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Algebra 1 also includes some statistics and probability and a small amount of geometry. Here are the modules for which you may need my support: -Expressions -Positive and Negative Numbers -Solving equations -Solving inequalities -Relations and functions -Linear equations -Polynomials -Factoring
Summary: This manual is organized to follow the sequence of topics in the text, and provides an easy-to-follow, step-by-step guide to help students fully understand and get the most out of their graphing calculator. The popular TI-83/84 Plus and the TI-84 Plus with the new operating system, featuring MathPrint'', are covered1575 +$3.99 s/h VeryGood Bookbyte-OR Salem, OR Manual. Has minor wear and/or markings. SKU:9780321744968-3-0 $22
"Single variable" means that it just covers calculus of a single variable. Typically, that covers about the first two semesters of a calculus sequence. A standard college Calculus text covers both single-variable and multivariable calculus. So the single-variable book probably covers about half the material of a standard text. Whether that meets your needs .... it all depends. If you're looking for a book for a class, ask your professor. If you're looking for it for self-study, it would probably be fine to start with the single-variable book.
eBook version Mathematical concepts are explained in this illustrated set, along with a fascinating historical overview of the field. It explores the uses and effects of math in daily life, and provides information on different career choices in this field. Each volume includes sidebars, bibliographies, timelines, charts, a glossary, a guide to resources on the Web, and individual and cumulative indexes. Review: "From 'Abacus' to 'Zero' this alphabetically arranged encyclopedia complements the hands-on approach of standard textbooks or resources...Boxed side notes, definitions of special terms, several see references, and, occasionally, small diagrams or black-and-white photos, enhance the entries...Libraries serving strong science programs will find this set particularly useful." -- School Library Journal
This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility... more... Researchers consider intrinsically noncommutative spaces from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. This work presents fresh ideas for the development of an intrinsically noncommutative geometry. It also covers Grothendieck categorical representations. more... Mathematics and Teaching uses case studies to explore complex and pervasive issues that arise in teaching. In this volume, school mathematics is the context in which to consider race, equity, political contexts and the broader social and cultural circumstances in which schooling occurs. This book does not provide immediate or definitive resolutions.... more... Praise for the Second Edition : "Serious researchers in combinatorics or algorithm design will wish to read the book in its entirety...the book may also be enjoyed on a lighter level since the different chapters are largely independent and so it is possible to pick out gems in one's own area..." — Formal Aspects of Computing This Third... more... Salient Features As per II PUC Basic Mathematics syllabus of Karnataka. Provides an introduction to various basic mathematical techniques and the situations where these could be usefully employed. The language is simple and the material is self-explanatory with a large number of illustrations. Assists the reader in gaining proficiency to solve... more... The book contains a selection of 43 scientific papers of the great mathematician, Ennio De Giorgi. All papers are written in English and 17 of them appear also in their original Italian version. The editors provide also a short biography of Ennio De Giorgi and a detailed account of his scientific achievements, ranging from his seminal paper on the... more... The origins of Graph Theory date back to Euler (1736) with the solution of the celebrated 'Koenigsberg Bridges Problem'; and to Hamilton with the famous 'Trip around the World' game (1859), stating for the first time a problem which, in its most recent version a" the 'Traveling Salesman Problem' -, is still the subject... more...
mathematics Quiz - Educational/Mathematics ... This program is designed for students aged 7 - 9 in Primary 1 - 3. There are over 1500 challenging Maths quizzes and problem sums to practise on. Topics include Addition, Subtraction, Multiplication, Division, Length, Weight, Time, Money, Fractions, Graphs, Permeter, Area, Volume, Geometry, etc. Questions are modelled closely to primary education curriculum. All test papers comes with model answers, fully automated marking system and performance report card. This personal e-tutor is also able to ... 5. Visual mathematics - Educational/Mathematics ... Visual mathematics is a highly interactive visualization software (containing -at least- 67 modules) addressed to High school, College and University students. This is a very powerful tool that helps to learn and solve problems by the hundreds in a very short time. Included areas: Arithmetic, Algebra, Geometry, Trigonometry, Analytic Geometry and miscellaneous.Visual mathematics, a member of the Virtual Dynamics mathematics Virtual Laboratory, is an Intuitively-Easy-To-Use software.Visual ... 6. Aviaion mathematics - Utilities/Other Utilities ... Project avmath implements a computational solution to the aviation wind triangle and is targeted towards learners that have completed pre-calculus and are headed for calculus. ... 7. SpeQ mathematics - Educational/Mathematics ... SpeQ is a small, extensive mathematics program with a simple, intuitive interface. All calculations are entered in a sheet. In there you can freely add, edit and execute all calculations. You can define variables and functions, and plot graphs of your functions. You can save your calculations for later re-use. ... 8. mathematics Tools - Educational/Other ... mathematics value of PI using the Probability - Explore the Fibonacci Number - Quiz Calculate It Quickly: help children in calculating - Calculate the Greatest Common Divisor or Least Common Multiple and lots of features will be update in the next version. ... 9. mathematics Worksheet - Educational/Teaching Tools ... Create ... 10. Web Components for mathematics - Utilities/Other Utilities ... A framework of configurable mathematical software components written in the Java language, meant to be used on instructional Web pages. This project will take the original version (called JCM) and modify it to use Swing and JavaBeans. ... Sample Pmp Certification Mathematics From Long Description 1. pmp Certficiation Requirements - Business & Productivity Tools/Other Related Tools ... pmpcertification Requirements - pmpcertification courses - Are you organized? What pmpcertification courses do you want to acquire your certification in challenge administration? Well, that solution is dependent very much on no matter whether or not you fulfill all of the pmpcertification prerequisites or not. pmpcertification courses - Are you geared up? What pmpcertification programs do you want to obtain your certification in venture administration? Perfectly, that response relies upon ... 2. Boson Practice Tests for Project Management Professional (pmp) Exams3. Project Management Professional Test from BosonMath Games Level 1 - Educational/Mathematics ... Undoubtedly, mathematics is one of the most important subjects taught in school. It is thus unfortunate that some students lack elementary mathematical skills. An inadequate grasp of simple every-day mathematics can negatively affect a person's life. ... Altdo Video To pmp Converter - Business & Productivity Tools ... Altdo Video to pmp Converter is a powerful multi-format conversion tool for pmp movie with high speed and without movie quality loss. It can convert .3gp, .avi, .asf, .mov, .wmv, .mp4, .m4v, .mpeg, *.mpg to pmp format.You can enjoy your favorite Movie on your PC, it is faster than other pmp Converter software, and just a few clicks is enough. It is designed for anyone who wants to watch multi-format movies on the PC.The interface is very vogue
A computer algebra system or graphing calculator and basic computer skills are strongly recommended. Prerequisite MATH C251 In Math C255 students are expected to consistently use the Cartesian, polar, cylindrical, and spherical coordinate systems effectively; use scalar and vector products in applications; use vector-valued products in applications; extend the concepts of derivatives, differentials, and integrals to include multiple independent variables; and solve simple differential equations of the first and second order. Students successfully demonstrating these Math C251 skills will be prepared for Math C255.
Conquering Your Math Anxiety Through Online Learning Recently, you may have been thinking about going back to school. Or perhaps you just started college after some time away from school. You may be hoping to take your career to another level, and you know that a college degree may open different job opportunities. College classes can provide valuable training. You've done your research and decided on an online program for the accommodations it can provide to your full-time job and family obligations. In fact, you're all set to take the plunge, but one thing is holding you back...math. If you are concerned that you will not be able to cope with the math requirements of your degree program, you should first understand that this is a common fear. Next, take heart that you can overcome math anxiety and still achieve your goals in the degree program you choose. Background on Math Anxiety Math anxiety is the feeling of nervousness you may get while learning math or even thinking about learning math. Fear of subjects like algebra is a real problem many students face. You are more susceptible to math anxiety if, in the past, you have not done well in the subject, but you can also experience anxiety if you have a tendency to get nervous in high-pressure situations. A great first step to dealing with your fears is by making your instructors aware so they can help boost your confidence and provide additional support throughout your math courses. You also can leverage your online studies in a way that helps you cope with your anxiety. Safety of Online Learning There is some safety provided by the online classroom structure that is not inherently present in a traditional classroom setting. Online classes offer you some protection against the three top triggers for math anxiety. Public displays: Remember back in middle and high school when your math teacher called on you to answer a question or, worse yet, to work out a problem at the chalkboard in front of the class? Not a chance! In online classes you can do your algebra and other work in the privacy of your own home, still receiving feedback from your instructor on your assignments in areas in which you're struggling. Time restraints: Pressure to rush is about the fastest way to make you forget everything you've learned. In high school, you may have been racing the clock to finish your assignments by the end of the period. In an online program, you have more flexibility, so you can plan to work around your schedule. As long as you manage your time well, you can work on your math skills when you have the time and environment to concentrate without added pressures all while meeting your assignment due dates. Learning Methods: In high school, everyone is expected to learn math the same way. Typically, the teacher delivers a lecture to the class and assigns a short practice assignment from your math book. Then there is homework. The problem is that not everyone learns the same way, and that may not have been the best method for you to learn math. The online approach gives you an opportunity to explore a variety of learning methods and to practice problem-solving with interactive programs that offer step-by-step explanations. If education is the right step for you at this point in your life and career, don't let math anxiety hold you back. The online learning environment is vastly different from the high pressure you may have faced in high school. Now, you can learn without the fear of ridicule and take advantage of novel teaching methods. Your instructors, and dedication to your studies can help you learn skills you need in your program, and even though math may still be a challenge for you, the online environment may help you cope with that challenge a little better. This article is presented by AIU. Contact us today if you're interested in an opportunity to develop knowledge and relevant skills with an industry-current degree program from AIU. Comments David Shamer •March 23, 2012 at 08:24 PM I have been re-instated to the school today and am looking forward to an online math class. I have experience at math anxiety in the conventional class room environment
9780138970lements of Real Analysis Comprehensive in coverage, this book explores the principles of logic, the axioms for the real numbers, limits of sequences, limits of functions, differentiation and integration, infinite series, convergence, and uniform convergence for sequences of real-valued functions. Concepts are presented slowly and include the details of calculations as well as substantial explanations as to how and why one proceeds in the given manner. Uses the words WHY? and HOW? throughout; inviting readers to become active participants and to supply a missing argument or a simple calculation. Contains more than 1000 individual exercises. Stresses and reviews elementary algebra and symbol manipulation as essential tools for success at the kind of computations required in dealing with limiting
Odyssey Trigonometry Purpose This Internet resource provides introductory information, concept or skill development, practice, and assessment in Mathematics for grade 9, 10, 11, and 12 students who are at grade level, Special Education, reading below grade level, advanced, or English Language Learners, in a single student, small group, whole class, or computer lab situation. Brief Description Odyssey Trigonometry combines curricula and assessment to create high-quality content. Each chapter contains lessons on various subtopics that include direct instruction, guided practice, and independent practice. Skills are taught explicitly and completely in the activity, and then practiced and applied in subsequent activities. Introduction: Included at the beginning of each lesson telling the student what topic they will be covering. Direct Instruction Videos: The video segments are 3-5 minutes in duration. Once a student has viewed the entire video, he can repeat sections again. Printable transcripts are available in the activity. Guided Practice: Re-teaches, hint buttons, and example problems support the emphasis on repetition and practice. Feedback in the guided practice sections is based on the critical mistake guidance which provides scaffolded support for students as the feedback guides them to understanding of why correct answers are correct and incorrect answers are incorrect. Hint: Hint buttons link students to specific help with the skill being taught. Vocabulary: The vocabulary tab leads students to a vocabulary list. Three levels of vocabulary support are provided and words are defined and pronounced for the student. Quizzes and Chapter Tests: Quizzes and chapter tests provide feedback for students and teachers about student mastery of the skills presented. Offline Worksheets: Printable worksheets provide additional practice opportunities. Toolkits: Toolkits include a calculator, charts and documents, algebra tiles, base ten blocks, calculator, coordinate grapher, counters, data representation tool, fraction tool, geoboard, number line, probability tool, solid shaper, and transformation tool.
Algebra Models are an exciting manipulative designed to model algebraic concepts through an area model! Your students will see abstract algebraic ideas and concepts come to life as they combine like terms, build rectangles and squares, use substitution to solve linear equations, find factors and quotients, determine area and perimeter, multiply binomials, factor trinomials and much more.
Everyone(The extended licence includes home use by teachers and pupils) EveryonePaul Kunkel, Steven Chanan, Scott Steketee. This collection of more than 55 activities compiled specifically for Algebra 1 including updated activities from Exploring Algebra with The Geometer's Sketchpad and many new ones. Click for longer description. Help Your Students Visualize Algebra 2 Concepts. More than 55 activities, some updated from Exploring Algebra with The Geometers Sketchpad and many new cover Algebra 2 from functions and relations to systems of equations to matrices.
Mathematics CLICK ON IMAGE FOR LARGER SIZE Point Grey has a strong mathematics program that is valued by our students. 90% of grade 12 students take Math 12 . WHAT IS THE PURPOSE OF THREE OPTIONS? Apprenticeship and Workplace Mathematics - this pathway is designed to provide students with the mathematical understanding and critical-thinking skills identified for entry into the majority of trades and for direct entry into the work force. Topics include algebra, geometry, measurement, number, statistics and probability. Foundations of Mathematics - this pathway is designed to provide students with the mathematical understanding and critical-thinking skills identified for post-secondary studies in programs that do not require the study of theoretical calculus. Topics include financial mathematics, geometry, measurement, number, logical reasoning, relations and functions, statistics and probability. Pre-calculus - this pathway is designed to provide students with the mathematical understanding and critical-thinking skills identified for entry into post-secondary programs that require the study of theoretical calculus. Topics include algebra and number, measurement, relations and functions, trigonometry, and permutations, combinations and binomial theorem. AN ACCELERATED CLASS takes the strongest students who have knowledge above the grade 7 level and complete Math 8 and Math 9 in one year. Students are selected on the basis of marks on an exam written at the school by the grade 7's in May. If a mark of 75% is attained in the acceleration class, students progress to Math 10 or Math 10 Honours the following year. ADVANCED PLACEMENT CALCULUS Grade 12 students may take Advanced Placement Calculus AB, which covers the first term of university math, plus one-third of the second term. If a student writes the AP exam (optional) and receives a mark of 4 or 5 out of 5, the student can receive credit for the first term of university Calculus. 85% of our AP Calculus students who write the exam, attain the necessary mark for advanced credit at university. MATH CONTESTS About 300 students write the mathematics competitions each year. We participate in the following contests: CNML - Feb. 18/25, 2014 (Grade 8) GAUSS - May 14, 2014(Grade 8) PASCAL - Feb. 20, 2014(Grade 9) CAYLEY - Feb. 20, 2014(Grade 10) FERMAT - Feb. 20, 2014(Grade 11) AMC - Feb. 5, 2014(Grade 12) AIME (invitational) - April 3, 2014(Grade 12) EUCLID - April. 15, 2014(Grade 12) Canadian Open Math Contest - Nov. 6, 2013 Each year, about 3 of the students who write the AMC contest receive a high enough mark that they are invited to write the Math Olympiad contest.
Geometry Math Made Easy's 5 DVD program provides a dynamic teacher-led review of geometry with step-by-step instruction.The program is very comprehensive and covers the entire geometry course. With a wide assortment of 'real life' examples and colorful computer graphics, our programs convey the material in a clear and visual format that ensures a thorough understanding of geometry. Our program takes the student from point A to point Z so that any student even those who have fallen far behind can quickly catch up and become top performers. What Makes Math Made Easy Tutorial Programs So Effective? The MATH MADE EASY programs are a unique combination of step-by-step instruction which are designed by creative and experienced mathematicians and approved by math educators nationwide. They are enhanced by colorful computer graphics and real life applications. Used by millions of students all across America in schools and homes, the MATH MADE EASY program can be the foundation of success in math and in life! "Very good visual and verbal presentations. For many students, learning and seeing the explanation just one more time is very valuable." National Council of Teachers of Mathematics "It's obvious from the immediate, positive response to your program from the time we first started using it that it is an excellent and effective program for presenting the fundamentals of math. We feel the positive response will continue to grow." Robert J. Sestill Director of Programming, The Learning Channel ."Finally! A math tutorial that can truly replace fear with motivation and understanding with a very special & enjoyable approach." Rona Miles, M.S. Ed., New York State, Math regents teacher and parent Math Made Easy Programs Feature: Simplification of complex topics into easy to understand compact lessons Colorful computer graphics which help students visualize geometry concepts Extensive interactive exercises that give students 'hands on practice' with a large variety of problems 'Real life math applications' which make geometry 'come alive' An emphasis on the critical underlying geometry concepts Free access to Math Made Easy Testing Site with hundreds of practice tests to measure your progress Ideal for general review and test preparation. With as little as thirty minutes per day with Math Made Easy, you'll master Geometry in thirty days! Circles; Lines Associated with Circles: Radius, Diameter, Chord, Tangent, Secant; the Equation of a Circle; Angles Associated with a Circle; Area and Circumference. Customer Reviews: Synthia.R (Monday, 28 January 2013) Rating: These dvd programs did wonders for my 10th grader. She was failing her geometry class, and now is getting A's and B's. The dvds explain the concepts very clearly and give a lot of graphic exercises, which are explained step by step. No flashy animation, but all in all a great buy. Zack32 (Sunday, 28 October 2012) Rating: This software was easy to follow. Great illustrations. It put me back on the right track in my geometry course. A little slow at times but overall I would give the a 9 out of 10. Everything is covered in depth and completely so you get your money's worth. Keneth Farber (Thursday, 18 October 2012) Rating: Nothing fancy, but these dvds absolutely work. Both my kids used the dvds to help them with geometry and both excelled because of them. I think the reason there so effective is they are very straightforward, and comprehensive. Just teaching the material and no gimmicks. Maryanne (Thursday, 18 October 2012) Rating: As a teacher in a parochial school, I often introduce new subjects on screen with Math Made Easy dvds. I have found the format easy to understand and students catch on very fast. They enthusiastically interact with the on screen presentation by calling out the answers. I would recommend these dvds to any parent of a child who is having trouble in math.
Basic Algebra Vocabulary Folder is set up to be a folder activity for vocabulary. Students match the vocabulary word to the definition; an answer sheet is provided. There are instructions at the bottom of the document on how to set up the activity on a manilla folder. Word Document File Be sure that you have an application to open this file type before downloading and/or purchasing. 47
A new year begins—midyear I've taught precalc a number of times at a state college. I think of it as building up a vocabulary of functions you need before doing college math. Polynomials, rational functions, exponentials, logarithms, and trig functions don't really have anything to do with each other, except that you need to know these functions to have examples for calc. One of the big early conceptual things to do is to emphasize how to tell if a word problem is linear or exponential (things change by the same amount every year or by the same percent) Thanks very much. So a lot of it is just building on what they learned on second year algebra and trig, deepening it? Then onto rational functions, particularly graphing them (which at my school, isn't covered in earlier years). How important are polar coordinatees and vectors? There's an old supposition that if a student goes on in mathematics that they'll be taking calculus. The calc professor will more or less assume the student knows the rules for all those functions and so that's what precalc is seen as providing at the college level. Of course, in reality a lot of your students are more likely to take statistics and never see calculus so they'd be better served by spending more time on fitting equations to data. Some precalc books do this weird thing where they try to over-motivate calculus concepts. For example, when introducing average rate of change for a function they'll define the term "difference quotient" but it's really ridiculous to have a special term for this if you're not going to take it's limit and call it the derivative. All of the books dance around the concept of limit since the rigorous treatment is too hard, but it's necessary to talk about asymptotes which are important for understanding the rational functions. Our college did cover polar coordinates in our precalc course, but the student wouldn't see them again unless they took complex analysis as a senior. You're probably safe de-emphasizing it or skipping it if you can get away with it. We didn't cover vectors and I think you'd be pretty safe not doing it. They'll use vectors if they take linear algebra, multidimensional calc, or a serious engineering or physics course. But if they're in that type of class, they'll pick up what you'd teach them about vectors on their own. A friend of mine–a real mathematician–swears that polar coordinates must be covered in pre-calc, but I can't understand why, since they aren't a big part of the AP curriculum Thanks again for the advice. The only thing I'm missing now is an incoming assessment test, but I think I'm just going to throw together some algebra II and trig questions, as well as some conceptual questions on various areas and see how they do.. A little bit of polar coordinates is useful is they are also taking physics. In physics they will have to add a horizontal and vertical vector to get a total vector, and resolve a total vector into horizontal and vertical components. The former is simply going from rectangular to polar coordinates without using the terms, while the latter is the reverse. If you are thinking about doing anything like this, you should check with the physics teacher. This is usually done fairly early in a physics course.
Find a BroadviewAlgebra Seeing Structure in Expressions Topics may include interpreting the structure of expressions and writing expressions in equivalent forms to solve problems. Arithmetic with Polynomials and Rational Expressions Topics may include performing arithmetic operations on polynomials, understan
Oxford AQA GCSE Maths The highly successful Oxford 4-book approach now available for AQA GCSE Due to popular demand, the uniquely effective Oxford four-book approach is now available specifically for AQA GCSE. This tried-and-tested method offers a choice of four levelled student books to give each student the one single book they really need to succeed - and they can easily be used for linear teaching. You can download a grid here showing simple routes to teaching in a linear way. Features You choose which of four levelled student books is right for each of your students Topics correspond accross all four levelled student books so teaching different levels in one class is easy One double-page-spread per lesson makes classroom management and planning simple Slimmer student books with less irrelevant material are less daunting and more cost-effective Levelled student books can dedicate a double-page to each grade, not just a single question Plenty of extra help to cope easily with new assessment objectives, QWC (quality of written communication), and functional skills
A big advantage of numerical mathematics is that a numerical solution can be obtained for problems, where an analytical solution does not exist. An additional advantage is, that a numerical method only uses evaluation of standard functions and the operations: addition, subtraction, multiplication and division. Because these are just the operations a computer can perform, numerical mathematics and computers form a perfect combination. An analytical method gives the solution as a mathematical formula, which is an advantage. From this we can gain insight in the behavior and the properties of the solution, and with a numerical solution (that gives the function as a table) this is not the case. On the other hand some form of visualization may be used to gain insight in the behavior of the solution. To draw a graph of a function with a numerical method is usually a more useful tool than to evaluate the analytical solution at a great number of points. In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize those aspects that play an important role in practical problems. In this introductory text we confine ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation. The techniques discussed in the introductory chapters, for e.g. interpolation, numerical quadrature and the solution of nonlinear equations, may also be used outside the context of differential equations. They have been included to make the book self contained as far as the numerical aspects are concerned.
Counting Supplementary Notes And Solutions Manual 9789812569158 9812569154 Summary: "This book is the companion to the authors' earlier book Counting, an introduction to combinatorics for junior college students. It provides supplementary material both for the purpose of adding to the reader's knowledge about counting techniques and, in particular, for use as a textbook for junior college students and teachers in combinatorics at H3 level in the new Singapore mathematics curriculum for junior colleg...e."--BOOK JACKET.[read more]
#3:Physics by Alan Giambattista Physics is intended for a two-semester college course in introductory physics using algebra and trigonometry. Our main goals in writing this book are • to present the basic concepts ofphysics that students need to know for later courses and future careers, • to emphasize that physics is a tool for understanding the real world, and • to teach transferable problem-solving skills that students can use throughout their lives. We have kept these goals in mind while developing the main themes of the book.
Advanced functions such as Ln and Exponential functions are also explained in the subject. The focus on differences become crucial when dealing with advanced mathematics. Calculus branches into two sections, differential and integral calculus
Algebra 2 Online algebra video lessons to help students with the formulas, equations and calculator use, to improve their math problem solving skills to get them to the answers of their Algebra 2 homework and worksheets.
Mathemania 3.0.4 description Mathemania enables you to quickly and easily generate math fact practice sheets to print. You simply specify the operations (addition, subtraction, multiplication, or division) and number ranges you want to cover and Mathemania generates a sheet to your specifications. You can also edit individual problems, customize the page header, and use custom fonts. The problems are generated on-the-fly, so every sheet will be different. You can also re-randomize a sheet at will, allowing you to create many different sheets from one set of options. Of course, corresponding answer sheets can be printed as well. Unlimited supply of randomly generated math sheets! Every sheet you make will be different! Combine any combination of Addition, Subtraction, Multiplication, and Division problems. Quiz students with both horizontal and vertical notations. Instantly create answer keys for easy correcting. Batch print 20, 30, or more sheets and corresponding answer keys at a time Orient the math sheets vertically or horizontally. Edit individual problems to tweak the final sheet. Save sheets for later reuse. Randomize a saved page giving you a completely new sheet using the same settings instantly! Edit the font settings separately for the header and problems. Easy to use! Most features are self-explanatory, but a full manual is included. If you have any questions just email us. Mathemania 3.0.4 Math Mechanixs is a general purpose math program with a Math Editor for solving mathematical problems and taking notes, extensive Function Library and Function Solver, 2D & 3D Graphing, and a Calculus Free Download
Elaborating on the lessons learned in Pre-Algebra and Algebra 1, Algebra 2 broadens its scope to include all the essential topics needed to be successful in College Algebra, Pre-Calculus or Trigonometry. Algebra 2 is supported by the informative, user-friendly Omega website. Topics include: functions, logarithmic functions, exponential functions, complex numbers and more. This course meets state standards and is based on the National Council of teachers of Mathematics (NCTM) standards. College Prep
VITEEE Maths Syllabus Engineering Entrance , VITEEE **Keep in mind, this syllabus is not for Biology stream students, go through biology syllabus for VITEEE for bio-medical courses entrance exam . MATRICES AND DETERMINANTS Types of matrices, addition and multiplication of matrices-Properties, computation of inverses, solution of system of linear equations by matrix inversion method. Rank of a Matrix - Elementary transformation on a matrix, consistency of a system of linear equations, Cramer's rule, Non-homogeneous equations, homogeneous linear system, rank method. Scalar Product - Angle between two vectors, properties of scalar product, applications of dot products. Vector Product - Right handed and left handed systems, properties of vector product, applications of cross product. Product of three vectors - Scalar triple product, properties of scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors. Lines - Equation of a straight line passing through a given point and parallel to a given vector, passing through two given points, angle between two lines. Skew lines - Shortest distance between two lines, condition for two lines to intersect, point of intersection, collinearity of three points. Planes - Equation of a plane, passing through a given point and perpendicular to a vector, given the distance from the origin and unit normal, passing through a given point and parallel to two given vectors, passing through two given points and parallel to a given vector, passing through three given non-collinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines, angle between two given planes, angle between a line and a plane. Sphere - Equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given. Definition of a Conic - General equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity. Parabola - Standard equation of a parabola tracing of the parabola, other standard parabolas, the process of shifting the origin, general form of the standard equation, some practical problems. Ellipse - Standard equation of the ellipse, tracing of the ellipse (x^2/a^2 )+(y^2/a^2 ) = 1 (a> b). Other standard form of the ellipse, general forms, some practical problems Hyperbola - standard equation, tracing of the hyperbola (x^2/a^2 )-(y^2/a^2 ) = 1 , other form of the hyperbola, parametric forms of a conics, chords, tangents and normals - Cartesian form and parametric form, equation of chord of contact of tangents from a point (x1 ,y1 ) Asymptotes, Rectangular Hyperbola -standard equation of a rectangular hyperbola.
Appendices This textbook is designed to teach the university mathematics student the basics of linear algebra and the techniques of formal mathematics. There are no prerequisites other than ordinary algebra, but it is probably best used by a student who has the "mathematical maturity" of a sophomore or junior. The text has two goals: to teach the fundamental concepts and techniques of matrix algebra and abstract vector spaces, and to teach the techniques associated with understanding the definitions and theorems forming a coherent area of mathematics. So there is an emphasis on worked examples of nontrivial size and on proving theorems carefully. This book is copyrighted. This means that governments have granted the author a monopoly --- the exclusive right to control the making of copies and derivative works for many years (too many years in some cases). It also gives others limited rights, generally referred to as "fair use," such as the right to quote sections in a review without seeking permission. However, the author licenses this book to anyone under the terms of the GNU Free Documentation License (GFDL), which gives you more rights than most copyrights (see appendix GFDL). Loosely speaking, you may make as many copies as you like at no cost, and you may distribute these unmodified copies if you please. You may modify the book for your own use. The catch is that if you make modifications and you distribute the modified version, or make use of portions in excess of fair use in another work, then you must also license the new work with the GFDL. So the book has lots of inherent freedom, and no one is allowed to distribute a derivative work that restricts these freedoms. (See the license itself in the appendix for the exact details of the additional rights you have been given.) Notice that initially most people are struck by the notion that this book is free (the French would say gratuit, at no cost). And it is. However, it is more important that the book has freedom (the French would say liberté, liberty). It will never go "out of print" nor will there ever be trivial updates designed only to frustrate the used book market. Those considering teaching a course with this book can examine it thoroughly in advance. Adding new exercises or new sections has been purposely made very easy, and the hope is that others will contribute these modifications back for incorporation into the book, for the benefit of all. Depending on how you received your copy, you may want to check for the latest version (and other news) at Topics. The first half of this text (through Chapter M:Matrices) is basically a course in matrix algebra, though the foundation of some more advanced ideas is also being formed in these early sections. Vectors are presented exclusively as column vectors (since we also have the typographic freedom to avoid writing a column vector inline as the transpose of a row vector), and linear combinations are presented very early. Spans, null spaces, column spaces and row spaces are also presented early, simply as sets, saving most of their vector space properties for later, so they are familiar objects before being scrutinized carefully. You cannot do everything early, so in particular matrix multiplication comes later than usual. However, with a definition built on linear combinations of column vectors, it should seem more natural than the more frequent definition using dot products of rows with columns. And this delay emphasizes that linear algebra is built upon vector addition and scalar multiplication. Of course, matrix inverses must wait for matrix multiplication, but this does not prevent nonsingular matrices from occurring sooner. Vector space properties are hinted at when vector and matrix operations are first defined, but the notion of a vector space is saved for a more axiomatic treatment later (Chapter VS:Vector Spaces). Once bases and dimension have been explored in the context of vector spaces, linear transformations and their matrix representation follow. The goal of the book is to go as far as Jordan canonical form in the Core (part C), with less central topics collected in the Topics (part T). A third part contains contributed applications (part A), with notation and theorems integrated with the earlier two parts. Linear algebra is an ideal subject for the novice mathematics student to learn how to develop a topic precisely, with all the rigor mathematics requires. Unfortunately, much of this rigor seems to have escaped the standard calculus curriculum, so for many university students this is their first exposure to careful definitions and theorems, and the expectation that they fully understand them, to say nothing of the expectation that they become proficient in formulating their own proofs. We have tried to make this text as helpful as possible with this transition. Every definition is stated carefully, set apart from the text. Likewise, every theorem is carefully stated, and almost every one has a complete proof. Theorems usually have just one conclusion, so they can be referenced precisely later. Definitions and theorems are cataloged in order of their appearance in the front of the book (\miscref{definition}{Definitions}, \miscref{theorem}{Theorems}), and alphabetical order in the index at the back. Along the way, there are discussions of some more important ideas relating to formulating proofs (\miscref{technique}{Proof Techniques}), which is part advice and part logic. Origin and History. This book is the result of the confluence of several related events and trends. At the University of Puget Sound we teach a one-semester, post-calculus linear algebra course to students majoring in mathematics, computer science, physics, chemistry and economics. Between January 1986 and June 2002, I taught this course seventeen times. For the Spring 2003 semester, I elected to convert my course notes to an electronic form so that it would be easier to incorporate the inevitable and nearly-constant revisions. Central to my new notes was a collection of stock examples that would be used repeatedly to illustrate new concepts. (These would become the Archetypes, appendix A.) It was only a short leap to then decide to distribute copies of these notes and examples to the students in the two sections of this course. As the semester wore on, the notes began to look less like notes and more like a textbook. I used the notes again in the Fall 2003 semester for a single section of the course. Simultaneously, the textbook I was using came out in a fifth edition. A new chapter was added toward the start of the book, and a few additional exercises were added in other chapters. This demanded the annoyance of reworking my notes and list of suggested exercises to conform with the changed numbering of the chapters and exercises. I had an almost identical experience with the third course I was teaching that semester. I also learned that in the next academic year I would be teaching a course where my textbook of choice had gone out of print. I felt there had to be a better alternative to having the organization of my courses buffeted by the economics of traditional textbook publishing. I had used TeX and the Internet for many years, so there was little to stand in the way of typesetting, distributing and "marketing" a free book. With recreational and professional interests in software development, I had long been fascinated by the open-source software movement, as exemplified by the success of GNU and Linux, though public-domain TeX might also deserve mention. Obviously, this book is an attempt to carry over that model of creative endeavor to textbook publishing. As a sabbatical project during the Spring 2004 semester, I embarked on the current project of creating a freely-distributable linear algebra textbook. (Notice the implied financial support of the University of Puget Sound to this project.) Most of the material was written from scratch since changes in notation and approach made much of my notes of little use. By August 2004 I had written half the material necessary for our Math 232 course. The remaining half was written during the Fall 2004 semester as I taught another two sections of Math 232. While in early 2005 the book was complete enough to build a course around and Version 1.0 was released. Work has continued since, filling out the narrative, exercises and supplements. However, much of my motivation for writing this book is captured by the sentiments expressed by H.M. Cundy and A.P. Rollet in their Preface to the First Edition of Mathematical Models (1952), especially the final sentence, This book was born in the classroom, and arose from the spontaneous interest of a Mathematical Sixth in the construction of simple models. A desire to show that even in mathematics one could have fun led to an exhibition of the results and attracted considerable attention throughout the school. Since then the Sherborne collection has grown, ideas have come from many sources, and widespread interest has been shown. It seems therefore desirable to give permanent form to the lessons of experience so that others can benefit by them and be encouraged to undertake similar work. How To Use This Book. Chapters, Theorems, etc. are not numbered in this book, but are instead referenced by acronyms. This means that Theorem XYZ will always be Theorem XYZ, no matter if new sections are added, or if an individual decides to remove certain other sections. Within sections, the subsections are acronyms that begin with the acronym of the section. So Subsection XYZ.AB is the subsection AB in Section XYZ. Acronyms are unique within their type, so for example there is just one Definition B, but there is also a Section B:Bases. At first, all the letters flying around may be confusing, but with time, you will begin to recognize the more important ones on sight. Furthermore, there are lists of theorems, examples, etc. in the front of the book, and an index that contains every acronym. If you are reading this in an electronic version (PDF or XML), you will see that all of the cross-references are hyperlinks, allowing you to click to a definition or example, and then use the back button to return. In printed versions, you must rely on the page numbers. However, note that page numbers are not permanent! Different editions, different margins, or different sized paper will affect what content is on each page. And in time, the addition of new material will affect the page numbering. Chapter divisions are not critical to the organization of the book, as Sections are the main organizational unit. Sections are designed to be the subject of a single lecture or classroom session, though there is frequently more material than can be discussed and illustrated in a fifty-minute session. Consequently, the instructor will need to be selective about which topics to illustrate with other examples and which topics to leave to the student's reading. Many of the examples are meant to be large, such as using five or six variables in a system of equations, so the instructor may just want to "walk" a class through these examples. The book has been written with the idea that some may work through it independently, so the hope is that students can learn some of the more mechanical ideas on their own. The highest level division of the book is the three Parts: Core, Topics, Applications (part C, part T, part A). The Core is meant to carefully describe the basic ideas required of a first exposure to linear algebra. In the final sections of the Core, one should ask the question: which previous Sections could be removed without destroying the logical development of the subject? Hopefully, the answer is "none." The goal of the book is to finish the Core with a very general representation of a linear transformation (Jordan canonical form, Section JCF:Jordan Canonical Form). Of course, there will not be universal agreement on what should, or should not, constitute the Core, but the main idea is to limit it to about forty sections. Topics (part T) is meant to contain those subjects that are important in linear algebra, and which would make profitable detours from the Core for those interested in pursuing them. Applications (part A) should illustrate the power and widespread applicability of linear algebra to as many fields as possible. The Archetypes (appendix A) cover many of the computational aspects of systems of linear equations, matrices and linear transformations. The student should consult them often, and this is encouraged by exercises that simply suggest the right properties to examine at the right time. But what is more important, this a repository that contains enough variety to provide abundant examples of key theorems, while also providing counterexamples to hypotheses or converses of theorems. The summary table at the start of this appendix should be especially useful. I require my students to read each Section prior to the day's discussion on that section. For some students this is a novel idea, but at the end of the semester a few always report on the benefits, both for this course and other courses where they have adopted the habit. To make good on this requirement, each section contains three Reading Questions. These sometimes only require parroting back a key definition or theorem, or they require performing a small example of a key computation, or they ask for musings on key ideas or new relationships between old ideas. Answers are emailed to me the evening before the lecture. Given the flavor and purpose of these questions, including solutions seems foolish. Every chapter of part C ends with "Annotated Acronyms", a short list of critical theorems or definitions from that chapter. There are a variety of reasons for any one of these to have been chosen, and reading the short paragraphs after some of these might provide insight into the possibilities. An end-of-chapter review might usefully incorporate a close reading of these lists. Formulating interesting and effective exercises is as difficult, or more so, than building a narrative. But it is the place where a student really learns the material. As such, for the student's benefit, complete solutions should be given. As the list of exercises expands, the amount with solutions should similarly expand. Exercises and their solutions are referenced with a section name, followed by a dot, then a letter (C,M, or T) and a number. The letter `C' indicates a problem that is mostly computational in nature, while the letter `T' indicates a problem that is more theoretical in nature. A problem with a letter `M' is somewhere in between (middle, mid-level, median, middling), probably a mix of computation and applications of theorems. So solution MO.T13 is a solution to an exercise in Section MO:Matrix Operations that is theoretical in nature. The number `13' has no intrinsic meaning. More on Freedom. This book is freely-distributable under the terms of the GFDL, along with the underlying TeX code from which the book is built. This arrangement provides many benefits unavailable with traditional texts. No cost, or low cost, to students. With no physical vessel (i.e. paper, binding), no transportation costs (Internet bandwidth being a negligible cost) and no marketing costs (evaluation and desk copies are free to all), anyone with an Internet connection can obtain it, and a teacher could make available paper copies in sufficient quantities for a class. The cost to print a copy is not insignificant, but is just a fraction of the cost of a traditional textbook when printing is handled by a print-on-demand service over the Internet. Students will not feel the need to sell back their book (nor should there be much of a market for used copies), and in future years can even pick up a newer edition freely. Electronic versions of the book contain extensive hyperlinks. Specifically, most logical steps in proofs and examples include links back to the previous definitions or theorems that support that step. With whatever viewer you might be using (web browser, PDF reader) the "back" button can then return you to the middle of the proof you were studying. So even if you are reading a physical copy of this book, you can benefit from also working with an electronic version. A traditional book, which the publisher is unwilling to distribute in an easily-copied electronic form, cannot offer this very intuitive and flexible approach to learning mathematics. The book will not go out of print. No matter what, a teacher can maintain their own copy and use the book for as many years as they desire. Further, the naming schemes for chapters, sections, theorems, etc. is designed so that the addition of new material will not break any course syllabi or assignment list. With many eyes reading the book and with frequent postings of updates, the reliability should become very high. Please report any errors you find that persist into the latest version. For those with a working installation of the popular typesetting program TeX, the book has been designed so that it can be customized. Page layouts, presence of exercises, solutions, sections or chapters can all be easily controlled. Furthermore, many variants of mathematical notation are achieved via TeX macros. So by changing a single macro, one's favorite notation can be reflected throughout the text. For example, every transpose of a matrix is coded in the source as {\tt\verb!\transpose{A}!}, which when printed will yield $\transpose{A}$. However by changing the definition of {\tt\verb!\transpose{ }!}, any desired alternative notation (superscript t, superscript T, superscript prime) will then appear throughout the text instead. The book has also been designed to make it easy for others to contribute material. Would you like to see a section on symmetric bilinear forms? Consider writing one and contributing it to one of the Topics chapters. Should there be more exercises about the null space of a matrix? Send me some. Historical Notes? Contact me, and we will see about adding those in also. You have no legal obligation to pay for this book. It has been licensed with no expectation that you pay for it. You do not even have a moral obligation to pay for the book. Thomas Jefferson (1743 -- 1826), the author of the United States Declaration of Independence, wrote, If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me. That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density in any point, and like the air in which we breathe, move, and have our physical being, incapable of confinement or exclusive appropriation. Letter to Isaac McPherson August 13, 1813 However, if you feel a royalty is due the author, or if you would like to encourage the author, or if you wish to show others that this approach to textbook publishing can also bring financial compensation, then donations are gratefully received. Moreover, non-financial forms of help can often be even more valuable. A simple note of encouragement, submitting a report of an error, or contributing some exercises or perhaps an entire section for the Topics or Applications are all important ways you can acknowledge the freedoms accorded to this work by the copyright holder and other contributors. Conclusion. Foremost, I hope that students find their time spent with this book profitable. I hope that instructors find it flexible enough to fit the needs of their course. And I hope that everyone will send me their comments and suggestions, and also consider the myriad ways they can help (as listed on the book's website at
Module 3G2 - Mathematical Physiology This course focuses on the quantitative modelling of biological systems. A wide variety of topics are touched upon, from biochemistry and cellular function to neural activity and respiration. In all cases, the emphasis is on finding the simplest mathematical model that describes the observations and allows us to identify the relevant physiological parameters. The models often take the form of a simple functional relationship between two variables, or a set of coupled differential equations. The course tries to show where the equations come from and lead to: what assumptions are needed and what simple and robust conclusions can be drawn.
Graphing Calculator MatchingManiaGraphing Calculator MatchingMania consists of 12 functions. Students work together using a graphing calculator to find the zeroes, minimums and/or maximums and the points of intesection of two functions. This is a great calculator review activity or learning activity to begin the school year with in advanced math classes. PDF (Acrobat) Document File Be sure that you have an application to open this file type before downloading and/or purchasing. 28.96
Aquasco ACT knows how to tap into each kid?s learning style. ItMy philosophy for studying is that it is insufficient to merely memorize formulas; it is necessary to understand the formula's derivation as well as its potential applications. This leads to a much greater understanding of the subject material.A solid algebra foundation is necessary for almost aIn essence, there is a systematic process that should be used to establish some of the fundamental principles young children need to become successful at future attempts at higher level mathematics. Ultimately, if there is a lack of sound mathematics skills, a student may experience some level o...
The calculus of differential forms has significant advantages over traditional methods as a tool for teaching electromagnetic (EM) field theory. First, films clarify the relationship between field intensity and flux density, by providing distinct mathematical and graphical representations for the two types of fields. Second, Ampere's and Faraday's laws obtain graphical representations that are as intuitive as the representation of Gauss's law. Third, the vector Stokes theorem and the divergence theorem become special cases of a single relationship that is easier for the student to remember, apply, and visualize than their vector formulations. Fourth, computational simplifications result from the use of forms: derivatives are easier to employ in curvilinear coordinates, integration becomes more straightforward, and families of vector identities are replaced by algebraic rules. In this paper, EM theory and the calculus of differential forms are developed in parallel, from an elementary, conceptually oriented point of view using simple examples and intuitive motivations. We conclude that because of the power of the calculus of differential forms in conveying the fundamental concepts of EM theory, it provides an attractive and viable alternative to the use of vector analysis in teaching electromagnetic field theory.
Practical Approach to Merchandising Mathematics, RevisedMerchandising math is a multifaceted topic that involves many levels of the retail process, including assortment planning; vendor analysis; markup and pricing; and terms of sale. A Practical Approach to Merchandising Mathematics, Revised 1st Edition, brings each of these areas together into one comprehensive text to meet the needs of students who will be involved with the activities of merchandising and buying at the retail level. Students will learn how to use typical merchandising forms; become familiar with the application of computers and c... MOREomputerized forms in retailing; and recognize the basic factors of buying and selling that affect profit. This peer-reviewed new edition is dedicated to helping students master the mathematical concepts, techniques and analysis utilized in the merchandise buying and planning process.
Matrices: Definition and Classification A rectangular array of symbols (which could be real or complex numbers) along rows and columns is called a matrix. Thus a system m × n symbols arranged in a rectangular formation along m rows and n columns and bounded by the brackets [.] is called an m by n matrix (which is written as m x n matrix) i.e. A = is a matrix of order m × n. In a compact form the above matrix is represented by A = [aij], 1 < i < m, 1 < j < n, where is, j ε i or simply [aij] m × n. The numbers a11, a12, ... etc of this rectangular array are called the elements of the matrix. The element aij belongs to the ith row and the jth column and is called the (i, j)th element of the matrix. Equal Matrices Two matrices are said to be equal if they have the same order and each element of one is equal to the corresponding element of the other. CLASSIFICATION OF MATRICES Row Matrix A matrix having a single row is called a row matrix. e.g. [1 3, 5, 7] Column Matrix A matrix having a single column is called a column matrix. e.g.. Square Matrix An m x n matrix A is said to be a square matrix if m = n i.e. number of rows = number of columns. For example: A = is a square matrix of order 3 × 3. Note: In a square matrix the diagonal from left hand side upper corner to right hand side lower corner is known as leading diagonal or principal diagonal. In the above example square matrix containing the elements 1, 3, 5 is called the leading or principal diagonal.
Pre-Geometry Guide Every day we use principles of geometry to help guide decision making and now the keys to this important subject can be at your fingertips! Geometry sharpens our reasoning, logic and problem solving skills and is one of those subjects we need to know not only to keep up, but to get ahead in the [...] Pre-Calculus Guide Calculus may not seem very important to you but the lessons and skills you learn will be with for your whole lifetime! Calculus is the mathematical study of continuous change. It helps you practice and develop your logic/reasoning skills. It throws challenging problems your way which make you think. Although you may never use calculus [...] Pre-College Math Math helps the mind to reason and organize complicated situations and problems into clear, simple, and logical steps. In our society, high paying jobs often demand someone who can take complicated situations and simplify them to a level that everyone can understand. Therefore, by knowing more math, you give yourself the competitive edge needed to [...]
2012-2013 2010-2011 2008-2009 ED 110) A consideration of selected topics from basic Euclidean geometry with emphasis on proper terminology and unification of concepts. Techniques available for teaching the basics are discussedED110) A consideration of selected topics from basic Euclidean geometry with emphasis on proper terminology and unification of concepts. Techniques available for teaching the basics are discussed A consideration of selected topics from basic Euclidean geometry with emphasis on proper terminology and unification of concepts. Techniques available for teaching the basics are discussed. 3:0:3 (From catalog 2004-2005)
Aplusix - Helping the children of the world to learn algebra: a research project that has been commercialised successfully Of all the subjects taught in schools, mathematics is arguably the most challenging to engage with. Algebra, one branch of mathematics, illustrates this perfectly, presenting many challenges through its abstract concepts of variables, definition of polynomials and factorisation, naming but a few. This case study, developed with Grenoble 1 University and CNRS in Grenoble, gives an overview of the Algebra Learning Assistant, Aplusix. 'It can motivate even those students who dislike mathematics and Algebra', claims Jean Francois-Nicaud, the project's Scientific Manger. 'It also enables teachers to monitor how their students are doing, taking prescriptive corrective action as and when needed'. What makes learning algebra with Aplusix so different? Many of the software learning programmes on the market at the moment are merely tools which mathematics students can use, but without offering the required feedback. Aplusix provides a fully-integrated user interface that incorporates pedagogical functionality. The project team is made up of engineers, scientists and business managers based at Floralis, which is an affiliate of Grenoble 1 University. Students become autonomous, teachers get more time to teach students that need help Aplusix has been created with both the student and teacher in mind and its main functionalities include an intuitive editor of algebraic expressions, verification of calculations, scores, commands and a map of exercises. Very importantly, the teacher is able to factor-in parameters for learning, set problems and exercises for students, as well as keep control of administrative applications. 'Our research shows that using Aplusix, students will gain confidence, work more autonomously and most importantly learn', stresses Dr Nicaud. 'Not only that, but we have found that teachers' time is saved as students' gain that autonomy. Using the software they can monitor what their students are doing, diagnose any problems, and rectify them. What makes this project so different? 'Firstly, it is a project that is already resulted in a commercialised product. We are, however, conducting ongoing research, to enable us to continually enhance the product. Recently this commitment has enabled us to incorporate a new display for problems, a new editor for creating exercises and problems to solve. We continue to examine how Aplusix can be adapted to suit different culturally specific contexts across countries. For example, in some countries, the curriculum demands that algebraic trees are included. We are also looking at how students better understand the structure of algebraic expressions. One exciting aspect of this is how the equivalence of expressions will correspond to identical graphical representations. What should policy makers know about Aplusix? Mathematics is surely a huge contributor to achievement of Europe's goals in becoming a more competitive, knowledge driven society. Aplusix demonstrates how sophisticated software can be developed which incorporates sound pedagogical practices. It supports teachers through enabling them to help their own students more efficiently and effectively. Those students that are forging ahead are able to push their boundaries further, whilst those that previously had no access to Aplusix, who may have struggled with mathematics, have shown demonstrable motivation towards learning. The teachers, being more in tune with the needs of their students, are able to adapt accordingly. Applications that motivate mathematics learners must represent an important step forward to creating a better-educated society. Who is on the Aplusix team? This case study can only be presented thanks to the various project members involved, drawing together experts from different disciplines:
Introductory concepts of modern algebra and their applications to the solution of polynomial equations over various fields. Elementary properties of groups, rings, integral domains, fields, and vector spaces; introductory Galois theory and applications including Abel's theorem and compass-straightedge constructions. (LA) Prerequisites: MATH 174 and MATH 205 for 321, 321 for 322, "C" or better in all.
ElementaryElementary Algebra"is typically a 1-semester course that provides a solid foundation in algebraic skills and reasoning for students who have little or no previous experience with the topic. The goal is to effectively prepare students to transition into Intermediate Algebra.
lucid introduction to some of the mathematical ideas which are useful to biologists. Professor Maynard Smith introduces the reader to the ways in which biological problems can be expressed mathematically, and shows how the mathematical equations which arise in biological work can be solved. Each chapter has a number of examples which present further points of biological and mathematical interest. interest. Professor Maynard Smith's book is written for all biologists, from undergraduate level upwards, who need mathematical tools. Only an elementary knowledge of mathematics is assumed. Since there are already a number of books dealing with statistics for biologists, this book is particularly concerned with non-statistical topics.
Book Description: This book is for students following a module in numerical methods, numerical techniques, or numerical analysis. It approaches the subject from a pragmatic viewpoint, appropriate for the modern student. The theory is kept to a minimum commensurate with comprehensive coverage of the subject and it contains abundant worked examples which provide easy understanding through a clear and concise theoretical treatment.
up-to-date, broad scope textbook suitable for undergraduates starting on computational physics courses. It shows how to use computers to solve mathematical problems in physics and teaches a variety of numerical approaches. It includes exercises, examples of programs and online resources at
Category Archives: Learning Tools The school term has just started and it was exciting to meet familiar faces and new ones in our weekly tuition classes for both O-Level Maths, O-Level Chemistry and A-Level H2 Chemistry. While I was teaching in my Secondary 3 Additional Mathematics class on the usage of their Scientific Calculator to solve linear simultaneous equations, one student pointed out there was a new calculator which is much more powerful in terms of functions. Another student in the O-Level class mentioned it too. I was excited about this new calculator! I went searching for calculators in our centre and managed to find one in the cupboard! Casio fx-95ES Plus. It looks exactly like my current Casio model except it has additional functions like: Displaying answers in surd forms! (Useful for Trigonometry, Surd! Solving quadratic inequality! (Many students can't seem to get this right!) However, when I went to the Ministry of Education Approved Calculator List, Casio fx-95ES Plus wasn't in that list. Since this calculator was bought by my colleague Sean Chua from Popular bookstore last November, I was thinking maybe MOE has yet to update the list so I emailed them to confirm. And attached was their reply. Lesson learnt: Not all calculators sold in Popular bookstores are approved for usage in major examinations. We must still learn our concepts well instead of relying only on calculator to help us! Well, I'm going into the topic of Quadratic Inequality in a few weeks time, join me in my weekly O-Level A-Maths tuition classes before it's too late! Go to NOW for the details!
Important Books For IIT JEE R.D Sharma is very famous among IIT-JEE aspirants.Every the one of the best books in Mathematics for beginners. It includes the exercises covering the entire syllabus of Mathematics pertaining to IIT JEE, AIEEE and other state level engineering examination preparation. Although all the topics are covered very well but the topics of Algebra have an edge over others. Permutations and Combinations, Probability, Quadratic equations and Determinants are worth mentioning. It's a one stop book for beginners. It includes illustrative solved examples which help in explaining the concepts better. Room for improvements (Why should I keep away from this book?) Though the book has a good collection of problems but it cannot be said to be self sufficient for the whole syllabus of Mathematics. An aspirant should also practice from other standard sources too. A good book for beginners not only for competitive examinations but also from 10+2 examination perspective. User Reviews: * for topers Posted On:May 27, 2012 08:11 PM Review By prem it is good book my mark in mathes iit jee 12 is 112 * 4 Posted On:Nov 16, 2011 10:33 PM Review By Caelii Absolutely first rate and copper-bottomed, gnetleemn! * Thopulaki thopu(topper than toppers) Posted On:Sep 30, 2011 02:14 AM Review By A Hemanth Kumar The thing is if u r not good at ALGEBRA,just do one thing GO FOR IT * Wide range of problems Posted On:Sep 15, 2011 07:41 AM Review By Abdul Wajid Excellent book for those who are IIT-JEE aspirants and covers the entire syllabus with wide range of problems. * BOOK Posted On:Jul 26, 2011 08:31 AM Review By RAJIV KHANNA SIR, i have objective mathematics for IIT and aieee of rd sharma. Is there any other book of rd sharma for the preparation of IIT?BECAUSE I HAVE HEARD ANOTHER BOOK OF RD SHARMA NAMED AS OBJECTIVE APPROACH TOO IIT JEE. * rd sharma Posted On:Jul 20, 2009 02:41 AM Review By purav it is a very great book and it gives a complete knowledgeRevise this book for IIT-JEE Posted On:Mar 17, 2009 08:20 AM Review By Anand Shankar As all of you must have already finished this book,therefore the only thing required for IIT-JEE is to revise it thouroughly.
MATLAB for Electrical and Computer Engineering Students and Professionals: With Simulink Author: Roland Priemer Year: 2013 Format:Paperback Product Code: SBPC5010 ISBN: 978-1-61353-188-4 Pagination: 450 pp. Stock Status: Pre-order The arrival date is May 2013 Your account will only be charged when we ship your item. £38.25 Pre-order price £29.25 Member price £45.00 Full price Description This book combines the teaching of the MATLAB programming language with the presentation and development of carefully selected electrical and computer engineering (ECE) fundamentals. This is what distinguishes it from other books concerned with MATLAB: it is directed specifically to ECE concerns. Students will see, quite explicitly, how and why MATLAB is well suited to solve practical ECE problems. This book is intended primarily for the freshman or sophomore ECE major who has no programming experience, no background in EE or CE, and is required to learn MATLAB programming. It can be used for a course about MATLAB or an introduction to electrical and computer engineering, where learning MATLAB programming is strongly emphasized. A first course in calculus, usually taken concurrently, is essential. The distinguishing feature of this book is that about 15% of this MATLAB book develops ECE fundamentals gradually, from very basic principles. Because these fundamentals are interwoven throughout, MATLAB can be applied to solve relevant, practical problems. The plentiful, in-depth example problems to which MATLAB is applied were carefully chosen so that results obtained with MATLAB also provide insights about the fundamentals. With this "feedback approach" to learning MATLAB, ECE students also gain a head start in learning some core subjects in the EE and CE curricula. There are nearly 200 examples and over 80 programs that demonstrate how solutions of practical problems can be obtained with MATLAB. After using this book, the ECE student will be well prepared to apply MATLAB in all coursework that is commonly included in EE and CE curricula. Book readership Freshman and sophomore students in electrical and computer engineering curricula. Professional electrical and computer engineers needing to learn MATLAB or needing a refresher.
Quadratic equations were really giving me a hard time. Then I got Algebra Buster , and it helped me not only with quadratic but also with pretty much any equation or expression I could think of! Hillary Sill, VI. Algebra homework has always given me sleepless nights but once I started using Algebra Buster it has been fun. Its made my life easy and study enjoyable. Bud Pippin, UT I am a 9th grade student and always wondered how some students always got good marks in mathematics but could never imagine that Ill be one of them. Hats off to Algebra Buster ! Now I have a firm grasp over algebra and my approach to problem solving is more methodical. Linda Taylor, KY As a math teacher, Im always looking for new ways to help my students. Algebra Buster not only allows me to make proficient lesson plans, it also allows my students to check their answers when I am not available. S.H., Texas08-21 : chinese primary school mathematics textbook math formulas (division of polynomials with divisor) multiplication@division of algebraic expressions in a power, the number used as a factor +how to do fractions on texas instruments TI-84 plus calculator left and right limit calculator mcdougal littell algebra 2 note taking guide teacher edition algebra 2 saxon key Glence algebra 2:Integration Application Connections calculater that can do exponential form pearson education solving equations isample problems for 3rd grade algebra questions exercise for standard 4th how to add quadratic formula into TI-83 Plus simplifying algebraic equations glencoe division answers gcd+formula solve slope problems intermediate free algebra powerpoint radicals with outside number free adding positive and negative integers figurate number solver equation solver for multiple variable how to simplify a cubed two variable expression Substitution Calculator free sample college algebra multiplying and dividing signed numbers worksheets mcgraw hill mathematics grade 6 student workbook free online rational expression calculator logarithmic lesson game adding/subtracting integers lesson plan mathematical trivia/4th year answers for my math homework multiply and divide fraction problems with answers why can't you divide a partial fraction to get a demoninator and numerator the same power
0764103032 9780764103032 more than 1,000 words, and directs readers to the page where the word is defined. Where needed, the definition is accompanied by examples. The book also features helpful illustrative diagrams--or instance, a full page demonstrating the geometry of the circle, another page showing quadrilateral geometric shapes, and still others showing ways of charting statistics, measuring vectors, and more. Here is an imaginative new approach to mathematics, a great classroom supplement, a useful homework helper for middle school and high school students, and a reference book that belongs in every school library. «Show less... Show more» Rent Barron's Mathematics Study Dictionary today, or search our site for other Tapson
A software to calculate expression, roots, extremum, derivateve, integral, etc.Features: Math Calculator is an expression calculator. You can input an expression including variable x, for example, log(x), then input a valueof x; You can also input an expression such as log(20) directly.Math Calculator is an equation solver Math Calculator can be used to solve equations with one variable, for example, sin(x)=0. Math Calculator is a function analyzer Math Calculator has the abilities of finding maximum and minimum.Math Calculator is a derivative calculator and calculus calculator. You can use this program to calculate derivative and 2 level derivate of a given function.Math Calculator is an integral calculator. Math Calculator has the ability of calculating definite integral
Required algebra in a clear, fun and approachable manner: functions, algebraic properties and linear equations Adventure Part 2: Standard Deviants - Algebra Adventure Part 2 DVD dives into the advanced principles of Algebra. The Standard Deviants tour of the world of algebra continues with complete coverage of quadratic equations, quadratic roots and factors, and higher order polynomials. Suitable for all ages, Algebra Part 2 clearly presents these principles in a fun and approachable manner. A completely stand-alone video! Part 1 is not required Algebra Adventure 2 Pack: Lost in a sea of variables and properties? Do you need help solving for X? No need to hire an expensive tutor! From High School Algebra I through College Algebra, the Standard Deviants will guide you through algebraic problems and linear equations with a relaxed format and plenty of examples. The Standard Deviants - Algebra Adventure 2 Pack contains Algebra Adventure and Algebra Introduction 2 Pack: Required pre-algebra and algebra in a clear, fun and approachable manner: functions, algebraic properties and linear equationsSave money! This four DVD set includes Basic Math, Algebra 1, Physics 1 and Spanish 1. Suitable for students of all ages, this CD-ROM clearly presents the three, basic principles of algebra in a clear, fun and approachable manner. For many students the study of algebra is similar to learning a new language, it can be very confusing and daunting. Our cast of young actors define those difficult algebra terms and use on-screen graphics to present step-by-step examples. This program puts the FUN into functions and other difficult algebra topics and is a must see for any student who is starting algebra or needs a refresher. Join us as we deep dive into some of the more advanced concepts and principles of Algebra: Equalities, Inequalities, and Graphing these equations. We unlock the world of simplifying the complex and use real-life scenarios to make algebra relevant! Less then, greater than, monomial, polynomials, oh my! The more we learn about Algebra, the more complex the equations and vocabulary become. Have no fear; Light Speed is here to make these equations, terms and concepts digestible. Interested in finding out how high a baseball can fly? Or how fast a record player will drop from a window? The quadratic formula can be used to figure out projectile motion – meaning, how high and how far a moving object travels. This program will present the equation, how it is graphed and how it can be solved. You'll soon be a quadratic expert! The Algebra Bundle includes all four Light Speed Algebra programs. Using a cast of young actors and on-screen graphics, this programs defines those difficult and daunting algebra terms and provides step-by-step explanations of key concepts. This program puts the FUN into functions and other difficult Algebra topics.
Crossing The River With Dogs : Problem Solving For College Students - (rev edition ISBN13:978-1931914147 ISBN10: 1931914141 This edition has also been released as: ISBN13: 978-0470412244 ISBN10: 0470412240 Summary: Students who often complain when faced with challenging word problems will be engaged as they acquire essential problem solving skills that are applicable beyond the math classroom. The authors of Crossing the River with Dogs: Problem Solving for College Students: Use the popular approach of explaining strategies through dialogs from fictitious students. Present all the classic and numerous non-traditional problem solving strategies (from drawing diagrams to matrix l...show moreogic, and finite differences). Provide a text suitable for students in quantitative reasoning, developmental mathematics, mathematics education, and all courses in between. Challenge students with interesting, yet concise problem sets that include classic problems at the end of each chapter. With Crossing the River with Dogs, students will enjoy reading their text and will take with them skills they will use for a lifetime
Hi, I am a freshman in high school and I am having trouble with my homework. One of my problems is dealing with the binomial theorem for dummies; can anyone help me understand what it is all about? I need to complete this asap. Thanks for helping. Hi! I guess I can give you ideas on how to solve your problem. But for that I need more details. Can you give details about what exactly is the the binomial theorem for dummies assignment that you have to solve. I am quite good at solving these kind of things. Plus I have this great software Algebra Buster that I got from a friend which is soooo good at solving math homework. Give me the details and perhaps we can work something out... Hi, just a month ago, I was stuck in a similar scenario. I had even considered the option of leaving math and selecting some other subject. A friend of mine told me to give one last chance and sent me a copy of Algebra Buster. I was at ease with it within an hour. My ranks have really improved within the last one month. Thanks a lot for the detailed information. We will definitely try this out. Hope we get our assignments finished with the help of Algebra Buster. If we have any technical questions with respect to its usage, we would definitely come back to you again. I remember having difficulties with graphing parabolas, hypotenuse-leg similarity and geometry. Algebra Buster is a really great piece of algebra software. I have used it through several algebra classes - Pre Algebra, Intermediate algebra and Intermediate algebra. I would simply type in the problem from a workbook and by clicking on Solve, step by step solution would appear. The program is highly recommended
Math Programs & Resources NEW MATHematics Illuminated This course is geared toward students who require math credit but are not math majors as well as teachers and adult learners. Throughout the series, experts explain in fascinating detail the historical perspective of the mathematics topics that helps students gain a greater understanding of the world around them. Visit the in-depth Web site for more information including the free access and downloadable online textbook Either Javascript is turned off in your web browser or you have encountered a server error. We truly apologize for the inconvenience. Please submit your request for our email newsletter by email. Thank you for your interest.
Lin McMullin Part 1: Winplot for Calculus - an introduction to Winplot and a demonstration of what it can do (handout 1) Part 2: Problems for CAS solution - a discussion of how CAS can be used in high school illustrated by a series of problems from pre-calculus and calculus (handout 2, handout 3) Pete Horton - North Harris County College a.k.a. "The Man of Knowledge" Will the real L'Hopital's Rule please stand up? And other things that make you go hmm. For the most part L'Hopital's Rule isn't stated to its fullest extent in Calculus books. I'll show why it can be extended and when it does or doesn't apply, derive a more powerful Nth Derivative Test using only basic Calculus ideas, look at the arclength and surface area of revolution formulas in a thought provoking way, examine the continuity and differentiability of powers of the Popcorn function (microwave not required), and also look at the famous continuous, but nowhere differentiable Blancmange function. Materials Workshop III November 11, 2006 Dan Kennedy - Baylor School, Chattanooga, TN What I Have Learned About Assessment from the AP Program. Part 2 :Nominations for the Ten Toughest Points on AP Calculus Exams. Biography Materials
\input zb-basic \input zb-matheduc \iteman{ZMATH 2010d.00087} \itemau{Ammann, Claudia; Frauendiener, J\"org; Holton, Derek} \itemti{German undergraduate mathematics enrolment numbers: background and change.} \itemso{Int. J. Math. Educ. Sci. Technol. 41, No. 4, 435-449 (2010).} \itemab \itemrv{~} \itemcc{B40 A45} \itemut{recruitment; retention; enrolment; tertiary education} \itemli{doi:10.1080/00207390903564629} \end
Thomas and received an A in the course. Linear Algebra is the study of matrices and their properties. The applications for linear algebra are far reaching whether you want to continue studying advanced algebra or computer science.
Loci: Developers Guidelines for Loci Authors The primary mission of Loci is to publish high-quality expository articles and class-tested, web-based learning materials in mathematics and the history of mathematics, with special emphasis on elements that go beyond what is possible with ordinary print. Historical articles should normally have a connection to the teaching of mathematics. Expository articles of general interest to readers of Loci will appear as Featured Items. The four Areas of Loci described below offer material grouped by more specific interest. Loci: Resources provides an exemplary collection of free online teaching and learning materials, all classroom tested and peer reviewed. This Area of Loci provides instructors with a set of tools ready for implementation in an existing curriculum as well as a forum for discussion of the issues surrounding the materials and their uses. The collection will also provide a snapshot of trends and thoughts on issues relevant to the use of technology in mathematics teaching and learning. Loci: Convergence provides a wealth of resources to help teach mathematics using its history. This Area of Loci provides instructors with materials which can be used within a curriculum to show historical context for the discovery and development of mathematical concepts. Loci: Developers provides resources of particular interest to those who develop online mathematics software. This Area of Loci offers tools and tutorial articles for learning and using advanced Web technologies relevant to publishing mathematical materials, as well as reviews of common tools and new technologies. Loci: Departments provides announcements, commentaries, and other materials of a more transient nature than what is to be found in the other Areas of Loci. This material is not subjected to as rigorous a review process as articles in the other Areas, but may provide topics of active and current discussion for Loci readers. Loci intends to make full use of the web as a medium for the communication of mathematics. Those "elements that go beyond print" include: Hyperlinking within the document and to other documents and resources on the web "Nonlinear" document structures that allow multiple paths through an article. Note that the Content Management System supporting Loci allows the use of jsMATH to display mathematical expressions. The following articles provide more information for authors of web-based mathematical documents (not just Loci authors). The second article gives a brief tutorial of the core web languages HTML, CSS, and JavaScript, as well as document templates, sample style sheets, sample script files, and a table of mathematical symbols in both image format and HTML markup. The third article describes a stylesheet which authors familiar with TeX may find more comfortable than HTML. Once you have an article prepared for the Editors to review, submit it following the instructions in How to Submit an Article. Loci welcomes contributors, referees, and readers from all countries. Both mathematics and education are international concerns and endeavors. Neither the Mathematical Association of America nor the National Science Foundation limits Loci in any way to national interests.
Fathom 2 is even more user friendly than the original and enables and motivates students to gather, graph, analyse and animate data of all kinds. The full colour design makes it easier to identify patterns and understand concepts. Build simulations to explore ideas in mathematics, statistics, science and social science and relate study to real world examples. Over 300 data sets are included and students can easily import data from any source. Whenever data is changed, every representation or calculation that the data occurs in updates automatically. Graphs can still be made with drag and drop ease but now it is possible to place more than one attribute on an axis. If attributes have units, then these units are used everywhere including algebraic formulas. Fathom 2 understands more than 90 units and can convert from one system to another. Over 100 functions are built in and users can also create their own formulas. A text editor, complete with mathematical typesetting is also included. Ideal for whiteboard presentations or use on individual machines Improved help system with movies showing basic skills New capabilities for Data, Graphs, Summary, Tables, Formulas and the Formula Editor, Statistical Objects plus many other improvements. Import your own data from the Internet or from other programs Use sliders as variable parameters to fit functions to data SCORM compliant
Hello, I recently purchased a used Macintosh G4 which came with Mathematica. I am a college student, and one of the classes I'm taking this symester is Prepatory Mathematics. Next symester I'll be taking College Algebra. What I'm wondering is: is Mathematica a suitable program for these rather low-level courses, or is it much too advanced? I really want to absorb Algebra, but I'm simply not sure if this is the right tool for the stage I'm at. My professor recommended the website but unfortunately it appears to be Windows-only. Also, how does the licensing work? Will I have to contact the person I purchased the computer from, or will I have to re-register? I know there is a student discount available, but I don't know if I'd have to buy that or not. Sorry for the neophyte questions, hopefully someone can help. Thanks!
This is the course homepage that also serves as the syllabus for the course. Here you will find homework assignments, our weekly schedule, and updates on scheduling matters. The Mathematics Department also has a general information page on this course. Course description Math 431 is an introduction to probability theory, the part of mathematics that studies random phenomena. We model simple random experiments mathematically and learn techniques for studying these models. Topics covered include methods of counting (combinatorics), axioms of probability, random variables, the most important discrete and continuous probability distributions, expectations, moment generating functions, conditional probability and conditional expectations, multivariate distributions, Markov's and Chebyshev's inequalities, laws of large numbers, and the central limit theorem. Probability theory is ubiquitous in natural science, social science and engineering, so this course can be valuable in conjunction with many different majors. 431 is not a course in statistics. Statistics is a discipline mainly concerned with analyzing and representing data. Probability theory forms the mathematical foundation of statistics, but the two disciplines are separate. From a broad intellectual perspective, probability is one of the core areas of mathematics with its own distinct style of reasoning. Among the other core areas are analysis, algebra, geometry/topology, logic and computation. To go beyond 431 in probability you should take next 521 Analysis, and after that one or both of these: 632 Introduction to Stochastic Processes and 635 Introduction to Brownian Motion and Stochastic Calculus. Prerequisites To be technically prepared for Math 431 one needs to be comfortable with the language of sets and calculus, including multivariable calculus, and be ready for abstract reasoning. Probability theory can seem very hard in the beginning, even after success in past math courses. Textbook A First Course in Probability, Eighth Edition, by S. Ross. Note that the 8th edition is not the newest edition. But other editions of Ross's book cover the subject matter also. The only possible harm from using a different edition is that you may have to look up the homework problems from the 8th edition. Evaluation Course grades will be based on homework and quizzes, three midterm exams, and a comprehensive final exam. Midterm exams will be in the evenings. No calculators, cell phones, or other gadgets will be permitted in exams and quizzes, only pencil and paper. Lecture 1 final exam 12/19/2013, Thursday 12:25 PM - 2:25 PM. Lecture 3 final exam 12/18/2013, Wednesday 5:05 PM - 7:05 PM. Here are grade lines that can be guaranteed in advance. A percentage score in the indicated range guarantees at least the letter grade next to it. A [100,90), AB [90,87), B [87,76), BC [76,74), C [74,62), D [62,50), F [50,0]. Weekly schedule Below is the weekly schedule last time I taught this course from Ross's book. The same topics will be covered in Fall 2013, perhaps in slightly altered order. Instructions for homework Observe rules of academic integrity. Handing in plagiarized work, whether copied from a fellow student or off the web, is not acceptable. Plagiarism cases will lead to sanctions. Homework is collected at the beginning of the class period on the due date. No late papers will be accepted. You can bring the homework earlier to the instructor's office or mailbox. Organize your work neatly. Use proper English. Write in complete English or mathematical sentences. Answers should be simplified as much as possible. If the answer is a simple fraction or expression, a decimal answers from a calculator is not necessary. But for some exercises you need a calculator to get the final answer. Answers to some exercises are in the back of the book, so answers alone carry no credit. It's all in the reasoning you write down. Put problems in the correct order and staple your pages together. Do not use paper torn out of a binder. Be neat. There should not be text crossed out. Recopy your problems. Do not hand in your rough draft or first attempt. Papers that are messy, disorganized or unreadable cannot be graded. The Math Club provides interesting lectures and other math-related events. Everybody is welcome.
College Algebra-enhanced Edition - 6th edition Summary: Accessible to students and flexible for Accessible to students and flexible for instructors, COLLEGE ALGEBRA, SIXTH EDITION, uses the dynamic link between concepts and applications to bring mathematics to life. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphi...show moreng calculators. Additional program components that support student success include Eduspace tutorial practice, online homework, SMARTHINKING Live Online Tutoring, and Instructional DVDs. The authors' proven Aufmann Interactive Method allows students to try a skill as it is presented in example form. This interaction between the examples and Try Exercises serves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the Sixth Edition, Review Notes are featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new
Get everything you need for a successful and pain-free year of learning math! This kit includes Saxon's 3rd Edition Algebra 1 textbook and tests/worksheets book & answer key. as well as the DIVE Algebra 1 CD-ROM. A balanced, integrated mathematics program that has proven itself a leader in the math teaching field, Algebra 1 covers signed numbers, exponents, and roots; absolute value; equations and inequalities; scientific notations; unit conversions; polynomials; graphs; factoring; quadratic equations; direct and inverse variations; exponential growth; statistics; and probability. The DIVE software teaches each Saxon lesson concept step-by-step on a digital whiteboard, averaging about 10-15 minutes in length; because each lesson is stored separately, you can easily move about from lesson-to-lesson as well as maneuver within the lesson you're watching. DIVE teaches the same concepts as Saxon, but does not use the problems given in the text; it cannot be used as a solutions guide.
Get the most out of Sketchpad® with these add-on curriculum modules. Builds upon the strengths of dynamic mathematical representations to enrich the study of first-year algebra. Topics include ratios and exponents; algebraic expressions; so7 2-55 Get the most out of Sketchpad® with this add-on curriculum module. This collection of Sketchpad® activities is an excellent introduction to Sketchpad® for both students and teachers. Topics include operations and a.. Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the United States may be charged additional distributor, customs, and shipping charges.
What is the most difficult mathematics? What is the most difficult mathematics? You can't answer such a question. All of the branches you listed are major parts of mathematics which means that they can be as hard or as easy as you like. The subjects are therefore very interconnected meaning that the answer to your second question is: it depends on the actual curriculum for the corse. Here's a related question: what is the mathematics that depends on the most other mathematics? If you continue in physics, you'll use algebra quite a bit. The algebra is usually where you say "math happens" then report a result. As far as the hardest part of math, it depends on the person. I'm very good at spacial reasoning, so Calc 3 was a breaze for me. I have trouble with more abstract thought, so higher math is a blur to me. I suppose it comes down to if you think of math in terms of the actual physical world that motivates it, or as an abstract thing that stands alone. I'm trying to learn functional analysis on my own right now, and it's by far the most difficult subject I have studied. (For those who don't know, it's basically linear algebra with infinite-dimensional vector spaces, but the methods used are more like the ones from an advanced calculus course than the ones from a linear algebra course). Seems like every page takes at least 2 hours to understand (sometimes a lot more) and the book has about 240 pages.Some maths might, indeed, be easier to learn for a bright teenager than other maths. For example: Maths that is strongly assosiated with visualization is generally easier to get a hold on than very formal proof structures, for example. And, the capacity for abstract logical thought is still developing during your teens, until the age 18-20 or so. (And then, everything goes downhill again..) But, I think you are well underway in developing that capacity, just being 14 and having a good grasp of integration already. My son scores good marks in all subjects except maths. He is afraid of maths. He is not good of analyzing problems. Last night he showed me a problem and told mom i am scared of this bigg problem, such a big problem "In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (see Fig). A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?" Can anyone tell me how simple can we explain solution to this problem
Pre-Calculus; Gr. 9-12 Pre-calculus bridges Algebra II and Calculus, and is a great way to get acquainted with the main ideas of calculus including functions and rates of change. Analyze angles and geometric shapes to find absolute values. Discover new ways to record solutions with interval notation, and plug trig identities into your equations Joseph Gayle Fee: $144 Program No. 8440-4006
Mathematics (SparkNotes.com) - WebCT.com & iTurf Inc. Over 100 guides for mathematics ranging from pre-algebra topics to advanced work in calculus, written by students and recent graduates of Harvard University. The site also includes message boards for beginner, high school, and advanced math, calculus, ...more>> Math Everywhere, Inc. (MEI) Online Internet mathematics courses that are written in interactive notebooks using Mathematica. Take a whole course, or part of a course in calculus, pre-calculus, differential equations, or the geometry of n-space with matrices. This program offers ...more>> Math Homework Help Email contact for homework help in pre-algebra, algebra I and II, college algebra, geometry, trigonometry, pre-calculus, and calculus. Site also contains a math history timeline; math dictionary; some basic differentiation and integration rules; trigonometric ...more>> Math Index - George Mason University A glossary of math terms with illustrated examples of problems and tips for understanding concepts, from addition of positive and negative numbers to the definition of the derivative. Part of the DAU (Defense Acquisition University) Math Refresher course. ...more>> MathMagic on the Web - Alan A. Hodson; The Math Forum MathMagic was a K-12 telecommunications project developed in El Paso, Texas. The intent of the project was to provide motivation for students to use computer technology while increasing problem-solving strategies and communications skills. MathMagic posted ...more>> Math Mistakes - Michael Pershan, editor Compilation, analysis, and discussion of the mathematical errors that students make. Pershan, who teaches high school math in New York City, has posted a new error on this blog every day since June, 2012 Right Now An interactive mathematics website which features real-time multimedia solutions and companion lessons for each question in a large database. Create your own individualized problem sets and practice exams from among topics in the areas of algebra, geometry, ...more>> Maths Online - Chris Vick Online maths tuition, via a private chat-room. Tutoring requires no special computer or browser components, with fees payable after each lesson, or in advance by block. Free calculator available on the site, as well as a currency converter. ...more>> Math Tools PreCalculus - Math Forum A community library of software tools for pre-calculus students and their teachers. PreCalculus is one section in the Math Forum's Math Tools digital library of software for computers, calculators, PDAs, and other handheld devices, with related lesson ...more>> Math Trivia - FunTrivia.com Online multiple-choice (MC) quizzes covering topics in algebra, geometry, statistics and probability, calculus, measurements, and more. Register to record your high scores on the site; Find out how many others have played a given game, and how they rate ...more>> The Math Tutor Center - Addison Wesley Longman, Inc. A service free for students who purchase a new Addison Wesley Longman math textbook included on the list of eligible textbooks and are enrolled in developmental, precalculus, calculus and introductory statistics courses. Qualified math instructors tutor ...more>> Math Warehouse - Vernon Morris Interactive programs that allow users to explore math concepts; a set of freely available worksheets for teachers; math store with books, puzzles, and games; and a newsletter. Covers a range of topics including linear equations, systems of equations,Math Worksheets Free worksheets for practicing arithmetic, geometry, pre-algebra, and algebra, accompanied by written explanations and instructional videos. Each worksheet comes with an answer sheet; select from a range of difficulty levels. ...more>> Math Worksheets Center Thousands of teacher-made K-12 math worksheets, lessons, homework assignments, quizzes, and tip sheets. Browse by grade level or student age; each math topic links to an index of the remedial math worksheets that point up the skills needed to get to that ...more>> MathWorld Interactive - Carolynn S. Mortensen Open-ended word problems and some answers from this now-defunct project. MathWorld began as MathMagic FidoNet in 1991, and was dedicated to helping educators and parents motivate their students to solve open-ended word problems, communicate mathematically, ...more>>
ID #1105-08 1. priority mail shipping with tracking. 2. out-of-print book. average used condition. may have marks and wear. it shows step-by-step solutions for every problem in the student textbook, even and odd. paperback. 408 pages. please check sample pages before ordering. the sale is final. 3. the book is used to the following student textbooks: isbn 0675131189 (1992) isbn 0028242270 (1995) ================================= click to order the companion QUIZZES AND CHAPTER TESTS WITH ANSWERS
Search Course Communities: Course Communities Lesson 35: Polynomial Functions Course Topic(s): Developmental Math \| Functions Beginning with the definition of a polynomial, polynomial multiplication and degree of polynomial products are introduced. Special products and factoring cubics are presented before modeling with polynomials is discussed.
Math BSI: This full-year course serves to reinforce the foundational knowledge from other mathematics courses. Students study basic skill clusters (1. Number and Numerical Operations, 2. Geometry and Measurement, 3. Patterns and Algebra, 4. Data Analysis, Probability, and Discrete Mathematics) of material which will help them succeed on standardized tests. Students will utilize workbooks, computer lab and online assignments, and various software. Pre-Algebra: This course is designed for those students who are in preparation for Algebra 1. Topics include graphing, writing algebraic expressions, solving equations and inequalities, operations with signed numbers, and applications. Algebra 1CP: The course includes the study of real number properties, solving equations and inequalities, finding solutions to word problems, solving systems of equations, and solving quadratic equations. Real world application and problem-solving techniques are stressed. Algebra 2H: This course focuses on and enhances subjects discussed in Algebra in grade 8. Topics include the study of linear, quadratic, polynomial, exponential and logarithmic functions, each integrating technology and real world applications. Geometry CP: This course includes the study of plane geometry. It is a structured course building upon concepts which develop logical thinking through deductive as well as inductive reasoning. Topics include the geometry of points, lines, and planes, properties of congruence and similarity, circles and spheres, coordinate geometry, area, and volume. Geometry H: The advanced level of geometry encompasses in greater depth all of the topics in Geometry. The course includes challenging problem-solving. Algebra 2CP: This course expands the study of algebra to include complex numbers, quadratics, conic sections and logarithms. These concepts are implemented through the use of cooperative learning with an emphasis on technology and real world applications. Precalculus CP: This course includes a semester of elementary functions, composite functions, logarithmic functions, and exponentials as well as a semester of trigonometry. Emphasis in the trigonometry portion of the course includes an analysis and graphic interpretation of the six trigonometric functions. Throughout the entire course, relevance to practical applications in the real world is stressed. Precalculus H: This rigorous course approaches the study of polynomial, exponential, logarithmic, rational and trigonometric functions: numerically, graphically, algebraically and analytically. Series, sequences, conic sections and their applications are developed and applied. Limits of continuous functions are defined and applied as a foundation for the calculus course. Calculus H: This honors level calculus course consists of a full year of development and application of derivatives and integrals. Several projects are introduced to enhance the understanding of the material. The course is designed to help students master their college calculus classes. AP Calculus (AB): In this course topics include elementary functions and limits with an emphasis on differential and integral calculus and their applications. Students must take the Advanced Placement CalculusAB examination for college credit. AP Calculus (BC): (7 periods per week includes 2 lab periods). This course includes all of the topics taught in AP Calculus (AB), but is more extensive and includes an emphasis on theory. Additional topics are complex integration, infinite series, vectors, and polar coordinates. Students must take the Advanced Placement Calculus BC examination for college credit. AP Statistics: This course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The four broad themes include: explaining data observing patterns and departures from patterns, planning a study deciding what and how to measure, anticipating patterns producing models using probability and simulating, and statistical inference guiding selection of appropriate models. Students must take the Advanced Placement AP examination for college credit. Statistics H: This course will cover all the topics of AP Statistics without the rigor and depth required in AP Statistics. Discrete Mathematics: Students in this course will apply the concepts and methods of discrete mathematics to model and explore a variety of practical situations. The course has five major themes, including systematic counting, using discrete mathematical models, applying literative patterns and processes, organizing information, and finding the best solutions using algorithms. Discrete topics include: graph theory, matrix models, planning and scheduling, map coloring, social decision making, and election theory. Students will also study descriptive and inferential statistics, which includes representing data visually, calculating measures of central tendency, and computing standard deviation and z-scores. During probability, laboratory experiments are used to explore how often particular events are expected to occur. Overall, the course incorporates individual and small group problem solving. Visual Computer Programming 1: In this course the student is instructed in principles of computer science. Using our computer labs in the high school, the student studies the structure, capabilities and limitations of computers. The student learns to program the computer using a high-level computer language and to use computers to assist problem-solving. Computer Programming H: The major topics for this course include programming methodology, features of programming languages, data types, and algorithms. AP Computer ScienceAB: This course continues the study of programming and includes additional features of programming languages, data structures, algorithms, and applications. Students must take the Advanced Placement Computer ScienceAB examination for college credit. Robotics: This course is designed to enhance computer programming skills through the study of robotics. Topics include mechanics, electronics, software, and sensory systems associated with the robot. Students also have the opportunity to do research, analyze, and implement independent projects throughout the school year. Presentation skills are developed throughout the course. Multivariable Calculus: This course is the final course in the accelerated course sequence. Topics included in this course are: vectors and the Geometry of Space, Vector-Valued Functions, Functions of Several Variables, Multiple Integration, and Vector Analysis. Vectors have many applications in geometry, physics, engineering, and economics. The student builds on many of the ideas of calculus of a single variable to calculus of several variables
for Concerning the last questionwhydiscretemath, "Why isn't discretemathematics offered to high school students without calculus :notbackground?" Not only is that possible, but it wasdonehadbeenthenorm in the past aspartofwithin the "New Math" movementcurriculum, when everyone had to learn about sets and functions inhighschool. This ended in a PR disaster andahugebacklashagainstmathematics, because generations of students were lost and got turned off by mathematics for life(; some of them later became politicians who decide on our funding!funding.Consequently,itwasabandoned.(Apparently,calculusinHSwasintroducedasapartofthesamepackageandsurvived.) I'd be interested to know if there are any high school -– college partnerships that offer discrete mathematics to H.S. students with strong analytical skills, and how do they handle the pre-requisitesprerequisites question. for the last question why discrete math isn't offered to high school students without calculus: not only is that possible, but it was done in the past as part of the "New Math" movement, when everyone had to learn about sets and functions. This ended in a PR disaster, because generations of students were lost and got turned off by mathematics for life (some of them became politicians who decide on our funding!) I'd be interested to know if there are any high school - college partnerships that offer discrete mathematics to H.S. students with strong analytical skills, and how do they handle the pre-requisites question.
Basic assumptions regarding mathematics education: ♦ all students will have access to calculators and computers; ♦ classroom activities will include student centered instructional strategies; ♦ all courses will have increased emphasis on estimation and number sense; ♦ articulation with the community college is critical for development of college readiness; ♦ benchmarks for Language Arts that include correct use of punctuation, capitalization, grammar and sentence structure are incorporated in this course to ensure success on college level placement tests; ♦ evaluation will include alternative methods of assessment; and ♦ all strands addressed in Next Generation Sunshine State Standards in Mathematics are developed across the PreK-12 curriculum. A. Major Concepts/Content The purpose of this course is to strengthen the skill level of high school seniors who have completed Algebra I, II, and Geometry and who wish to pursue credit generating mathematics courses at the college level. The content should include, but not be limited to, the following: Functions and Relations Polynomials Rational Expressions and Equations Radical Expressions and Equations Quadratic equations Logarithmic and Exponential Functions Matrices Simple and Compound Interest Descriptive Statistics Vocabulary Edit Writing for Correct Use of Punctuation, Capitalization, Grammar and Sentence Structure Strategies for College Readiness Materials Needed: Supplies: -3 ring binder -Pencils -Scientific or Graphing Calculator Grading/Evaluation: Grade Category Weights: Tests: 50% You will have multiple opportunities to prove mastery of the material. Traditional tests will be graded on the number of correct answers. You will have the opportunity to take tests up to three times. Retakes will have to be on your own time and you must have your homework assignment complete and accurate before you retake the test. Homework: 10% Should be done on separate paper and turned in on due date. It will not be accepted late. Once you are considered "college ready" as determined by the ACT, SAT, or PERT, you will get an automatic 100% for your homework grade for the rest of the year. Class work/Quiz: 40% This category includes participation, class work and quizzes. Participation is graded based on being at school, being on time, being prepared and being productive in class. Your class work grade will be based on what you do in class each day. You will need a composition book for notes and a different composition book for class work. I can and will ask you at various times without notice to see your two composition books. This part of your grade is determined by what you can show me you're doing in class on a daily basis.
Calculus Courses General Calculus Tracks Calculus Refresher If you haven't already, go to the About Page for details on how this site is set up. Reading this will help you save time by knowing how to navigate around and quickly find what you need. Next, read the page on How To Study Calculus. Many people don't realize that studying math requires different techniques and skills than studying almost any other material. There are some great ideas on that page to help maximize your learning with the minimum of time and effort. You need a really good textbook. I recommend Larson Calculus ETF. You can get a copy from the Bookstore. You don't need the latest edition (unless you need it for a class). You can usually get an older edition (3rd or 4th) very cheap, for about $10. Okay, so now that you know how to study, how this site is set up and your textbook, you are ready to start learning. If your textbook has an algebra review section, make sure you go through that and that you understand most of the topics. Work a few practice problems in each section and then review the material as you feel like you need to. Strong algebra skills are very important in calculus. Calculus is not difficult. The algebra can be difficult if you are not ready. As you work through each chapter in the textbook, go to the course pages on each topic (links on the left under Courses). The Larson textbook mentioned above is great and this site will give you more information. Work practice problems from the textbook and on this site until the concepts start to come back easily. The videos on this site will help solidify concepts in your head. Self-Learning If you are trying to learn calculus on your own or you are struggling with your class and need major help, this is the site for you. You need to follow the same steps as someone trying to refresh their calculus knowledge. However, you need to work lots more practice problems. Solving lots problems on your own will allow you to become familiar with the material and learn when you can apply a technique or concept and how you use your newly learned calculus. Another consideration is your textbook. If your textbook is not helping you, it is okay (and good) to get another one that WILL help you. I recommend Larson Calculus ETF. You can find a copy in the Bookstore. If you are not required to get a specific edition for your class, you can get an earlier edition for as low as $10. This book is well written with good examples and practice problems. Additionally, solutions (not just answers but worked out solutions) to the odd problems are found online. Home Schooling As a home school student, you are probably far ahead traditional school students. You are very fortunate and you have a great chance to succeed in calculus and life in general. You are actually a self-learner as well, so the discussion above, in the Self-Learning section applies to you. However, you need to do a couple of things differently. First, you need to get a copy of a good textbook. I highly recommend Larson Calculus ETF found in the Bookstore. You can get an older edition and the cost is very low. Secondly, you need to try to work as much on your own as possible and learn to teach yourself. Once you get into college, you will find yourself in a class with a teacher that is difficult to understand, either because they think differently than you or because they are a bad teacher (sorry). So don't rely on your parents (or your home school teacher) to help you. Now is the time to start learning independently. Single Variable Calculus Courses Multi-Variable Calculus Courses Courses in multiple variable calculus are listed below. The course details are on separate pages depending on subject. Click the link below for the course you wish to study. Note: No courses are currently available. The entire multi-variable calculus section is under construction.
Functional Skills in Mathematics Rob Apperley and Gill Colley Focus on key skills All current GCSE specifications now require a proportion of questions to have embedded 'functional elements', testing everyday mathematics skills. At foundation tier this applies to up to 40% of questions, and it remains a key concern even in higher tier papers. Functional Skills in Mathematics is specifically designed to develop the skills that all students will need, as applied to real life and workplace situations. It contains materials to test and then reinforce the following mathematical concepts: numbers calculations ratio and proportion fractions, decimals and percentages equations and formulae discrete and continuous data statistical methods probabilities area, perimeter and volume of common shapes 2D representations of 3D objects metric and imperial measures. Once they have taken their initial test, students then work on the areas where they need most reinforcement, using step-by-step worked examples and practice questions. Full teacher's guidance and useful Web links are also included. Essential grounding for later life Mathematics departments need to make sure that their students have a firm grounding in functional skills, both to comply with the requirements of the new GCSE and other examination syllabuses, and to give students the basic capabilities they will need in later life. Functional Skills in Mathematics gives you a bank of copiable resources designed for the purpose, which can be used to support a programme of study or as reinforcement or exam preparation for particular students. Convenient format Functional Skills in Mathematics is supplied on a CD-ROM and comes with a full site licence, meaning that it can be placed on a network for the whole department to use. Students needing reinforcement can access the materials independently, and teachers can find and use material whenever they need it.
The book is the first to give a comprehensive overview of the techniques and tools currently being used in the study of combinatorial problems in Coxeter groups. It is self-contained, and accessible even to advanced undergraduate students of mathematics. The primary purpose of the book is to highlight approximations to the difficult isomorphism problem... more... The book introduces readers in the often-overlooked math-related fields to the ideas of writing-to-learn (WTL) and writing in the disciplines (WID). It offers a guide to the pedagogy of writing in the mathematical sciences, and gives theoretically grounded means by which writing can be used to help undergraduate students to understand mathematical... more...
TLE Online Companion is a 32 page USER'S GUIDE with online PIN-code access to THE LEARNING EQUATION lessons, bundled with Tussy/Gustafson's INTERMEDIATE ALGEBRA, SECOND EDITION. Delivered entirely over the Internet, students can access 15 lessons per course, hand-picked by Alan Tussy to enhance the presentation of specific concepts in the course. The TLE ONLINE COMPANION is adapted from the full version of THE LEARNING EQUATION line of developmental mathematics courseware products. Designed for learner-focused, computer classroom, lab-based, and distance learning courses, the pedagogical model employs a "Guided Inquiry" approach whereby students construct their own understanding of concepts. Instead of passively being fed information, students are actively involved in tasks requiring them to discover or apply mathematical concepts. Each lesson has seven interactive components: Introduction, Tutorial, Examples, Summary, Practice and Problems, Extra Practice, and Self Check. The interactive learning content is the perfect compliment to the textbooks, designed to engage and enrich the student's learning experience by addressing multiple learning styles. Using the power of the most comprehensive and powerful course management system available, student progress is tracked from whatever location they choose to learn. The auto-enrollment feature via PIN codes, customizable grade book, world-class test generator for printed and on line assessments, and outstanding communication tools makes managing the learning experience fast and easy. Popular Searches The book Student Guide for Acerra's The Learning Equation Online Intermediate Algebra Lessons by Acerra (author) is published or distributed by Brooks Cole [053440717X, 9780534407179]. This particular edition was published on or around 2003-3-24 date. Student Guide for Acerra's The Learning Equation Online Intermediate Algebra Lessons
Beginning Algebra - 9th edition Summary: Get the grade you want in algebra with Gustafson and Frisk's BEGINNING ALGEBRA! Written with you in mind, the authors provide clear, no-nonsense explanations that will help you learn difficult concepts with ease. Prepare for exams with numerous resources located online and throughout the text such as online tutoring, Chapter Summaries, Self-Checks, Getting Ready exercises, and Vocabulary and Concept problems. Use this text, and you'll learn solid mathematical skills ...show morethat will help you both in future mathematical courses and in real life!62.33 +$3.99 s/h Acceptable BookSleuth Danville, CA Fast Shipping ! Used books may not include access codes, CDs or other supplements. $79.69
MathPro Press BOOKSTORE Olympiad Problem Books Many countries hold an annual mathematical olympiad competition for high school students. These contests are typically the culmination of a series of preliminary examinations. Contests usually consist of about 6 essay questions, requiring the students to write proofs of challenging problems. Although these problems can be quite difficult, they require no advanced mathematics, only a thorough knowledge of high school math topics and the ability to handle non-routine problems. Contestants are typically given an hour or more to solve each problem. Winners of the national olympiad often then represent the country at the prestigious International Mathematical Olympiad (IMO).
Integrated Arithmetic and Basic Algebra 9780321442550 ISBN: 0321442555 Pub Date: 2007 Publisher: Addison-Wesley Summary: A combination of a basic mathematics or prealgebra text and an introductory algebra text, this work provides an integrated presentation of the material for these courses in a way that is beneficial to students
What couldhelpmewouldbegoodtoknowWhichthingsWhat could help me before starting my undergraduate studies to become a good mathematician? Which things could help meI'm starting my undergraduate studies in september. I was studying computer science but I'm switching majors. Now I'm going to study mathematics. I want to graduate as soon as I can, while learning all I can. I feel like I might fail, so I'm gathering information on how to not fail. You can help me by answering some questions: What would you have liked to know before starting studying mathematics about studying mathematics? What undergraduate courses are generally considered the most difficult, or what were the most difficult for you? Now that you have graduated, what do you think you should have done to make them less difficult? If I wanted to start studying mathematics right now, assuming I know basic calculus (differentiation, integration, series), where should I start? Do you have any books that you value the most? Any that you think are the best in what they teach? Something like the best analysis book for undergraduates you've read.
Video Summary: This learning video presents an introduction to graph theory through two fun, puzzle-like problems: "The Seven Bridges of Königsberg" and "The Chinese Postman Problem". Any high school student in a college-preparatory math class should be able to participate in this lesson. Materials needed include: pen and paper for the students; if possible, printed-out copies of the graphs and image that are used in the module; and a blackboard or equivalent. During this video lesson, students will learn graph theory by finding a route through a city/town/village without crossing the same path twice. They will also learn to determine the length of the shortest route that covers all the roads in a city/town/village. To achieve these two learning objectives, they will use nodes and arcs to create a graph and represent a real problem. This video lesson cannot be completed in one usual class period of approximately 55 minutes. It is suggested that the lesson be presented over two class sessions
Course Home Description Based on the book, "Fifty Challenging Problems in Probability with Solutions" by Frederick Mosteller. It is intended to solve one problem each weekly and submit assignments by the end of the week. The assignments can be self-evaluated using the solutions provided in the book. Those who don't have the book can use google.com/books for the problems. This will be a great refresher for people who have completed a course in Probability or those who like solving problems in general, or both! (If you see the initial problems they hardly appear to present a problem, betraying the title of the book, but nevertheless we will solve all problems 01 through 56 for completeness.) Prerequisites and Difficulty A Course in Probability Materials and Technical Requirements None. Questions will be posted on the course webpage. How Curious Reef Works The purpose of the class is to learn collaboratively with others. The course creator has organized the course information for everyone.
Calculus hasnt changed, but your students have. Many of todays students have seen calculus before at the high school level. However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the read more... Discrete Mathematics provides an introduction to some of the fundamental concepts in modern mathematics. Abundant examples help explain the principles and practices of Discrete Mathematics. The book intends to cover material required by readers for whom mathematics is just a tool, as well as read more... The seventh edition of this classic text has retained the features that make it popular, while updating its treatment and inclusion of Computer Algebra Systems and Programming Languages. The exercise sets include additional challenging problems and projects which show practical applications of the read more... Once considered an unimportant branch of topology, graph theory has come into its own through many important contributions to a wide range of fields and is now one of the fastest-growing areas in discrete mathematics and computer science. This new text introduces basic concepts, definitions, read more... This is a complete revision of a classic, seminal, and authoritative text that has been the model for most books on the topic written since 1970. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model read more...
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Algebra can be applied to almost every situation you encounter in life. Remember sitting in algebra class, trying to comprehend the concept of the all-mysterious "X"? This idea of finding an unknown may have seemed meaningless and maybe even cruel at some times, but these mathematical foundations are almost critical to everyday life. For instance, let's take the basic example of someone trying to figure out how much gas they can afford when filling up their car. Say Peter only has $20.00 for gas and gas costs $3.50 per gallon, how many gallons would Peter be able to afford? Most likely without knowing, in this situation, Peter is trying to solve for an unknown variable. Peter remembers his seventh grade algebra teacher telling him to divide the total amount of money by the cost per gallon. These basic principles would tell him that he could afford approximately 5.7 gallons. Or let's say Marie wants to take her daughter to Disney World, but she wants to know how much spending money she'll have after purchasing airfare and lodging. By subtracting all the fixed values from her total available budget, Marie can have a general idea of how much money she will have left over. Most of the time, these algebraic equations aren't dressed up in math books or put in your kids' summer math workbook, they occur in the most relevant of life situations. Beside for basic everyday life situations, algebra is essential for nearly all careers. Want to be a chef? A chef has to convert, add, and subtract measurements constantly. Or how about a painter? Well, how big do you want the area of your canvas to be? Hmm, or maybe a professional athlete? You'll most likely need to understand how your stats are calculated in order to better your game. And besides, you'll need to know how to add up all those huge paychecks somehow. As you can see, there's really no career that does not involve the basics of math. From the time algebra was being researched by the Greeks to current day research, the concept of algebra has grown to new depths. What started off as figuring out how to solve linear equations has transformed into current day physicists trying to delve deeper into the concept of vectors. The topic of algebra has grown from more simplistic to abstract. In the work force today, there is great range of how algebra is used. For example, anyone who enters data into a system needs to use algebraic expressions to input data into spreadsheets on the computer. In a more advanced scenario, computer scientists are configuring algorithms to help perform programs. And in an even more advanced situation, NASA workers are using algebra to understand a shuttle's flight trajectory. For instance, as shown in recent news, the Curiosity rover, that just landed on the planet Mars, required a tremendous amount of algebra. From the computers, transportation system, and communication system located on the rover, the amount of algorithms and programming is tremendous. The flight trajectory of the rover had to be tracked intensely for the eight months it was traveling to Mars. There is no doubt that without the basic understanding of algebra, the Mars rover could not have been built, let alone function. With all the different outlets available for algebra, the understanding of algebra is critical to the success of one's future. Even the most right-brain oriented jobs require the use of algebra. So the next time your child walks through the door after school exclaiming, "Why do I even need this stuff?!", remind them how the most simple of math equations can show up anywhere. Because who knows, they might need it to figure out how much gas they can afford, or maybe even program the next rover to Mars.
Algebra 1 - Student Activities Teacher Edition (old) The Algebra I Activities Manual offers 10 additional activities per chapter. It is not a workbook—the teacher chooses which activities to use. Activity Pages include math history, Bible integration, drill, enrichment, and review work. This Teacher Edition includes the student pages with overlaid answers.
Upon completion of this course you will effectively learn the most important factors to be considered when answering questions in a maths exam. You will be aware of the most common mistakes in maths exams. You will gain a good knowledge of first and second order differential equations and second derivatives. You will learn about kinematics including acceleration, distance and velocity. You will understand Newton's laws of motion, Newton's laws of cooling, and Euler's method for solution of differential equations. This course will teach you the resolution of forces and how to calculate vectors.
--- calculations. The program comes on a 5.25 inch disk, with instructions on disk, on cassette, and in large type, and a summary of functions and commands in braille. COMPATIBILITY: Apple. SYSTEM REQUIREMENTS: Apple II with at least 128K or RAM. For complete speech accessibility, it requires an Echo or Slotbuster synthesizer
Sample Worksheet: Algebraic Shortcuts for the SAT, GRE, GMAT Most students taking the SAT, GRE, or GMAT know their algebra fairly well, but many find they can't complete all the problems in the allowed time. Why? It's NOT because those students are just naturally slow: it's because they're doing more work than they need to! It's not their speed but their very approach --- the very way they conceive of the process of problem-solving --- that's flawed. To ace the math sections of standardized tests, you have to learn how to attack problems in new ways so that you get the right answers by doing as little work as possible! (Part of the reason so many students don't already know how to do this is that it's not taught well throughout middle and high school math classes. Learning how to think quickly and deeply often requires UNLEARNING habits your math teachers instilled in you in school!) To see if you're up to par, try the following problems, which test your ability to make deep algebraic connections that will save you time. If your algebraic skills are what they really should be, you should be able to do all the problems in TWENTY SECONDS OR LESS! If you can't, send me an email and start working with me today! EXERCISE SET: ALGEBRAIC SHORTCUTS Suppose 2x+7=19. Find the value of each of the following expressions WITHOUT solving for x
Mr. X takes the mystery out of math... Hello, I'm Steve Roberts, Mr. X, Mentor of Mathematics. I created this website to help both students and teachers. Students need to understand the principles of mathematics and teachers need every resource they can get to convey the essence of those principles. I emphasize practice. My goal is to help everyone to use the language of numbers more effectively. There are three types of presentations: Glossary Terms, Math Lessons and Solved Math Problems. I have made six curricula available: Arithmetic, Basic Algebra, Geometry, Advanced Algebra, Trigonometry and Calculus, all with one consistent voice at the affordable price of $15/month. Register now for a no-risk 30-day trial.
NONRESIDENT TRAINING COURSE August 1986 Mathematics, Introduction to Statistics, Number Systems and Boolean Algebra NAVEDTRA 14142 DISTRIBUTION STATEMENT A: Approved for public release; distribution is unlimited. Although the words "he," "him," and "his" are used sparingly in this course to enhance communication, they are not intended to be gender driven or to affront or discriminate against anyone. DISTRIBUTION STATEMENT A: Approved for public release; distribution is unlimited. COMMANDING OFFICER NETPDTC 6490 SAUFLEY FIELD ROAD PENSACOLA FL 32509-5237 7 Aug 2002 ERRATA #1 Specific Instructions and Errata for Nonresident Training Course MATHEMATICS, INTRODUCTION TO STATISTICS, NUMBER SYSTEMS AND BOOLEAN ALGEBRA NAVEDTRA 14142 1. No attempt has been made to issue corrections for errors in typing, punctuation, etc., which do not affect your ability to answer problems/questions. 2. In the assignment portion of the course, a question with no choices is a True/False question. For True/False questions, answer 1 for True and 2 for False. PREFACE By enrolling in this self-study course, you have demonstrated a desire to improve yourself and the Navy. Remember, however, this self-study course is only one part of the total Navy training program. Practical experience, schools, selected reading, and your desire to succeed are also necessary to successfully round out a fully meaningful training program. COURSE OVERVIEW: In completing this nonresident training course, you demonstrate an understanding of the following subjects: numbering systems used in digital computers and computer programming; Boolean algebra: binomial theorem; statistics, statistical inference, matrices, and determinants; and calculus. THE COURSE: This self-study course is organized into subject matter areas, each containing learning objectives to help you determine what you should learn along with text and illustrations to help you understand the information. The subject matter reflects day-to-day requirements and experiences of personnel in the rating or skill area. It also reflects guidance provided by Enlisted Community Managers (ECMs) and other senior personnel, technical references, instructions, etc., and either the occupational or naval standards, which are listed in the Manual of Navy Enlisted Manpower Personnel Classifications and Occupational Standards, NAVPERS 18068. THE QUESTIONS: The questions that appear in this course are designed to help you understand the material in the text. VALUE: In completing this course, you will improve your military and professional knowledge. It can also help you study for the Navy-wide advancement in rate examination. If you are studying and discover a reference in the text to another publication for further information, look it up. 1986 Edition Published by NAVAL EDUCATION AND TRAINING PROFESSIONAL DEVELOPMENT AND TECHNOLOGY CENTER NAVSUP Logistics Tracking Number 0504-LP-026-7970 i Sailor's Creed "I am a United States Sailor. I will support and defend the Constitution of the United States of America and I will obey the orders of those appointed over me. I represent the fighting spirit of the Navy and those who have gone before me to defend freedom and democracy around the world. I proudly serve my country's Navy combat team with honor, courage and commitment. I am committed to excellence and the fair treatment of all." ii INSTRUCTIONS FOR TAKING THE COURSE ASSIGNMENTS assignments. To submit your assignment answers via the Internet, go to: The text pages that you are to study are listed at the beginning of each assignment. Study these pages carefully before attempting to answer the questions. Pay close attention to tables and Grading by Mail: When you submit answer illustrations and read the learning objectives. sheets by mail, send all of your assignments at The learning objectives state what you should be one time. Do NOT submit individual answer able to do after studying the material. Answering sheets for grading. Mail all of your assignments the questions correctly helps you accomplish the in an envelope, which you either provide objectives. yourself or obtain from your nearest Educational Services Officer (ESO). Submit answer sheets SELECTING YOUR ANSWERS to: Read each question carefully, then select the COMMANDING OFFICER BEST answer. You may refer freely to the text. NETPDTC N331 The answers must be the result of your own 6490 SAUFLEY FIELD ROAD work and decisions. You are prohibited from PENSACOLA FL 32559-5000 referring to or copying the answers of others and from giving answers to anyone else taking the Answer Sheets: All courses include one course. "scannable" answer sheet for each assignment. These answer sheets are preprinted with your SUBMITTING YOUR ASSIGNMENTS SSN, name, assignment number, and course number. Explanations for completing the answer To have your assignments graded, you must be sheets are on the answer sheet. enrolled in the course with the Nonresident Training Course Administration Branch at the Do not use answer sheet reproductions: Use Naval Education and Training Professional only the original answer sheets that we Development and Technology Center provide—reproductions will not work with our (NETPDTC). Following enrollment, there are scanning equipment and cannot be processed. two ways of having your assignments graded: (1) use the Internet to submit your assignments Follow the instructions for marking your as you complete them, or (2) send all the answers on the answer sheet. Be sure that blocks assignments at one time by mail to NETPDTC. 1, 2, and 3 are filled in correctly. This information is necessary for your course to be Grading on the Internet: Advantages to properly processed and for you to receive credit Internet grading are: for your work. • you may submit your answers as soon as COMPLETION TIME you complete an assignment, and • you get your results faster; usually by the Courses must be completed within 12 months next working day (approximately 24 hours). from the date of enrollment. This includes time required to resubmit failed assignments. In addition to receiving grade results for each assignment, you will receive course completion confirmation once you have completed all the iv PASS/FAIL ASSIGNMENT PROCEDURES For subject matter questions: If your overall course score is 3.2 or higher, you E-mail: n3222.products@cnet.navy.mil will pass the course and will not be required to Phone: Comm: (850) 452-1001, Ext. 1520 resubmit assignments. 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To In the discussion of the complementary law, the simplify the expression logic state of the output is considered. This law indicates that when any letter or expression is AB ANDed with its complement, the output is 0. When any letter or expression is ORed with its we write complement, the output is 1; that is, AB = AB AA = 0 and the expression and A+A=1 AB + C = AB + C The logic state of Notice that we removed only two bars from above AB. (A + B) (A + B) = 0 To simplify the expression and the logic state of (A + B + C) + C + (A + B) AB + AB = 1 we use the laws which we have discussed to this point and write To simplify the expression A+B=A+B ABC + A(CB) and we write C=C ABC + A(CB) therefore ABC + ABC (A + B + C) + C + (A + B) and notice that equals ABC (A + B + C) + C + (A + B) is the complement of then by removing the parentheses and applying ABC the commutative law write therefore A+A+B+B+C+C ABC + A(CB) = 1 then by the idempotent law this equals PROBLEMS: Simplify the following expres- A+B+C sion. PROBLEMS: Simplify the following expres- 1. AAA sions. 2. (A + A) AA 1. (ABC + D) E + F 3. A(BC) D + (AB)(CD) 2. (ABC + D) (D + B AC) ANSWERS: ANSWERS: 1. 0 1. (ABC + D) E + F 2. 0 2. ABC + D 3. 1 144 Assignment Questions Information: The text pages that you are to study are provided at the beginning of the assignment questions. 2-53. Find the area under a curve from z equals 2-59. A certain type altimeter averages 0.80 -0.9 to z equals 1.7. failures per week. What is the probability 1. 0.1395 that more than 2 altimeters will be broken 2. 0.4557 in a given week? 3. 0.5334 1. 0.047 4. 0.7713 2. 0.078 3. 0.110 2-54. What is the area between x equals 82 and 4. 0.129 x equals 91 if the mean is 85 and the deviation is 4? (Assume a normal Learning Objective: distribution.) 1. 0.7066 Identify and use normal to binominal approximation 2. 0.7211 in solving probability problems. 3. 0.7632 4. 0.7845 2-60. Which of the following equations may use the normal to approximate the binomial? 2-55. If a set of grades has a mean of 78 and a 1. np = 1 standard deviation of 5, what is the 2. np < 3 probability that a grade selected at 3. np < 5 random will be higher than 86? (Assume a 4. np = 7 normal distribution.) 1. 0.2124 2-61. Which of the following is not a step in 2. 0.1020 using the normal to approximate the 3. 0.0862 binomial? 4. 0.0548 1. np = µ Learning Objective: 2. √npq = σ Identify requirements for and solve problems using 3. Use the normal table the Poisson formula of probability and the distribution table. 4. To find more successes, add 0.5 to x 2-56. Which of the following is not a requirement Refer to table 4-1 in your textbook in for Poisson's formula of probability? answering items 2-62 through 2-64. 1. The average or mean must remain constant 2. The number of possible occurrences in 2-62. If the probability of a defective item is any unit is large. 0.10 and a sample of 400 items is taken 3. The particular occurrences in one unit from a large population, what is the do not influence the particular probability of 28 or less defective items? occurrences in another unit. 1. 0.0274 4. The probability of a particular 2. 0.1250 occurrence is large. 3. 0.2020 4. 0.4545 2-57. A boiler has been breaking down on the average of three times per month. By the 2-63. If the probability of a defective item is use of Poisson's probability formula, what 0.1 and a sample of 900 out of a large is the probability that the boiler will population is used, what is the probability break down only one time in a given month? of exactly 102 defective items? 1. 0.134 1. 0.0090 2. 0.152 2. 0.0180 3. 0.169 3. 0.0142 4. 0.184 4. 0.0211 Refer to table 4-2 in your textbook in 2-64. If the probability of a success in one try answering items 2-53 and 2-59 1 is 4 what is the probability of at least 2-58. If sailors randomly enter the mess hall on 17 successes in 48 tries? the average of 1.2 every 10 seconds, what 1. 0.3333 is the probability of four sailors 2. 0.1542 entering the mess hall in a selected 3. 0.0932 10-second period? 4. 0.0668 1. 0.022 2. 0.026 3. 0.089 4. 0.126 14 4-31. In what diagrams does the shaded area represent a maxterm class? 1. (A) and (C) 2. (C), (D), (E) 3. (B), (C), (D), and (F) 4. (A), (C), (D), and (F) 4-32. Let A represent cruisers and B represent flagships. If the shaded area of diagram (A) represents all ships that are neither cruisers nor flagships, the universal class with respect to this diagram con- sists of all 1. ships 2. cruisers and flagships 3. ships and objects that are not ships 4. ships that are neither cruisers nor flagships 4-33. What class (written in Boolean algebra notation) is represented by the shaded area in diagram (D)? 1. AB 2.A+B 3.A+B 4.B+A 4-34. Classes represented by the shaded areas of which of the two diagrams are complements of each other? 1. (A) and (B) 2. (B) and (E) 3. (C) and (D) 4. (D) and (F) Figure 4A.--Venn diagram Learning Objective: Items 4-28 through 4-34 refer to figure 4A. Identify logic operations in relation to Venn 4-28. The class "not A or not B" is represented and logic diagrams, truth tables, and switching circuits. by the shaded area in diagram 1. (A) 4-35. If A = 1 and B = 0, what is the value of 2. (C) f(A,B) = AB? 3. (E) 1. 0 4. (F) 2. 1 4-29. In what diagrams does the shaded area 3. 10 represent a minter-m class? 4. 0 < f(A,B) < 1 1. (A) and (E) 2. (B) and (E) 3. (A), (B), (E) 4. (B), (C), (D), and (F) 4-30. What class is represented by the unshaded area in diagram (F)? 1. A and not B 2. B and not A 3. A or not B 4. B or not A 23
Saturday, September 22, 2012 A year ago, I began this blog with the goal of uncovering some satisfying essential questions in algebra. These were to be questions that addressed the fundamental essence of algebra, while also being able to extend beyond a single discipline... and of course, they needed to be intriguing to both my students and to myself. A few months later I wrote that one of the qualities of a REALLY good math teacher is having a 'second set of objectives that go beyond the mastery of today's content.' A reader challenged me to identify these objectives, which I slyly avoided. But this week, in honor of my one year blogoversary, I present six essential questions or 'higher objectives' for my algebra classes. It's a start. In the spirit of UbD, expositions are voiced in the language of enduring understandings. How is algebraic thinking different from arithmetic thinking? It is my hope that my students will understand that algebra is a language of abstraction, where patterns are generalized and symbols are used to represent unknown or variable quantities. Arithmetic involves counting and manipulation of quantities where algebra relies more heavily on reasoning and generalizing the patterns that are observed from arithmetic procedures. It is my ultimate hope that they come to appreciate the power and utility of generalization. What makes one solution better than another? I would like my students to understand that numerical accuracy is only one piece of a good solution. The measure of a comprehensive and satisfying solution involves a subtle balance of precision, clarity, thoroughness, efficiency, reproducibility, and elegance (yes, elegance). I want my students to be masters of the well-crafted solution. How do I know when a result is reasonable? I want my students to understand that in math, as in life, context is supreme. There is no 'reasonable' or 'unreasonable' without an understanding of context. I hope that they can refine the skills to analyze and dissect problems that are both concrete and abstract, applied and generalized. I want them to develop habits of inquiry, estimation, and refinement. Ultimately, I hope that they will improve their sense of wisdom. Do I really have to memorize all these rules and definitions? Students will understand that mathematics is a language of precision. Without explicit foundations (axioms and properties) and precise definitions, reason gives way to chaos. On the other hand, they should understand that many perceived 'rules' in mathematics are simply shorthand ways to recall a train of logical reasoning (like formulas and theorems). It is my hope that they will appreciate precision but also understand the value of reason over recall. Isn't there an easier way? Without destroying their fragile spirits, I want my students to appreciate the benefits of struggle. I want them to realize that insight and higher knowledge are gained by approaching a problem from different angles and with multiple methods and representations. I want them to understand that knowledge about how mathematics works is on a higher echelon than the solution to a particular problem. In my ideal classroom, the students will understand how to spark their inner intrigue in order to move themselves beyond answers to seek connections, generalizations, and justifications. Do I really need to know this stuff? By sheer repetition and example, my students will know that the practical applications of algebraic thinking are numerous, especially in the rapidly changing fields of science, engineering, and technology. Beyond these undeniably important applications, they will know that confirmed correlations have been made between success in algebra and improved socioeconomic status. But ultimately, I hope that they will understand that the beauty and intrigue of mathematics is vast, and the limit of its power to improve the quality of their lives is unknown. I want them to glimpse infinity. Sunday, September 9, 2012 Lately, I've been following some of the conversation around the big ideas in an advanced algebra/pre-calculus course. The Global Math Department* hosted an interesting panel discussion around this topic a couple of weeks ago. I appreciated the thoughtfulness and complementary ideas of the presenters (John Burk, Dan Goldner, Michael Pershan, and Paul Salomon), and especially the thoughts behind proof and 'the well-crafted solution.' Without entirely reaching a consensus, the focus of the discussions tended to lean towards prediction as the overarching theme for algebra ii. The reasoning was thoughtful and grounded, but this theme did not satisfy me. While I can certainly see it, I also think that prediction is the theme for statistics. Can Algebra 2 and Statistics have the same theme? They can, I suppose, but it is not satisfying enough. Some of the new bloggers from the New Blogger Initiative also tackled this topic last week. gooberspeaks got me thinking about the focus on families of functions and David Price included ideas about varying ways of representing functions and modifying their behavior. Kyle Eck has a strong bent towards applications which resonates with the GMD theme of predictions. And all these ideas muddled around in my brain for a long time before emerging as a single construct that currently satiates my desire for deeper inspection. Algebra 2 is all about: generalizing patterns of behavior in bivariate relationships. But that's my academic's definition. In the UbD-influenced language of a high school classroom, I'd say that Algebra 2 asks these questions: How can we communicate the behavior of a relationship between two ideas? Are there rules of behavior that apply to all relationships? Why is it important to be able to generalize patterns of behavior? Functions certainly play a large role here, because it's easier to generalize patterns when there are overt rules of behavior to follow. But just as importantly, we also look at conic sections and the elusive inverses of even polynomials and periodic functions, because these ideas give us essential insight about the comforting nature of functions that are both one-to-one and onto, and about the obstacles presented by relationships that are not. Graphing also plays a large role, because it is a most excellent tool for alternate representations of bivariate relationships. Seeing patterns emerge in the shape of coordinate graphs can be enlightening long before symbolic manipulation clears a path through the brain... and I thank the math gods for that! I am wary though of too much graphical emphasis, for our well-loved coordinate system has obvious limits as our brains allow us to consider relationships with more variables. And applications clearly play an important role too, especially in the attempt to answer that third question. But I hesitate to put applications at the forefront of an advanced algebra theme. I think that is perhaps better handled by a physics class. In algebra we are attempting to represent scenarios with a generalized pattern of behavior, and manipulate this generalization to highlight useful information. I think I agree with Paul Salomon in that proof and 'well-crafted solutions' may trump (but certainly not replace) applications in the hierarchy of an overarching theme in algebra. To end, I'll just say that my desire to ask (and attempt to answer) the big questions is never entirely satiated, but I do so enjoy the conversations that emerge from them. I welcome your thoughts, criticisms, and further insights. The discourse is what makes being a mathematician so much fun. *Megan Hayes-Golding, where have you been all my life? What a terrific thing the GMD is, and one of these Tuesday nights, I will not have bedtime routines or NBI deadlines to worry about and will be able to attend a session while it is actually happening! Thanks to you and all others who are making this happen. Tuesday, September 4, 2012 I imagine that you, like me, have taught, or retaught, or referred to parentheses in the traditional manner: Parentheses are used in mathematical expressions to denote modifications to normal order of operations (precedence rules). In an expression like , the part of the expression within the parentheses, , is evaluated first, and then this result is used in the rest of the expression. Nested parentheses work similarly, since parts of expressions within parentheses are also considered expressions. Parentheses are also used in this manner to clarify order of operations in confusing or abnormally large expressions. (from Wolfram Math World) Wolfram goes on to define seven other mathematical uses for parentheses, including interval notation, ordered pairs (0, 5), binomial coefficients , set definitions, function notation, etc. With so many uses, it's perhaps no minor miracle when students are able to emerge with any working facility of parentheses at all! Honestly, I feel for my students. Even to me, mathematical definitions can sometimes seem inconsistent and confusing. Like the difference between terms (things that are added) and factors (things that are multiplied). I can hardly keep my own head on straight to describe the number of terms (2) and factors (0) in the following expression: (To be fair, the first term consists of two factors, each containing two terms each, and the second term has four factors.) And then recently, I reviewed a prealgebra curriculum that described parentheses as symbols that tell us to "treat part of the expression as one quantity." (from onRamp to Algebra) The book goes on to further implore the teacher to forgo the order of operations description in lieu of the 'one quantity' idea. I knew that... So WHY have I NEVER thought to describe it that way??? Parentheses are grouping symbols that tell us to treat the group as a single entity.Period. No confusion. A function input is a single argument. An ordered pair is a single location. An interval is a single, uninterrupted region. A matrix is a single array. A set is a single collection. A binomial coefficient is a single combination. An expression in parentheses is a single quantity. For some reason, this simple statement of an idea that seems so obvious is completely enlightening to me. The Common Core lists "Look for and make use of structure," as one of its Standards for Mathematical Practice. To me, this 'single entity' idea is paramount to the mastery of this standard: the key to seeing structure in long complicated algebraic expressions. I find a subtle beauty in tiny moments of enlightenment, even if it is only my own. It's got to rub off on someone! Sunday, August 26, 2012 In my town, school starts this week. My children have new backpacks and lunchboxes and shiny pencil cases with 5 newly sharpened pencils in each. The New Blogger Initiative is filled with stories of first day jitters and school year goals. This is a hard time for me. Ask me what I do, and I'll tell you that I am a math teacher. I have taught in urban, rural, and suburban schools. Unfortunately, life handed me a pink slip last year. It happens. Budgets get cut and new jobs are not stable jobs. But even without a classroom, I am still a math teacher. You are what you are. At the risk of sounding vainglorious, I know I am a good teacher. Not REALLY good, but working towards it. So this past year I took the pink slip as an opportunity to reflect, learn, write, grow, and move into a new era. I started this blog (and thank the Initiative for kicking my butt into keeping it up). I took a very close and critical look at lots of stuff in my filing cabinet. I have made a little money by offering some of these things for sale. I know the mathtwitterblogosphere is a sharing culture. I have lots to share, but I have mixed emotions about sharing everything. So I may not be as avuncular as Sam Shah, but I hope to create a helpful space here on my blog. Here's my first day syllabus. I've used it for a lot of years and it probably needs an update, but I still like it. syllabus I use this same format for all my classes, with tweaks to supply lists and calculator guidelines etc. The editable Word file is here, although it doesn't translate very well in Word (I use Publisher mostly, but no one else seems to). You'll have fun making it your own. I do. Now, before you start feeling sorry for me and sending me job listings, I'm being picky. I know what it's like to be me as a teacher. It's a 50+ hour/week commitment, with lots of worry and stress. I'm at a stage in my life where I don't wish to handle too many other external stressors. 10 minutes is about my limit on commuting time. Besides the extra time, I just like teaching close to home, in my own community, where I run into kids on the street and their parents at the grocery store. Some people don't want this, but I do. So in the meantime, I have a job. I edit math curricula at a huge publishing operation. I spend lots of time thinking intensely about tiny details, which is a wonderful contrast to teaching - where you have teeny amounts of time to maneuver a plethora of calamities. In the past several months I have been able to deepen my appreciation for: The pervasive misunderstanding of the difference between the terms inverse and opposite. The art of posing just the right question to provoke intrigue and deepen student understanding. The subtle mathematical properties of okra. Okay, maybe not that last one, but the point is that even without actually being in the classroom, I still find myself improving as a teacher. I see that there is a long and fascinating road both before and behind me. There are things to share and things to learn. Luckily, the company continues to be great, and just keeps getting better. Thanks for YOUR contributions to this fabulous community. And there it is, my reflections on the transformations of my past year. Hardly Hemingway-esque, but veracious nonetheless. Tuesday, August 21, 2012 Joe "Math Guy" was one of the first lessons I ever created. I drew this comic strip 'hook' for a sample class that I taught on inverse functions during a job interview. Years later, it's still one of my favorite lessons to teach. One problem with algebra is that there is often a disconnect between the meaning/understanding and the computations/doing. We try our darndest to bridge the gap between the two, but I find that the meaning often gets muddied by cumbersome symbolic computations. For me, I like the way inverse functions lend themselves to the meaning first, and symbolic abstraction second. And when I do it well, a beautiful aha moment can occur. Step1: Start Simple. Functions are a series (composition) of one or more actions (functions) that maps one object onto another (as long as each input is related to only one output). For example, "Take something, add two and then multiply by 5," is a function. [It's also important to note that symbolic notation can differ in representations of the same function: like 5x + 10 and 5(x + 2). Why?] Inverse functions are a series of reverse actions that undo the actions of a function. So, "Divide by 5 and then subtract 2," would be the inverse of the above function. A function and its inverse, when composed together (in either order), always 'do nothing'. Then we practice finding inverses of simple functions by first identifying the sequence of actions and reversing it. It's wonderfully intuitive and students 'get it' right away, just as long as Joe and I keep it relatively simple. Challenges at this point come in the form of four and five step functions, and not rational and quadratic curveballs. Step 2: Complicate Things Suddenly we find ourselves confronting rational functions and functions with multiple x's and our intuition begins to meet its match. At this point either I or someone in the class will throw up their hands and beg for a methodical way. I'll mention that one of my colleagues told me that I could just solve for x and that would be my inverse function. Dubious, but worth a shot. And so we try it, and yes it works. WHY??? Will that always work? What is going on? Why is finding an inverse like solving an equation? It is at this point that we talk about notation and graphs and all the algebraic aspects of inverse functions, keeping a tight grip on meaning: inverse functions 'undo' functions... no. 1 application for us right now? solving equations. Have you noticed that we have not yet encountered any functions that don't have inverses? We do a lot of practice with functions that do have inverses before we even think about ones that don't. Step 3: Complicate Things Again So, now Joe finds himself confronted with two more functions and builds two more function machines. The problem is, Joe just cannot get back all of the numbers he threw into the original function! Why not? What's wrong with these inverse machines? Is there any way we could tell in advance that these functions would have inadequate inverses? Is there any way to compensate for the missing values? I purposely try to stay away from formal language at the beginning of this topic, but suddenly there is a lot of talk about inputs and outputs and mapping two inputs onto the same output. So the formal definitions come out, and lo and behold, they don't seem like jibberish. If I'm lucky, something wonderful happens. They see a connection between this new topic and what they've been doing all along (solving equations). MAYBE they begin to appreciate the need for abstraction, formalization, and making compensations for small discrepancies. And when that happens, my head rests peacefully on my pillow at night. Thursday, August 9, 2012 Recently I found myself in a situation where intermediate rounding seemed inevitable, and so I sat there wondering, "Is there some kind of rule that would help me to discern an appropriate amount of rounding that is acceptable in the middle of a problem, so to not impact the final answer?" For example, if I need my final answer to be correct to the nearest whole number, would intermediate rounding to the nearest thousandth have an impact on the results of my final answer? Potentially, it only takes 0.01 error to impact a final value rounded to the nearest whole number. That is, 2.49 would round down to 2, but 2.50 would round up to 3. Rounding intermediately to the nearest thousandth only introduces a maximum error of 0.0005 (say, from rounding 10.2745 up to 10.275 or rounding 5.25749999… down to 5.257). Clearly, I could see that the answer to my conundrum would be a definitive "It depends." Of course, it would depend on what happened in my problem between the intermediate rounding and the final answer. As it turns out, there are lots of fascinating intricacies that play out in the solution of this problem. It's almost too embarrassing to admit just how much brain real estate I have dedicated to thinking about this. But here's one particular aspect that struck me hard. If I am introducing an error of 0.0005 and then multiply this value by some factor, then my error would also be multiplied by this same factor. OK, so in this particular scenario, a factor of 20 would be sufficient to potentially impact the final whole number value. What if I square the value? My instinct says that the error would also be squared, which would lead to an insignificant impact on my scenario. But my instinct is wrong. The reality is that the resulting error relies entirely on the initial value. For example, a value of 256.0235 that was rounded up to 256.024 and then squared would be off by more than 0.25, clearly enough to make a significant impact. And a larger number, like 10,000.0005 that gets rounded up to 10,000.001 and then squared would be off by more than 10. BAM! I find myself in the body of an awkward teenager, struggling with the most famous algebraic misconception: You see, I haven't made this mistake in years, but yet am amazed to find that the inner instinct still remains. I'm not sure what this means exactly, but at the very least it sheds some light on my teaching and perceptions of student understanding. Too often this particular misconception gets blamed on a misapplication of the Distributive Property. What if, instead of insisting that "exponents do not distribute," or "the Distributive Property does not apply here," I allowed students to explore their misconceptions and discover that the Distributive Property does indeed apply? What if we embraced this instinct and used it to delve more deeply into quantities as factors? What if I finally realized that even if they remember the rules and get this problem right every time it appears in symbolic form, that maybe, just maybe they still don't quite understand what it means?
Search Loci: Dynamic Mathematics with GeoGebra In this article we introduce the free educational mathematics software GeoGebra. This open source tool extends concepts of dynamic geometry to the fields of algebra and calculus. Loci Modeling the Mirascope Using Dynamic Technology 5. Conclusion The mirascope provides a worthwhile task to engage prospective and inservice mathematics teachers in the exploration of an appealing physical phenomenon and the development of genuine problem solving skills in STEM-oriented classes. In the beginning, little was clear about the mathematical mechanism underlying the mirage effect of a popular toy. We did not even know how to get started or how to manage the complexity. Through problem analysis, we came to understand the essence of the problem, which involves the properties of light and those of a parabola. The mirage is simply the optical projection of a small object placed at the bottom. To model the parabolic mirrors, we chose to use algebraic forms for accuracy and ease of control. To simulate the light reflection processes, we chose to start with an arbitrary point on the object and use geometric reflections to establish the paths of light. In enacting the reflection procedures, we were guided by our overarching conceptual understanding of the mirascope, thus integrating both conceptual and procedural aspects of the dynamic construction. The resulting mathematical mirascope does not only illustrate how the mirascope works, but also allows us to address other hypothetical what-if and what-if-not questions [1] about the physical mirascope. The mirascope project, with its various levels of scaffolding and starting points, could be implemented by readers who are interested in bringing meaningful STEM content into teacher education and middle and secondary mathematics classrooms and those we seek to teach big ideas of mathematics using new technologies. Similar projects can be found in professional journals [5] that showcase the integration of algebra and geometry in real-world and physical situations. Those interested in obtaining a physical mirascope can search for mirascope at an online store such as amazon.com or visit OPTI_GONE International, one of the original makers of the Mirage®. For further information about the physics of light and optical microscopy, please refer to the Optical Microscopy Primer. Acknowledgements The author would like to thank the two anonymous reviewers and the journal editors for their encouragments and constructive recommendations regarding an earlier version of the article. Yazan Alghazo and Michaell Bu reviewed drafts of the dynamic designs and asked thoughtful questions about the mirascope and related mathematical ideas, which are incoporated into the present article. About the Author Lingguo Bu is an assistant professor of Mathematics Education in the Department of Curriculum and Instruction at Southern Illinois University Carbondale. He is interested in the use of interactive and dynamic learning technologies in support of mathematical modeling in school mathematics and in preservice and inservice mathematics teacher development. Discuss this article Will other shapes? by Lingguo Bu (posted: 05/20/2011 ) Since the publication of article, I have received several emails about the mirascope and its GeoGebra-based explorations. Among them are (1) can we use a sphere? (2)how could you use it in the dark (place a LED inside)?, (3) what is the point of having students make their own? I welcome your ideas and suggestions. Thanks for your interest. The role of models for transferring understanding by Rob Schoen (posted: 05/20/2011 ) I have a mirascope on my desk in my office. Based on the interactions I see between office visitors and the mirascope, it is the single most intriguing object in my office (and yes, this does check my ego). I put it on my desk because of a conversation I overheard one day while sitting in a coffee shop. There were two male university students next to me, and they were highly intrigued by a question that one of them had posed. He asked "Why does our brain confulse left and right when we see a reflection in a mirror, but we don't get confused with the up and down direction in the reflections?" These two people generated several possible explanations (I suppose I might call them hypotheses), and all of their reasons were based on incoherent bits of knowledge about psychology and neuroscience rather than notions about optics or even a passing reference to a physical model. They eventually encountered their reflections in the spoons on their table, dared to ask each other how their reflection could be upside down, and thus they were completely baffled (ending the conversation with a shrug and apparent feeling of helplessness). I had a laptop with GeoGebra on my table. I was dying to introduce them to a model that might help them tie these incoherent ideas together, but I chose to finish my work so that I could return home to play with my one year old daughter. If I had known of this article, I would have shown it to the two university students and let them disentangle their ideas. Lingguo Bu has very elegantly taken these ideas to the next level with a beautiful GeoGebra-based model of the basic optics involved in the mirascope, showing a complex integration of basic ideas that result in a fascinating phenomenon. Does the author or my fellow readers know of other GeoGebra models of basic ideas and related ideas that may be even more complex? I would love to put them together into a coherent unit related to optics and geometry.
Mathematics is a highly dynamic discipline, with a wide variety of modern applications. At the university level, mathematics provides technical "know-how" in diverse areas such as economics, engineering, physics, biology, chemistry, psychology, business, and computer science. It is also a desirable prerequisite for almost any area of learning, since it can serve as an extremely effective tool for training in logical reasoning.
The primary goal of this course is to provide students with the knowledge and skills needed to analyze ODE models of physical, chemical, or biological systems. By the end of this course you will be able to find the steady states of a model described by a system of ODEs and compute their stability. We will find that this process can become rather involved, even for relatively simple models, so a secondary goal for this course is for you to become familiar with some computer tools. The first of these is the CAS Maple, which is useful for solving for steady states, plotting vector fields, and solving (analytically and numerically) differential equations. To investigate asymptotic behavior, we will use the xrk simulation program. Other secondary goals are for you to work in teams on extended problems and communicate your results. As part of the communication, we will be making use of the WWW for distributing class materials. You will also be strongly encouraged to use the web for communicating with each other, as well as with me.
You are here Courses << back MAT-152 Calculus II4 credits Prerequisites: MAT-151 or equivalent course with a minimum grade of C. MAT-152 is a continuation of MAT-151. A further study of differential and integral calculus of real functions of one real variable. Topics include further techniques of integration, applications of the integral (volume, arc length, work), and sequences and series.
Abstract Algebra The three primary topics of this course are groups, rings, and fields. Groups will be studied, including homomorphisms, normal subgroups, and the symmetric and alternating groups. The theorems of Lagrange, Cauchy, and Sylow will be developed and proven. Rings, including subrings, ideals, quotient rings, homomorphisms, and integral domains will be covered. Lastly, finite and infinite fields will be discussed. Prerequisite: MATH295.
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Appropriate for upper level undergraduate and graduate courses in Mathematical Modeling offered in math, engineering departments, and applied math departments. Prerequisite is some exposure to differential equations and to matrices. This accessible and practical text is designed to nurture a "m...
MAA Review [Reviewed by Peter Olszewski, on 12/11/2012] William Briggs, Lyle Cochran, and Bernard Gillett have written, in my opinion, a successful Calculus text. The true success of this text is that it reflects how today's college Calculus students learn: beginning with the exercises and referencing back to the worked out examples within the text. The book has well thought out examples that will be clear to the student. Many pictures are given through out the text to aid students' understanding of the concepts. While reading the text, it was as though I was sitting in a Calculus class and my instructor was talking to me. In addition, there was a lot of handholding, but not overbearing handholding. The text is to the point! I fully enjoyed the pure mathematical examples with the well thought out pictures; they show the years of teaching experience of each author. One of the first things I noticed in Chapter 1 was the way domain and range were treated from a graphical perspective, by taking any point on the curves and mapping it back to the x and y axes. The use of color is also helpful. In addition, I liked how the authors introduced the concept of secant lines early. In most other texts, they aren't introduced until the following chapter, which is typically about limits. What I also really enjoyed about Chapter 1 was the review of trigonometry in Section 1.3. Many of my calculus students have forgotten the basic concepts of trigonometry, so it is a wonderful idea to have a review available, to be used at the instructors' choice. As the title states, this text is for Scientists and Engineers, so it is fitting for secant lines to be quickly connected to velocity. The motivation for considering the slope of secant lines is very well done and the diagrams on page 41 are excellent. This is what the students need to see. Jumping to the middle of the book, I strongly believe students are overwhelmed when it comes down to sequences and series. In most other texts I've read, sequences and series and all related topics are contained in one big chapter. Having these concepts broken into two chapters is more digestible for the students. Of course, there are places where the book can be improved. I only mention a few. In Chapter 1, the authors discuss domains and ranges of functions but not for compositions of functions. I would like to see examples of these, with graphics to support the solutions. In addition, having examples of finding domains and ranges of piecewise defined functions and domains and ranges of transformations of functions would further enhance this section. It has been my experience that students need extra guidance in finding domains and ranges. After Theorem 2.2, I would recommend stating another theorem about using direct substitution of a polynomial and rational function followed by examples. In addition, I would like to see more examples following Example 6 on "other techniques" for finding limits analytically. Many times, students forget simple algebraic concepts needed for Calculus. In the exercise set for Section 2.3, I believe the authors should limit the amount of problems where the limits of functions are tending towards a number a. I believe it would be more useful for students to see the direct numerical results as this is what they are more likely to see in their careers. For Section 2.4, as an aid to help students understand the logic of when functions tend to zero and to infinity, it's useful to have an informal statement that 1/large tends to 0 and 1/small tends to infinity. This will help students quickly recall these two critical facts. In Section 2.6, I feel as though there should be an example using the Intermediate Value Theorem involving a function before proceeding to the financial application. The section on higher order derivatives in Section 3.2 is out of place. I strongly believe higher order derivatives need a section all their own, as there are many examples students need to see. My suggestion for Sections 3.5 and 3.6 is that they be flipped. If the Chain Rule is learned first, many Chain Rule applications problems can be woven into the section on derivatives as rates of change. I believe the statement of the Second Derivative Test in Section 4.2 will confuse students. Instead of saying, "If f′′(c) = 0, the test is inconclusive; f may have a local maximum, local minimum, or neither at c" I would suggest, "In such a case, the First Derivative Test can be used to determine if f is a local maximum, minimum, or neither." While Example 3 is excellent in Section 4.3, I believe another example is needed before Example 3 involving a rational function that contains both vertical and horizontal asymptotes and a hole in the graph. In addition, Section 2.5 should be inserted in Chapter 4 before this section since the important connection to limits at infinity can now be made with the summary of curve sketching. I was hoping to see more examples in Sections 4.5–4.7. I also feel as though Section 4.7, L'Hôpital's Rule, is out of place with the rest of the text. I believe this section should be either contained in Section 7.6 or be a new section before Section 7.6. Reading further into the text, I believe there could be many more applications presented. For example, in Chapter 13, there are too many proofs in the homework set for dot products and the section on cross products ends very quickly with not enough applications. Section 13.7 is much better as the authors give many more applications. I especially enjoyed reading through Examples 5 and 6 in this section. So many times, students are told to ignore friction and air resistance. Here is a problem were the angle must be found to adjust the flight of a ball. Moving to Section 13.9, once again, I believe there are too many proofs and not enough applied problems. After all, part of the title of the book is "for Scientists and Engineers"! In the past, when I have taught engineering students, they wish to see how the mathematics they learn, whether it be calculus or matrices, will be used. Perhaps having student projects at the end of each chapter or section, specifically for the Sciences and Engineers could further enhance the text. The teaching and writing style of this text is excellent but I believe more applications would further student's motivation, creativity, and problem solving skills. Peter Olszewski is a Mathematics Lecturer at Penn State Erie, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Pennsylvania Alpha Beta Chapter Advisor of Pi Mu Epsilon. He can be reached at pto2@psu.edu. Webpage: Outside of teaching and textbook editing, he enjoys playing golf, playing guitar, reading, gardening, traveling, and painting landscapes.
Intermediate Algebra + Text-Specific DVDs ISBN10: 1-111-49154-2 ISBN13: 978-1-111-49154-3 AUTHORS: Kaufmann/Schwitters INTERMEDIATE ALGEBRA employs a proven, three-step problem-solving approach—learn a skill, use the skill to solve equations, and then use the equations to solve application problems—to keep students focused on building skills and reinforcing them through practice. This simple and straightforward approach, in an easy-to-read format, has helped many students grasp and apply fundamental problem-solving skills. The carefully structured pedagogy includes learning objectives, detailed examples to develop concepts, practice exercises, an extensive selection of problem-set exercises, and well-organized end-of-chapter reviews and assessments. The clean and uncluttered design helps keep students focused on the concepts while minimizing distractions. Problems and examples reference a broad array of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life. Also, as recommended by the American Mathematical Association of Two-Year Colleges, many basic geometric concepts are integrated in problem-solving scenarios. The text's resource package—anchored by Enhanced WebAssign, an online homework management tool—saves instructors time while also providing additional help and skill-building practice for students outside of class. Additional versions of this text's ISBN numbers Purchase Options List$226

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