponds to Chapters 1--3 and selected parts of Chapters 4, 5, 7, 8, and 9 of Niven, Zuckerman, and Montgomery. Alternatives: Math 475 (Elementary Number Theory) is a non-honors version of Math 575 which puts much more emphasis on computation and less on proof. Only the standard topics above are covered, the pace is slower, and the exercises are easier. Subsequent Courses: All of the advanced number theory courses Math 675, 676, 677, 678, and 679 presuppose the material of Math 575. Each of these is devoted to a special subarea of number theory. Background and Goals: One of the great discoveries of modern mathematics was that essentially every mathematical concept may be defined in terms of sets and membership. Thus Set Theory plays a special role as a foundation for the whole of mathematics. One of the goals of this course is to develop some understanding of how Set Theory plays this role. The analysis of common mathematical concepts (e.g. function, ordering, infinity) in set-theoretic terms leads to a deeper understanding of these concepts. At the same time, the student will be introduced to many new concepts (e.g. transfinite ordinal and cardinal numbers, the Axiom of Choice) which play a major role in many branches of mathematics. The development of set theory will be largely axiomatic with the emphasis on proving the main results from the axioms. Students should have substantial experience with theorem-proof mathematics; the listed prerequisites are minimal and stronger preparation is recommended. No course in mathematical logic is presupposed. Content: The main topics covered are set algebra (union, intersection), relations and functions, orderings (partial, linear, well), the natural numbers, finite and denumerable sets, the Axiom of Choice, and ordinal and cardinal numbers. Alternatives: Some elementary set theory is typically covered in a number of advanced courses, but Math 582 is the only course which presents a thorough development of the subject. Subsequent Courses: Math 582 is not an explicit prerequisite for any later course, but it is excellent background for many of the advanced courses numbered 590 and above. Student Body: Grad students and advanced undergrads in Math, Computer Science and Philosophy. Background and Goals: Can we be convinced that a proof is correct, even if we only check it in three places? Can a proof convince us that a statement is true, while giving us no aid in convincing anyone else that the statement is true? The answer to both is affirmative. How? Using randomness and interaction, two elements missing from traditional deductive proofs. Why? Checking a proof in just a few places is useful for checking computer-generated proofs that are too long to read; there are also surprising connections to showing that certain functions cannot be computed or approximated efficiently. A "zero-knowledge proof" might be used, for example, for a customer to prove to a merchant that the customer is the rightful owner of a credit card, without giving the merchant any ability to prove (fraudulently) that the merchant is the owner of that credit card. Content: Probabilistically-checkable proofs, zero-knowlege proofs, and interactive proofs are studied and their computational, cryptographic, and other advantages discussed. The course will include a presentation of the necessary background material from mathematics (including probability theory and error-correcting codes) and computer science (including randomized computation). Motivations and applications in other fields, such as the security of credit card transactions and the philosophical nature of proof and knowledge, are briefly discussed. Alternatives: Math 490 (Introduction to Topology) is a more gentle introduction that is more concrete, somewhat less rigorous, and covers parts of both Math 591 and Math 592 (General and Differential Topology). Combinatorial and algebraic aspects of the subject are emphasized over the geometrical. Math 591 (General and Differential Topology) is a more rigorous course covering much of this material and more. Subsequent Courses: Both Math 591 (General and Differential Topology) and Math 437 (Intro to Differentiable Manifolds) use much of the material from Math 590 Students should have had a previous course equivalent to Math 512 (Algebraic Structures).
1439819084In the traditional curriculum, students rarely study nonlinear differential equations and nonlinear systems due to the difficulty or impossibility of computing explicit solutions manually. Although the theory associated with nonlinear systems is advanced, generating a numerical solution with a computer and interpreting that solution are fairly elementary. Bringing the computer into the classroom, Ordinary Differential Equations: Applications, Models, and Computing emphasizes the use of computer software in teaching differential equations. Providing an even balance between theory, computer solution, and application, the text discusses the theorems and applications of the first-order initial value problem, including learning theory models, population growth models, epidemic models, and chemical reactions. It then examines the theory for n-th order linear differential equations and the Laplace transform and its properties, before addressing several linear differential equations with constant coefficients that arise in physical and electrical systems. The author also presents systems of first-order differential equations as well as linear systems with constant coefficients that arise in physical systems, such as coupled spring-mass systems, pendulum systems, the path of an electron, and mixture problems. The final chapter introduces techniques for determining the behavior of solutions to systems of first-order differential equations without first finding the solutions. Designed to be independent of any particular software package, the book includes a CD-ROM with the software used to generate the solutions and graphs for the examples. The appendices contain complete instructions for running the software. A solutions manual is available for qualifying instructors. What People Are SayingEditorial Reviews
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This book is a research-based curriculum that focuses on developing students' conceptual understanding and skills through step-by-step instruction. The focus is on key ideas in mathematics, rich problem-solving lessons that build the reading and writing skills necessary for powerful problem solving
Product Details See What's Inside Product Description By Gary Kader, Tim Jacobbe, Patricia Wilson, Rose Mary Zbiek How does working with data in statistics differ from working with numbers in mathematics? What is variability, and how can we describe and measure it? How can we display distributions of quantitative or categorical data? What is a data sample, and how can we choose one that will allow us to draw valid conclusions from data? How much do you know<&hellip>and how much do you need to know? Helping your students develop a robust understanding of statistics requires that you understand fundamental statistical concepts deeply. But what does that mean? This book focuses on essential knowledge for mathematics teachers about statistics. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to statistics, the book will broaden and deepen yourFocus on the ideas that you need to understand thoroughly to teach confidently. Related Products proof and the process of proving. It is organized around five big ideas, supported by multiple smaller, interconnected ideas—essential understandings. This book focuses on essential knowledge for teachers about mathematical reasoning. It is organized around one big idea, supported by multiple smaller, interconnected ideas—essential understandings.Taking you beyond a simple introduction to mathematical reasoningBy 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 students. Like algebra at any level, early algebra is a way to explore, analyze, represent, and generalize mathematical ideas and relationships. This book shows that children can and do engage in generalizing about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3–5. 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.
Students will learn how to solve systems of linear equations using the methods of: graphing, substitution, and elimination. Nebraska State Curriculum Standards: 12.2.1 By the end of twelfth grade, students will solve theoretical and applied problems using numbers inequivalent forms, radicals, exponents, scientific notation, absolute values, fractions, decimals, and percents, ratios and proportions, order of operations, and properties of real numbers. 12.2.2 By the end of twelfth grade, students will justify the reasonableness of solutions. 12.2.3 By the end of twelfth grade, students will perform estimations and computations mentally, with paper and pencil, and with technology. 12.4.4 By the end of twelfth grade, students will apply coordinate geometry to locate objects and to describe objects algebraically. 12.4.7 By the end of twelfth grade, students will apply deductive reasoning to arrive at valid conclusions. 12.6.1 By the end of twelfth grade, students will interpret algebraic equations and inequalities graphically and describe geometric relationships algebraically. 12.6.2 By the end of twelfth grade, students will apply and solve problems involving equations and inequalities. 12.6.3 By the end of twelfth grade, students will apply and solve problems involving systems of equations, and systems of inequalities and matrices. Make informed choices among technology systems, resources, and services. Students match the technology tools and resources for the intended task or audience (i.e.charting data to represent complex information). Collaborate with peers, experts, and others to contribute to a content-related knowledge base by using technology to compile, synthesize, produce, and disseminate information, models, and other creative works. 1. Capture the attention of the learners by connecting them to the concept in a personal way. (Example: Select a game, story, song, video, or discussion which will hook the students into the concept by relating to prior learning.) Show the students a video that describes each of the three methods used in solving systems of linear equations. 2. Guide the students to reflect on the activity. (Example: Reflect on what happened in the previous activity.) Discuss with students the specific method that will be learned that day. Make sure to discuss when it is more efficient to use one method over another method. 3. Give the learners a new and wider view of the concept by connecting to their personal knowing of the concept. (Example: Direct the learners to draw a visual representation of the concept in their world) Provide the students with a scenario in which you have two different mixtures of anti-freeze and water. Have them try to determine how much of each mixture they will need to use to obtain desired results. Provide the students with a scenario in which they own a pencil manufacturing company, and they need to determine how many wood, and mechanical pencils they need to manufacture to maximize their company's profits. 4. Provide an acknowledged body of information related to the concept. (Example: The learners use lecture,reading and online information to gain a common language and understanding of the parts of the concept.) Have students graph two linear systems and determine the solution set. Teacher demonstrate how to use substitution to solve a linear system. Teacher demonstrate how to use elimination to solve a linear system. 5. Provide a hands-on activity for practice and mastery of the elements of the concept. (Example: Students complete a worksheet based on the information found online or in the text. Another option is for online or Emil discussion of the topic.) Students complete book assignments, worksheets, and board-work to practice methods of solving linear systems. Include story problems that require problem solving skills. 6. Learners apply the concept to a constructive project. (Example: Students build a web page explaining understanding of the concept.) Algebra Project Chapter 7 Complete Sections A, B, and C. SECTION A Description: Create a hyperstudio program that demonstrates your knowledge of the three methods (graphing, substitution, elimination) that can be used to solve a system of linear equations. Utilize only the systems of equations provided by the teacher to demonstrate this knowledge. Systems of Equations: You must use at least two systems, but you do not have to use all three systems. { x + y = 1 {3x - 4y = 21 { x + 4y = -1 { 3x - y = -5 {4x + 2y = 6 {2x - y = 7 SECTION B (NO NOTES) Description: Demonstrate your knowledge of linear systems and linear inequalities by completing both of the following problems. Problems: Complete both 1 and 2. 1. Describe how many solutions the following systems have, then describe the graphic relationship of the lines (parallel lines, intersecting lines, same line). This must be determined by using either the substitution or elimination method. {2x + 3y = 4 { x - 4y = 2 { x + y = 7 {3x + 3y = 5 {2x - 8y = 4 { x - y = -5 2. Graph and label the region bounded by the following system of linear inequalities. After graphing the system, write the coordinates of vertices of solution region. { 3x + 2y < 12 { x + 2y < 8 { x > 0 { y > 0 SECTION C Description: Demonstrate your problem solving abilities by completing one of the following problems. 1. You are the manager of a store that sells home computers. You are getting ready to order next month's stock and are trying to decide how many of each of two models of monitors to order to obtain a maximum profit. -Model A: Your cost is $250; your profit over the cost is $45. -Model B: Your cost is $400; your profit over the cost is $50 -Your combined sales of Model A and B will not exceed 250 units. -You do not want to spend more than $70,000 for both models. How many of each model should you order to obtain a maximum profit? What is the maximum profit you can obtain? 2. A total of $10,000 is invested in two funds paying 5% and 7% annual interest. The combined annual interest is $644. How much of the $10,000 is invested in each fund? 3. You are in charge of ordering softballs for three different leagues. The Pony league uses an 11-inch softball priced at $2.25. The Junior and Senior League use a 12-inch softball priced at $2.75. The invoice smeared in the rain. You can still read the totals, 80 softballs for $210. How many of each size did you order? BONUS: Correctly solve #1 from section C of this test. If you already solved #1 while doing section C, then correctly answer #2 or #3 for bonus points. 7. Refine and edit work. (Example: Check work against the criteria listed in the instructor's rubric.) Algebra Project Linear Systems Grading Rubric Section A Graphing Substitution Elimination Product Method and Process (0 points to 5 points) Method and Process (0 points to 5 points) Method and Process (0 points to 5 points) Effectiveness (0 points to 5 points) Calculations and Accuracy (0 points to 5 points) Calculations and Accuracy (0 points to 5 points) Calculations and Accuracy (0 points to 5 points) Creativity (0 points to 5 points) Solution (0 points to 2 points) Solution (0 points to 2 points) Solution (0 points to 2 points) Usability (0 points to 5 points Section B First System Second System Third System Method Used (0 points to 3 points Method Used (0 points to 3 points Method Used (0 points to 3 points Relationship of Lines (0 points to 2 points) Relationship of Lines (0 points to 2 points) Relationship of Lines (0 points to 2 points) Solution to System (0 points to 2 points) Solution to System (0 points to 2 points) Solution to System (0 points to 2 points) System of Linear Inequalities Lines Graphed (0 points to 5 points) Labeled Vertices (0 points to 3 points) Shaded Region (0 points to 3 points) Section C Assigned Problem Method Used (0 to 3 points) Equations Used (0 to 3 points) Calculations (0 to 2 points) Solution (0 to 2 points) Bonus Problem Method Used (0 to 3 points) Equations Used (0 to 3 points) Calculations (0 to 2 points) Solution (0 to 2 points) 8. Share the work with others. (Example: Post student pages on the school's WWW homepage.) Post some of the student's hyperstudio project on the schools homepage.
its eighth edition, this text masterfully integrates skills, concepts, and activities to motivate learning. It emphasises the relevance of ...Show synopsisNow in its eighth edition, this text masterfully integrates skills, concepts, and activities to motivate learning. It emphasises the relevance of mathematics to help students learn the importance of the information being covered. This approach ensures that they develop a sold mathematics foundation and discover how to apply the content in the real world
Geometria - Stelian Dumitrascu A Java program in interactive solid geometry. Solids can be revolved, cut, joined, built from scratch, measured, and drawn upon. View demo applet online or download a shareware version of the program. (Geometria can be run as a stand-alone application ...more>> Geometria - Valerio Capello A program for computing lines, surfaces and volumes of the main plane and solid figures, through direct and indirect formulas. Select the figure you are working on, choose the kind of calculation from the list provided, and then click the Compute button ...more>> Geometry Assistant - ThinkQuest 1998 An applet/application for drawing dynamic geometry constructions: move any movable point and Geometry Assistant will automatically recalculate and redraw the whole construction. The site includes a place to add your unsolved geometry problem, and a Library ...more>> The Geometry Center - University of Minnesota The Center for the Computation and Visualization of Geometric Structures: an NSF Science and Technology Research Center. The Center has a unified mathematics computing environment supporting math and computer science research, mathematical visualization, ...more>> Geometry Playground - Exploratorium An exhibit from San Francisco's Exploratorium. People-sized exhibits let you use your hands, brain, and body to play with physical demonstrations of geometry concepts. Exhibits fall under the categories of seeing, moving, and fitting things together, ...more>> geometry-software-dynamic - Math Forum A discussion group accessible as a Web-based discussion, a mailing list, or a Usenet newsgroup. This group focuses on discussion of such geometry software programs as The Geometer's Sketchpad and Cabri Geometry II. Read and search archived messages; and ...more>> Google Public Data Explorer - Google Labs The Google Public Data Explorer is available for beta testing and comment. It is designed to make large datasets easy to explore, visualize and communicate. As the charts and maps animate over time, the changes in the world become easier to understand. ...more>> Grapher - Cary and Michael Huang Enter a linear, quadratic, cubic, trigonometric, logarithmic, or other equation, then press an "evaluate" button to watch it render on the Cartesian plane, from left to right. Vary speeds and colors; zoom in and out. ...more>> Graphing Applet - Greg Vogl This graphing Java applet illustrates variable substitution and function composition by encouraging the user to experiment with variables and look at a range of functions -- logarithmic, trigonometric, exponential, and more. Parameters include xmin and ...more>> raphing Vector Calculator - Paul Flavin An interactive Java applet which, given two vectors, will add or subtract them, producing graphical and numerical solutions almost instantly. The vectors are drawn on a labeled grid, the numerical representations are aligned in matching colors, and a ...more>> GraphPanel - David Binger; Centre College A Java application that supports the interactive editing of simple graphs with labels. The program can produce PostScript images of the graphs, and these PostScript files can be included directly in TeX documents or converted (using other programs) to ...more>> Graph Theory Tutorials - Chris K. Caldwell A series of short interactive tutorials introducing the basic concepts of graph theory, designed with the needs of future high school teachers in mind and currently being used in math courses at the University of Tennessee at Martin. An Introduction to ...more>> Great Circle Mapper - Karl L. Swartz Enter two locations on Earth (latitude and longitude, or airport codes) and see a map depicting the great circle path between them and a computation of the distance along that path. The Great Circle Mapper also displays the area within a given range of ...more>>
Volume 8, Number 46 17 November 2003 Vol. 8, No. 46 THE MATH FORUM INTERNET NEWS Dr. Math Explains Algebra \| Mathematical Moments - AMS Second Annual Drexel Math Contest DR. MATH EXPLAINS ALGEBRA by the Math Forum @ Drexel John Wiley & Sons ISBN 0-471-22555-X We are pleased to announce that "Dr. Math Explains Algebra" has joined our first book, "Dr. Math Gets You Ready for Algebra," in bookstores this month. With the holidays approaching consider giving both books as gifts! The second book includes dozens of letters from kids who've had trouble understanding algebraic concepts, along with answers from trained volunteers drawn from a pool of college students, mathematicians, teachers, and professionals from the mathematical community. Topics covered include linear equations, systems of equations, polynomials, factoring, quadratic equations, and much more. For more information and a link to purchase the book from Amazon.com, please visit: We hope the books will find a place in classroom, library, and home collections. We invite you to display a link from your school's website to our book information page. Feel free to use the information on this page: -\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|- MATHEMATICAL MOMENTS PROGRAM - AMS The American Mathematical Society's Mathematical Moments is a series of illustrated "snapshots" designed to promote appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. Since we last featured Mathematical Moments, the AMS has added nine new topics: - Tracing Your Routes - Charging Through Space - Beating Traffic - Making Connections - Bringing Robots to Life - Expressing Yourself - Cutting the Cord - Revolutionizing Computing - Defeating Disease Download standard PDFs or short versions of these and other examples of scientific, technological, and cultural applications of math. For further investigation into a Mathematical Moment, link to its related resource, an authoritative website that expands on the topic. -\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|- SECOND ANNUAL DREXEL MATH CONTEST High school students are invited to compete in the Second Annual Drexel Math Contest on Tuesday, December 16, 2003 from 9:15 am to 1:30 pm, at Drexel University. Teachers are encouraged to attend, and to bring up to 10 of their best math students as contestants. While the students are competing, teachers will have brunch with faculty and staff from the Drexel Mathematics Department and the Math Forum @ Drexel. While the exams are graded, the students will have lunch and participate in a mathematical activity. Campus tours will also available. To register, or obtain further information, please visit the web site: - Registration Information - Directions to the Site - The Schedule of Events - Content of the Exam - Prizes We hope to see you there!Mathematics Library Math Tools Teacher2Teacher Discussion Groups Join the Math Forum Send comments to the Math Forum Internet Newsletter editors Donations Ask Dr. Math Books
Download Description/Abstract This report provides a review of ICT tools of particular relevance to mathematics education. The review cover a large range of hardware, software, and teaching materials including hardware for Whole class displays (data projectors, interactive whiteboards, TV adaptors, OHP pads), hand-held technology (such as calculators, graphical calculators, and other hand-held devices), "small" software programs (which address particular aspects of the mathematics curriculum), programming languages (such as Logo), general purpose software (such as spreadsheets, data-bases, word-processors), mathematics-specific software (such as graph plotters, dynamic geometry software, data-handling tools, computer algebra systems, integrated mathematics packages), and resources such as data-loggers, the Internet and CD-ROMS, digital image technology, and video conferencing. Also included is a section of advice on planning for the effective use of ICT in the teaching and learning of mathematics. Item Type: Monograph (Project Report) Additional Information:
Initially developed by NJCATE and a team of math, science, communications and technology faculty, this learning module employs the NJCATE Integrated Curriculum Model to integrate core and technical material. Accessing... In this animated and interactive object, students read how to use the IMCONJUGATE() function to convert complex numbers to their conjugate in rectangular form. Target Audience: 2-4 Year College Students
This online course includes elements from an undergraduate seminar on mathematical problem solving. The material will help students develop their mathematical and problem solving skills. A few topics that are covered... In this lesson from Math Machines, students will complete the programming for a calculator program which will automate a pulley to move a stick. The goal will be to line the stick up between two points on a pegboard.... MathGrapher is a stand-out graphing tool designed for students, scientists and engineers. Visitors can read the Introduction to get started, as it contains information about the various functions that the tool can...

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