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Math Mammoth Geometry 2 continues the study of geometry and is suitable for grades 6-7. The main topics include:angle relationships, classifying triangles and quadrilaterals. angle sum of triangles... More > and quadrilaterals, congruent transformations, including some in the coordinate grid, similar figures, including using ratios and proportions, review of the area of all common polygons, circumference of a circle (Pi),area of a circle,conversions between units of area (bothmetric and customary), volume and surface, area of common solids, conversions between units of volume (both metric and customary),some common compass-and-ruler constructions.< Less The key to doing well on the SAT Math is knowing how to set up and solve word problems. The SAT Math Review Book for People Who Hate Math differs from the other books on the market because it gives... More > you in-depth teaching on word problems. By studying this book, you will learn how to set up and solve different kinds of word problems: distance, rate of work, mixture, age, money, Pythagorean Theorem problems and many more. In addition to word problems, the book contains a complete review of arithmetic, algebra, and geometry Instead of spending four years at your "safety school," get into the college of your dreams by scoring well on the SAT.< Less
provides a working knowledge of precalculus and its applications. It begins with a review of algebraic... see more This course provides a working knowledge of precalculus and its applications. It begins with a review of algebraic operations. Emphasis is on solving and graphing equations that involve linear, polynomial, exponential and logarithmic functions. Students learn to graph trigonometric and inverse trigonometric functions and learn to use the family of trigonometric identities. Other topics include conic sections, arithmetic and geometric sequences, and systems of equations
Description Integrated course of algebra, geometry and trigonometry. Practical applications to vocational and technical programs are emphasized through the use of contextualized small-group classroom activities and guided practical problem solving. Topics include graphing in the Cartesian coordinate system; graphing and solving linear equations and systems of linear equations; geometric concepts of angles (degree and radian measure) and triangles, including the Pythagorean theorem and similar triangles; trigonometric concepts of sine, cosine, and tangent, and solving right triangles. Prerequisite: Grade of C- or better in OCSUP 106 or MATH 72B, or appropriate placement score. Intended Skills and Attitude Outcomes A. Students will gain knowledge of the basic fundamental definitions of Geometry B. Students will understand measurement of angles and their properties C. Students will understand polygons and their properties D. Students will understand triangles and their properties E. Students will gain knowledge of how to find the area of triangles and polygons F. Students will be able to calculate volume of cones and irregular shapes G. Students will apply thinking skills to job tasks, including decision-making and reasoning H. Students will gain knowledge of circles, parts of circles, and their properties I. Students will be able to calculate area and circumference of circles and parts of circles J. Students will gain knowledge of ellipses and their properties K. Students will be able to solve problems and make decisions in work related situations L. Students will understand relationship between radians and degrees M. Students will know the six basic trigonometric functions N. Students will gain knowledge and apply the law of sines O. Students will understand and apply the law of cosines P. Students will understand and apply sine and cosine curves to application problems Q. Students will gain knowledge and compute specific problems using right-triangle trigonometry R. Students will know and understand the Pythagorean Theorem S. Students will be able to solve circles and arcs using specific formulas T. Students will be able to problem solve and present interpretation of information using critical thinking U. Students will understand and use plane geometry V. Students will be able to apply interpersonal skills in relating to others W. Students will be able to apply systematic techniques and algorithmic thinking to represent, analyze, and solve problems
The following article was written by Nayoung Ahn and Phillip Zhang, students at Torrey Pines High School (TPHS) in San Diego, California. Originally published by the Torrey Pines High School Falconer, a student newspaper, it describes an advanced new math curriculum introduced by teacher Abby Brown and made possible with Mathematica. 'Math Topics' adds creativity By Nayoung Ahn & Phillip Zhang STAFF WRITERS Advanced Topics in Mathematics II is a new course being offered at TPHS for the first time this school year and is taught by Math Department Chair Abby Brown. Students in the class are to apply high school math concepts to real-world projects. Their primary tool is Mathematica, a computer algebra system program developed by Wolfram Research, which also holds the Wolfram Technology Conference that Brown will attend this October, in Champaign, Ill. There, she will present materials she developed at Wolfram Research over the summer. Students accompanying her--Ryan Chuang (12), Samantha Patterson (12), Jenny Tan (12) and Jeffrey Tsao (11)--will also present work they did using Mathematica, a mathematics software program. "It's a great opportunity for us," Tsao said. "We're meeting all these professionals, and we're just high school students." Ideas for projects include making an interactive tool to teach logarithms, or a simulation of momentum for a physics class. "For community service projects we will be seeking out ideas from other [teachers] so that we can develop materials to [help them teach]," Brown said. A flexible curriculum gives students plenty of freedom and independence, and is cited as one of the primary attractions of the class. "We enjoy [exploring topics of our own choosing], and we get some learning out of it," said Matt Schotz (12). "[The freedom] keeps me interested." No tests are given and lessons--on Mathematica--are given on a need-to-know basis. "It's not really traditional. [Brown will] teach you how to use Mathematica, and you go from there," Jamie Ding (11) said. Even so, the students are there to work. Most of them, including Ding, have already exhausted the TPHS math courses, including college courses Calculus C/D and Linear Algebra. "I felt that Discrete Math and Statistics weren't my thing," Ding said. "So I felt that this was the best choice." For students, Advanced Topics was a chance to take their study of math to the next level. "Right now, we are just getting started, but I have big ideas as to where this can go and how many students it may touch," Brown said. Originally published by the Torrey Pines High School Falconer, September 22, 2006. Reprinted with permission.
Master Math: Probability is a comprehensive reference guide that explains and clarifies the principles of probability in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced, the book helps clarify probability using step-by-step procedures and solutions, along with examples and applications. A complete table of contents and a comprehensive index enable readers to quickly find specific topics, and the approachable style and format facilitate an understanding of what can be intimidating and tricky skills. Perfect for students studying probability and those who want to brush up on their probability skills.
My Insight about Calculus In the first term of my Calculus, I had a hard time to review all my previous Math subjects, like Trigonometry and Algebra. I don't have any idea in Calculus; I just know that it's harder and more complicated than my previous Math subjects. After the midterm of this Semester I somehow know what Calculus for is, I learned that Differential Calculus can be use in finding the change in ratio. I also know that Calculus can be use to find the maximum and minimum rate of objects. It can also apply in other situation that involve changing and math. Using the concept of function derivatives, it studies the behavior and rate on how different quantities change. Using the process of differentiation, the graph of a function can actually be computed, analyzed, and predicted. Though it is complicated to use well, calculus does have a lot of practical uses - uses that you probably won't comprehend at first. The most common practical use of calculus is when plotting graphs of certain formulae or functions. Using methods such as the first derivative and the second derivative, a graph and its dimensions can be accurately estimated. These 2 derivatives are used to predict how a graph may look like, the direction that it is taking on a specific point, the shape of the graph at a specific point (if concave or convex), just to name a few. When do you use calculus in the real world? In fact, you can use calculus in a lot of ways and applications. Among the disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution. For example, in physics, calculus is used in a lot of its concepts. Among the physical concepts that use concepts of calculus include motion, electricity, heat, light, harmonics, acoustics, astronomy, and dynamics. In fact, even advanced physics concepts including electromagnetism and Einstein's theory of... [continues]
many think of algorithms as specific to computer science, at its core algorithmic thinking is defined by the use of analytical logic to solve problems. This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer ex&les from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures. The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies-exhaustive search, backtracking, and divide-and-conquer, among others-will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary on the puzzle's origins and solution methods. The only book of its kind, Algorithmic Puzzles houses puzzles for all skill levels. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking through more difficult puzzles. {"currencyCode":"USD","itemData":[{"priceBreaksMAP":null,"buyingPrice":18.29,"ASIN":"0199740445","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":24.72,"ASIN":"098478280X","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":29.96,"ASIN":"1479274836","isPreorder":0}],"shippingId":"0199740445::dcUUxuynmcY%2BhXqLZe0S6wdHYuic%2Bx3Y2cn2Zr9N2exYgpG2jE71sHT%2FUmUsKWf0bdo8pEy1D5aNOetDE8PTSGa4pwoI%2BEjScxtgW%2F6PywW3o0HufV72uQ%3D%3D,098478280X::ieU9B4griXmO5tYxTQq1dKCHm%2BhxMBG8udvfssQO%2FR0diH02MaYrIKF2mFFWzG%2FfipsMx9CXnMGH6rTfc40MXY60e8b68RTjKx5CK4u%2BcmiQSurLhfbesg%3D%3D,1479274836::farDclNAb4sK%2F7HiAI7axPYkTMsoImHQ3YpOWHxiGLXmFAbzDiw%2BIoFkM1YF38%2FoS9L1vigFvPHtC%2FrgAlwGmQKOmKkDjvSvCGZqRki02e40ZlP5VT3ugorithmic Puzzles by Anany Levitin and Maria Levitin is an interesting and novel style of puzzle book. The emphasis lies in training the reader to think algorithmically and develop new puzzle-solving skills: the majority of puzzles are problems where we are asked to find the shortest distance or the fewest moves to get from A to B, or construct a proof that a puzzle has no solution. the book provides plenty of puzzles to keep even the most avid problem-solvers busy for a long time, all with varying levels of difficulty and different styles/contexts. The solutions provided are comprehensive and explain themselves in a friendly, constructive manner, complete with illustrations. In addition to questions and answers, a section of brief hints is also provided to assist the reader in their puzzle-solving endeavours." -- Graham Wheeler, Significance About the Author Anany Levitin is a professor of Computing Sciences at Villanova University. He is the author of a popular textbook on design and analysis of algorithms, which has been translated into Chinese, Greek, Korean, and Russian. He has also published papers on mathematical optimization theory, software engineering, data management, algorithm design, and computer science education. Maria Levitin is an independent consultant. After some years working for leading software companies and developing business applications for large corporations, she now specializes in web-based applications and wireless computing. I bought this book on sight. It's possibly my favorite book of any and all books I own. The puzzles are not only ubiquitous and exciting... they're educational and provide many "Aha!" moments. I've been looking for a book like this for years, and I recommend it to those looking for fun and challenging puzzles of varying difficulty levels. Being a computer science major, many of the puzzles are also fun to implement and solve using programming, emphasizing the "algorithmic" component in the title.
To introduce the basic mathematical tools for generating and solving the governing equations of fluid dynamics. Vector calculus and partial differential equations are the primary topics covered. Materials The main text is the second volume of the book I wrote with the title Advanced Engineering Mathematics, Addison-Wesley-Longman, 1998. The text is augmented with notes that I have placed on my homepage at Description The course, which is primarily taught to junior level students majoring in oceanography, mechanical engineering and mathematics, covers the basic materials of vector calculus and partial differential equations in the context of fluid flows. After a thorough review of the vector operations (grad, div and curl), conservation laws of mass and linear momentum are introduced. Numerous examples of flows that one typically encounters in a basic fluid dynamics and geophysical fluid dynamics setting are introduced and visualized using Mathematica's symbolic and numerical capabilities. The course ends with the derivation of the Navier-Stokes equation in a rotating frame with special emphasis on the Coriolis force and its impact on the so-called Ekman tranport solution. The primary goal of the course is to demonstrate the natural relationship between several topics in mathematics and fluid dynamics and oceanography. Mathematica is the primary tool used throughout the course as a symbolic manipulator as well as a numerical workhorse. Visualizing flows, especially through animations, is one of the main strengths of this course. Another strength of the course is the set of computer projects that the students carry out as part of the grade requirement. Examples of past projects include a) Flow past cylinder, b) Oseen vortex, c) Rayleigh-Benard flow, d) Lorenz and Veronis models of convection, and e) Serrin's tornado model.
A Timeline of Mathematics by Michael Waski Two timelines connect key mathematicians from different cultures and eras directly to content areas including geometry, algebra, trigonometry, and calculus. The set includes a third blank timeline with moveable parts that can be tailored to the needs of the students and classroom teacher. The timelines are intended for use in an adolescent classroom.
Trigonometry - 9th edition Summary: Larson's TRIGONOMETRY is known for delivering sound, consistently structured explanations and exercises of mathematical concepts. With the ninth edition, the author continues to revolutionize the way students learn material by incorporating more real-world applications, ongoing review, and innovative technology. How Do You See It? exercises give students practice applying the concepts, and new Summarize features, Checkpoint problems, and a Companion Website reinforce understanding of...show more the skill sets to help students better261.21 +$3.99 s/h New StudentSolutions Stone Mountain, GA Brand New Title. We're a Power Distributor; Your satisfaction is our guarantee! $261.65 +$3.99 s/h New ShopSpell Wharton, NJ Brand New item. 100% Guaranteed. Reliable customer service. $282.54 +$3.99 s/h New PROFESSIONAL & ACADEMIC BOOKSTORE Dundee, MI 1133954332310.60 +$3.99 s/h New Russell Books Victoria, BC Hardcover New 1133954332 Special order direct from the distributor. $349.95 +$3.99 s/h New textsforsale Manvel, TX Hard cover New. No dust jacket. 100% BRAND NEW ORIGINAL US STUDENT 9th Edition / Mint condition / Never been read / Shipped out in one business day
Almost every student has to study some sort of mathematical proofs, whether it be in geometry, trigonometry, or with higher-level topics. In addition, mathematical theorems have become an interesting course for many students outside of the mathematical arena, purely for the reasoning and logic that is needed to complete them. Therefore, it is not... more... This is the first treatment in book format of proof-theoretic transformations - known as proof interpretations - that focuses on applications to ordinary mathematics. It covers both the necessary logical machinery behind the proof interpretations that are used in recent applications as well as - via extended case studies - carrying out some of these... more... Learn how to develop your reasoning skills and how to write well-reasoned proofs Learning to Reason shows you how to use the basic elements of mathematical language to develop highly sophisticated, logical reasoning skills. You'll get clear, concise, easy-to-follow instructions on the process of writing proofs, including the necessary reasoning techniques... more... The Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals... more...
This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control.
Book summary In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears. [via]
Algebra Survival Guide Workbook 9780965911375 ISBN: 0965911373 Publisher: Midpoint Trade Books Inc Summary: Following on the success of the Algebra Survival Guide, the Algebra Survival Guide Workbook presents thousands of practice problems (and their answers) to help children master algebra. The problems are keyed to the pages of the Algebra Survival Guide, so that children can find detailed instructions and then work the sets. Each problem set focuses like a laser beam on a particular algebra skill, then offers ample prac...tice problems. Answers are conveniently displayed in the back. This book is for parents of schooled students, homeschooling parents and teachers. Parents of schooled children find that the problems give their children a "leg up" for mastering all skills presented in the classroom. Homeschoolers use the Workbook - in conjunction with the Guide - as a complete Algebra 1 curriculum. Teachers use the workbook's problem sets to help children sharpen specific skills - or they can use the reproducible pages as tests or quizzes on specific topics. Like the Algebra Survival Guide, the Workbook is adorned with beautiful art and sports a stylish, teen-friendly design. Rappaport, Josh is the author of Algebra Survival Guide Workbook, published under ISBN 9780965911375 and 0965911373. Four hundred sixty seven Algebra Survival Guide Workbook textbooks are available for sale on ValoreBooks.com, one hundred fifty three used from the cheapest price of $3.35, or buy new starting at $8.38
Product Details The book includes two appendices: one listing the problems with their prerequisites, and a second which groups problems by subject matter. These make the book useful for teachers looking for extra challenges for their students. _CHOICE Here is a collection of 208 challenging, original problems, with carefully worked, detailed solutions. In addition to problems from The Wohascum County Problem Book, there are about 80 new problems, many of which involve experimentation and pattern finding. The problems are intended for undergraduates; although some knowledge of linear or abstract algebra is needed for a few of the problems, most require nothing beyond calculus. In fact, many of the problems should be accessible to high school students. On the other hand, some of the problems require considerable mathematical maturity, and most students will find few of the problems routine. Over four-fifths of the book is devoted to presenting instructive, clear, and often elegant solutions. For many problems, multiple solutions are given. Appendices list the prerequisites for individual problems and arrange them by topic. This should be helpful to classes on problem solving and to individuals or teams preparing for contests such as the Putnam. The index can help, as well, in finding problems with a specific theme, or in recovering a half-remembered problem.
This course introduces some basic concepts of number theory and modern algebra that underlie elementary and middle grade arithmetic and algebra odd Papick, I.J. (Pearson) Recommended Course Objectives To progress from a procedural/computational understanding of mathematics to a broad understanding encompassing logical reasoning, generalization, abstratction, and formal proof. To use technology (calculator and computer) as a learning and teaching tool for mathematics. To learn the algorithmic approach to problem solving. To display an understanding of the nature of rigorous proof. To write elementary proofs, especially proofs by induction and basic number theory proofs. Measurable Learning Outcomes: Know the basic properties of integers such as divisibility, primes, and congruence. Know the basic properties of the real numbers including commutativity, associativity, identity, distributivity. Apply the Euclidean Algorithm to find the greatest common denominator. Determine whether or not a set of three numbers is a Pythagorean Triple and it is primitive. Apply the algorithm to generate Primitive Pythagorean Triples. Represent patterns algebraically. Recognize and generate arithmetic and geometric sequences and find the sums of a finite number of terms of the sequence. Calculate numbers of possible outcomes of elementary combinatorial process using the sum and product rules, permutations, and combinations
Understanding Calculus II: Problems, Solutions, and Tips Professor Bruce H. Edwards Solve a wide array of problems in the physical, biological, and social sciences, engineering, economics, and other areas with the skills you learn in Understanding Calculus II: Problems, Solutions, and Tips. This second course in the calculus sequence introduces you to exciting new techniques and applications of one of the most powerful mathematical tools ever invented. Professor Bruce H. Edwards of the University of Florida enriches these 36 lectures with crystal-clear explanations, frequent study tips, pitfalls to avoid, and—best of all—hundreds of examples and practice problems that are specifically designed to explain and reinforce key concepts. Understanding Calculus: Problems, Solutions, and Tips Professor Bruce H. Edwards Immerse yourself in the unrivaled experience of learning—and grasping—calculus with Understanding Calculus: Problems, Solutions, and Tips. These 36 lectures cover all the major topics of a full-year calculus course in high school at the College Board Advanced Placement AB level or a first-semester course in college. Award-winning Professor Bruce H. Edwards guides you through hundreds of examples and problems, each of which is designed to explain and reinforce the major concepts of this vital mathematical field. Algebra I Professor James A. Sellers Algebra I is an entirely new course designed to meet the concerns of both students and their parents. These 36 accessible lectures make the concepts of first-year algebra—including variables, order of operations, and functions—easy to grasp. For anyone wanting to learn algebra from the beginning, or for anyone needing a thorough review, Professor James A. Sellers will prove to be an inspirational and ideal tutor. Open yourself up to the world of opportunity that algebra offers by making the best possible start on mastering this all-important subject. How to Become a SuperStar Student, 2nd Edition Professor Michael Geisen Give your student the vital skills that will carry him or her through high school, college, and well into the challenges of adult life. Professor Michael Geisen, the 2008 National Teacher of the Year, has packed How to Become a SuperStar Student, 2nd Edition with advice, tips, tricks, and resources on everything from homework and class participation to giving group presentations and preparing for tests. This masterfully updated version of our highly popular study guide course has the power to transform your student's education into a world-class learning experience. Whether you're a high-school student preparing for the challenges of higher math classes, an adult who needs a refresher in math to prepare for a new career, or someone who just wants to keep his or her mind active and sharp, there's no denying that a solid grasp of arithmetic and prealgebra is essential in today's world. In Professor James A. Sellers' engaging course, Mastering the Fundamentals of Mathematics, you learn all the key math topics you need to know. In 24 lectures packed with helpful examples, practice problems, and guided walkthroughs, you'll finally grasp the all-important fundamentals of math in a way that truly sticks. Algebra II Professor James A. Sellers Make sense of Algebra II in the company of master educator and award-winning Professor James A. Sellers. Algebra II gives you all the tools you need to thrive in a core skill of mathematics. In 36 engaging half-hour lectures, Professor Sellers walks you through hundreds of problems, showing every step in their solution and highlighting the most common missteps made by students. Designed for learners of all ages, this course will prove that algebra can be an exciting intellectual adventure and not nearly as difficult as many students fear. Mathematics Describing the Real World: Precalculus and Trigonometry Professor Bruce H. Edwards Finally make sense of the mysteries of precalculus and trigonometry in the company of master educator and award-winning Professor Bruce Edwards. In the 36 intensively illustrated lectures of Mathematics Describing the Real World: Precalculus and Trigonometry, he takes you through all the major topics of a typical precalculus course taught in high school or college. You'll gain new insights into functions, complex numbers, matrices, and much more. The course also comes complete with a workbook featuring a wealth of additional explanations and problems. Chemistry, 2nd Edition Professor Frank Cardulla Discover why success in chemistry depends only on a genuine understanding of the field's concepts and ideas. Chemistry, 2nd Edition provides a foundation for future success by giving students a deep and thorough grasp of the fundamental problem-solving skills needed to study chemistry. Veteran science teacher and Professor Frank Cardulla's 36 carefully designed lectures are valuable tools for struggling students, students looking to perform better, home-schooled students, or anyone interested in finally understanding this important science. Prove It: The Art of Mathematical Argument Professor Bruce H. Edwards Mathematical proof is the gold standard of knowledge. Once a mathematical statement has been proved with a rigorous argument, it counts as true throughout the universe and for all time. Imagine, then, the thrill of being able to prove something in mathematics. But you don't have to imagine the exhilaration of constructing a proof—you can do it! Prove It: The Art of Mathematical Argument initiates you into this thrilling discipline in 24 lectures by Professor Bruce H. Edwards of the University of Florida. This course is suitable for everyone from high school students to the more math-savvy. High School Level—Geometry Professor James Noggle Professor Noggle's lectures on geometry are exceptionally clear and well organized. He has an evident love for the topic, and a real gift for conveying the elegance and precision of geometric concepts and demonstrations. You will learn how geometrical concepts link new theorems and ideas to previous ones. This helps you see geometry as a unified body of knowledge whose concepts build upon one another. Understanding Calculus II: Problems, Solutions, and Tips & Understanding Calculus: Problems, Solutions, and Tips (Set) Professor Bruce H. Edwards Understand the beauty and utility of calculus and solve a wide array of problems in the physical, biological, and social sciences, engineering, economics, and other areas with the skills you learn in this course set by award-winning Professor Bruce H. Edwards. These two courses together cover all the major topics of two full years of high school calculus at the College Board Advanced Placement AB and BC levels or of two semesters in college. These lectures are enriched with crystal-clear explanations, frequent study tips, pitfalls to avoid, and—best of all—hundreds of examples and practice problems that are specifically designed to explain and reinforce key concepts. Save Up To $470 Understanding Calculus II: Problems, Solutions, and Tips & Mastering Differential Equations: The Visual Method (Set) Various Professors Gain mastery of the mathematics you need to solve differential equations, and learn a computer graphics approach to approximating and displaying solutions to problems involving motion in this clear and accessible course set. In Understanding Calculus II: Problems, Solutions, and Tips, you learn exciting techniques and applications to solve a wide array of problems in the physical, biological, and social sciences, engineering, economics, and other areas. And in Mastering Differential Equations: The Visual Method, you learn the visual method that can start you on the road to mastering this beautiful application of the ideas and techniques of calculus. Understanding Calculus II: Problems, Solutions, and Tips & Prove It: The Art of Mathematical Argument (Set) Professor Bruce H. Edwards Expand your knowledge of one of the most powerful mathematical tools ever invented and experience for yourself the thrill of proving something in mathematics with this clear and practical course set that helps you see how all of mathematics is connected. In Understanding Calculus II: Problems, Solutions, and Tips, learn exciting techniques and applications to solve a wide array of problems in the physical, biological, and social sciences, engineering, economics, and other areas. And in Prove It: The Art of Mathematical Argument, grasp the art of constructing a mathematical proof and, in the process, gain insights that are invaluable for mastering key concepts in every branch of mathematics, from algebra to number theory, from geometry to calculus and beyond.
MAPLE is a computer algebra system that was first developed at the University of Waterloo in Canada, and Dr. Otto Wilke, math professor at Texas State Technical College Waco, has produced Contemporary Math Using MAPLE or TI-89 that teaches students how to use the software to work problems in areas such as algebra, geometry, logarithms and basic trigonometry. It is the first textbook taught in a math survey course that teaches problem solving using MAPLE specifically. In addition, the book includes instructions on how to work problems with a TI-89 calculator.
Borrowing from the Past: Using 17th Century Technology to Inform 21st Century Undergraduate Mathematics There is interest in undergraduate mathematics for close study of proofs for various planar loci in the Cartesian plane. They add significantly to a student's understanding of trigonometry, geometry, and to the ability to think of mathematical structures in abstract terms. Certainly, application-style problems using the procedures and theorems of trigonometric concepts provide necessary introduction into the sort of real-world situations encountered by future engineers and analysts. But studying the underlying structures and abstract nature of mathematics at a pre-calculus or early calculus stage, as well as studying the history behind the development of these ideas, would go a long way toward enriching the experiences of early mathematics students. In particular, the seventeenth century provides an interesting confluence of mathematical ideas surrounding conic sections and coordinate geometry from the ancient Greeks to Descartes that would soon lead to the development of the calculus in Europe. This project draws upon the mathematical understanding and technology available in the seventeenth century in order to create interesting problems and lessons for the twenty-first century undergraduate classroom. Historical perspectives, profiles of various mathematicians, and mathematical proofs are presented, as well as animated graphics of planar loci that describe conic sections. Additionally, one or more problems for classroom use will be offered.
If you are having difficulty with algebra, these pages may be of some help because they offer different sorts of explanations, in some sense more "psychologically complete", than are usually found in algebra texts. It is my belief that the way algebra is typically presented to students leaves out some ideas and explanations that are helpful, even sometimes necessary, for them to be able to do algebra well and to have a "feel" for it. There are at least three different kinds of things taught in algebra courses: (1) language conventions, (2) logical numerical manipulations using those conventions, and (3) deducing answers to problems by using the conventions and the logical manipulations of them. I will explain as I go. But it is important for students to keep in mind whether in a given lesson they are supposed to be learning a convention, a manipulation, or a way of solving problems by using conventions and manipulations. It is also my belief that school "culture" is such that, even contrary to good teachers' warnings, students will often think they are simply supposed to memorize formulas and recipes in math, rather than (also) understand them. Such memorization becomes a problem in courses, such as algebra, where understanding is at least as important as specific knowledge. This is a two-fold problem. (1) Teachers need to try to give useful and helpful explanations -- and they need to be aware of as many typical student misunderstandings and confusions as they can; and teachers need to constantly try to monitor students for confusion and misunderstandings about what has been presented; waiting until there are test results is often too late. But also, (2) students need to know that THEY are the ones who will have to ultimately make the material make sense to them, and that they need to keep trying until it does. They may have to consult others, find a different book, or just sit down and think about the material, if they cannot understand their teacher's explanation about some aspect of algebra or other. There is simply no guaranty that any particular explanation will provide automatic understanding. Understanding requires reflective thinking of one's own. Explanations often are only a help to such thinking; and what serves as a great explanation for one student may not be helpful at all to another. (My own first difficulty in "pre"-algebra was not understanding what letters such as "x" had to do with anything, and why letters were chosen to represent quantities at all, or how you worked with them when you had them. I vividly remember when the light dawned on me about this particular lack of understanding, in part because I still do not know why or how the teacher's particular explanation "worked" on me. She was saying that doing algebra was like unwrapping a package in the reverse way it was wrapped to begin with. It may be that I figured out what I needed to know while she was talking instead of because of what she specifically said, or it may be that what she said had some sort of meaning to me subconsciously somehow. I don't know, since "unwrapping" is not the way I see (or even then saw) algebra. But what follows are explanations of the sort that seem to me the most meaningful about some aspects of algebra many students typically have trouble with. Further explanations of other aspects of algebra can be found at A supplemental introduction to the first chapter of an algebra book and at Rate, Time Problems.) The following question was asked on the Math-Help forum. It is typical of the kinds of problems had by students who don't really understand in general "what is going on" in algebra -- why you do certain manipulations of formulas, or how you choose which manipulations to do. Particular algebraic manipulations do not make sense to them because they don't have a general sense of what algebra is about, or what the point of the manipulations is. After I give the response to this question, a response which will include both general and specific problem-solving ideas, I will make come comments about how a typical algebra course is structured, and why it is structured that way. I have a big exam Monday in algebra and I have no idea how to do linear equations! Can someone please help quick? Her are examples of a few that I am having problems with. 3(3 - 4x) + 30=5x - 2(6x-7) and 5x²-[2(2x²+3)]-3=x²-9 I am also having a few problems with this: x + 3 + 2x = 5 + x + 8 (5) I am supposed to figure out if 5 is the answer, and tell how I got the answer. My response: It looks to me from this last problem that you perhaps don't have an UNDERSTANDING of what doing algebra with equations is all about, which makes doing any problems a bit difficult. But let's see what we can do for you here. The following may be too much for you to absorb before your test, though I hope not; but I think it is stuff you will need to know for future tests as well, so maybe it will help you for them even if it is too much for tomorrow's test. Take the last problem first. Do you understand that if "five is the answer," that simply means that IF YOU WERE TO SUBSTITUTE 5 AS THE VALUE EVERYWHERE THERE IS AN X, THE STATEMENT THAT THE LEFT SIDE OF THE EQUATION EQUALS THE RIGHT SIDE WOULD BE TRUE? If 5 is NOT the solution, then when you make the substitution, the statement will not be true that the left side of the equation is equal to the right side. Take a simple case first: X = 27 - 4 There is only one number X can be for this statement to be true; 23, right? So 19 would NOT be a solution to this equation; that is, X cannot equal 19 and the statement still be true that the left side equals the right side. Now make it just a bit harder: X + 3 = 27 - 4 There is still only one number this can work for but it is a different number, because now we know that it is not X that equals 23, but some number that, when you add 3 to it, gives you 23. So what number gives you 23 when you add 3 to it? 20, right? That means X must be 20 in that equation. It gets a little harder when you start putting X's on both sides of the equations and add or subtract some multiplications and divisions, etc., but the idea of what is going on is the same. So if we look at the equation you gave last: if X does equal 5 in the equation x + 3 + 2x = 5 + x + 8, then that would mean 5 + 3 + 10 should equal 5 + 5 + 8. Does it? If it does, then X does equal 5; if it doesn't, then X cannot equal five. If we thought X might be some other number, such as 2, then we would have to replace X with 2 to check. Would 2 + 3 + 4 = 5 + 2 + 8? If not, then X cannot equal 2 and the above equation still be true. All the "X" does is to tell you which number it is you don't know, and the problem is something like: I have a bag with some number of cookies in it; and if we add three more cookies to the bag and then add twice as many cookies as we had in the bag to begin with we get the same number of cookies as if we had taken the bag and added 5 cookies and then 8 more. There is only one number that could be in the bag to begin with that would make this statement be true; and that number is what X represents. Now, of course, this sounds like a silly way to tell someone you had a bag of five cookies, but they make up silly problems like this so you can have practice learning the things you need to in order to learn how to solve real problems where you don't know a missing number that you need to figure out. Like in my business, I need to enter in my books how much people paid me for photographs and how much they paid for the sales tax that I have to turn in to the government. Sometimes all I have is a check to go by that has the total amount, so I need to figure out how much of it was tax and how much of it was for the photography itself. I work where I must charge 8% sales tax. If I get a check for $37.80 I have to compute how much the photography was and how much the tax was. If I let X represent the price of the photography, then I know that: X + .08X = 37.80, since that means that the price of the photograph plus 8% of the price of the photograph is equal to the amount on the check. And I thus have an equation I can solve to let me know which part of the $37.80 is for tax and which part is for me. Back to your equations. The idea is that you sometimes need to "multiply out" factors, and sometimes need to factor products into components in order to be able to get the X's and the numbers to such a point that you can see what the X is. If I told you that 3X = 9, you would know right off that X = 3, right? Well, there are strategies for getting the X's where you can tell what they are supposed to be, when you can't see it right off or any other way. Let's go back to your last equation: x + 3 + 2x = 5 + x + 8 Normally, what you need to do is to find out how many X's you have altogether and what the total quantity is that those X's altogether give you. And to do that, you normally want to try to get all the X's on one side of the equal sign and all the quantities that don't have an X in them on the other, so you can find out that, say, 3X = 9 Well, in your equation, you have 3X's and a quantity 3 on the left side, and on the right side you have 1X and 13. So we need to try to get the X's to one side and the numbers that don't have X's to the other. You have to understand that (when you see no other way to solve the problem) the most important concept, or principle, or tool is: Whenever you have any equation, where you are saying the left side = the right side you can always change either side of the equation by any amount you want to AS LONG AS YOU CHANGE THE OTHER SIDE BY THE EXACT SAME AMOUNT. That way, both sides will still be equal to each other even though both will be different from what you started with. There is a purpose for doing this with equations. (That is, if someone gives you and me the same amount of money, we can know that no matter how much money that is -- even if we don't know how much it is -- that if we each double our money, we will still have the same amount as each other. And we know that if we each triple our money and then lose half of it and then add $5 to that, we still will have the same amount as each other -- whatever that will be. No matter what you do with your money, you can know that IF I do the same thing with mine, we will still end up with the same amount of money as each other, no matter how much or how little that will be.) And, unless we see some other way to figure out the unknown quantities, such as "X", we use this principle over and over in almost every problem in order to get the X's on one side and the nonX quantities on the other. And hopefully, then, we can get to a point where we can tell what X must be equal to, since if you can get any equation into the form of so-many X's = a kabillion, you can figure out what ONE X is by dividing a kabillion by however many "so-many" is. The Purpose The difficult part is to figure out which changes to make to both sides that will be useful and helpful for you to figure out what the variables (or "unknown quantities" or "unknowns") are. Some changes will be more useful than others. Many won't be helpful at all. Normally, but not always, you want to try to do whatever manipulations will help you get down to a quantity that is equal to ONE variable, that is, one X or one Y or whatever letter(s) you chose to represent the quantity you are trying to figure out. But it is not always easy to see which manipulations might help you do even that. Understanding, combined with practice, help; but solving any particular (new) problem may also take some trial and error, a flash of insight, or some luck. So, back to your equation: x + 3 + 2x = 5 + x + 8 we added all the X's up and all the numbers up on each side of the equation, and we found out that 3X +3 = X + 13. Well, we can subtract the X on the right side in order to "get rid" of it AS LONG AS WE ALSO subtract X from the left side. Hence, we get: 2X + 3 = 13 (Or, in intuitive terms, you might see that if we DON'T add the X to the 13 on the right side, that is the same as not having added one of the X's in on the left side to begin with, which would have just given us 2 X's on that side.) If you still can't see how much X must be for this to be true, we can use the same principle, this time subtracting 3 from each side of the equation, so that we are left only with 2X = 10 (which just says that some number multiplied by 2 equals 10). If these were big numbers and you still couldn't see it, then we would divide both sides by what we are multiplying the X by (in this case "2") in order to see how much 1 X is; 5. If we had 33X = 9999, you would divide both sides by 33 in order to get what one X is. Do you get the idea here? Now we go back to the first problems: Take 3(3 - 4x) + 30=5x - 2(6x-7) first. They have added an extra wrinkle to this one, because instead of telling you how many X's you have on each side, they have told you that you have some X's that get manipulated by subtractions and multiplications, etc. So the first thing to do, usually, but not always (I'll give a counter-example at the end of all this) is "multiply out" the quantities, giving: 9 - 12X + 30 = 5X - 12X + 14 (Time out, in case you need it: do you see why it is PLUS 14 here, instead of minus 14? If not, click HERE.) Back to working out the above equation. We had it to: 9 - 12X + 30 = 5X - 12X + 14 (There are at least two ways we could proceed from here. I am going to go through the "standard" way in the text and put the non-standard way HERE.) Now it is just like the one we did before where we had some X's and some non-X quantities mixed together on each side of the equal sign. In this case we have: 39 - 12X = -7X +14 At this point we start trying to do things equally to BOTH sides of the equation in order to try to end up with all the X's on one side and all the non-X's on the other side. So we can either try to get the non-X's on the right and the X's on the left, or we can try to get the non-X's on the left and the numbers on the right. It doesn't really matter from a technical standpoint which way you choose, but from a psychological standpoint, it is usually easier to work with positive numbers than negative numbers, so instead of subtracting 39 from both sides and ending up with -25 on the right side, it is psychologically easier to subtract 14 from both sides and end up with 25 on the left: 25 - 12X = -7X Then, if you add 12X to both sides, you end up with 25 = 5X, and since that just means five times some quantity is equal to 25, you know the quantity must be 5. So X = 5. (If we had gone "the other way" and started out by subtracting 39 from both sides of the above equation, we would have got -12X = - 7X - 25, and then to get the X's all on the left, we would have had to add 7X to both sides, giving us -5X = -25, which will still mean that X = 5, but it is usually psychologically more difficult to work with and to see that way.) Now, it is important to make sure you did it right and got the right answer. To make sure you did it right, you go back to your original equation and put 5 back in wherever there is an X, and see if it comes out true: This one is something of a trick AT THE LEVEL YOUR ARE STUDYING because when you have Xsquared = something, you get TWO answers: a plus and a minus answer; e.g., if X2 = 9, X can be either plus 3 or negative 3, since (-3)(-3) = 9 just as (3)(3) does. It will turn out that when you graph equations that have squares (in their most simplified version), you don't get straight lines, so they are not straight-line or "linear" equations. So the trick here must be that either the X2 will all disappear, leaving you with a linear equation or something else will happen where you end up with something like X2= 36 and you know X will be either 6 or -6, or something else weird will happen (and it is this last thing that actually happens here -- your book or your teacher must have a sense of humor, perhaps a slightly sadistic one?). So, let's see what happens when we do all the operations in order to get to a simplified statement of the equation: 5x²-[2(2x²+3)]-3=x²-9 Multiply it all out and you get: 5X2 - [4X2 + 6] - 3 = X2- 9 X2 - 6 - 3 = X2 - 9 which is just to say that X2 - 9 = X2 - 9 or 9=9 In other words, this equation will be true for every value of X since the equation is something like: X + 12 = X + 12, which is always true, no matter what X is. Weird problem to give you. Finally, above I said that you USUALLY need to multiply out all the factors they give you, BUT you don't have to ALWAYS multiply factors out, if you happen to see that a factor is duplicated somewhere, or duplicated on each side of the equation in a way you can get rid of it. Suppose we had: 3(2x - 5) + x = 4 + 3(2x - 5) Since there is a 3(2x - 5) on both sides of the equation, we can subtract that quantity from both sides without having to figure out WHAT it is. That would give us x = 4 without having to do all the work of multiplying and regrouping and everything. Or, if you had 6(2x - 5) divided by 3(2x - 5), you can know that is equal to 2, no matter what (2x - 5) equals. The Structure of Algebra Courses Typically Typically students are taught a number of principles and manipulations that seem to many of them to have nothing to do with anything. Then they are given practice in using those principles or performing those manipulations -- principles and manipulations which may or may not make any sense to them. For example, they are taught about association and commutation, and given practice "simplifying" or "multiplying out" expressions such as a(b + c) or (a +b)(3c - 5d). They are taught the rules for "order of operations" and then given practice calculating expressions that are written without parentheses. Or they are taught to factor expressions like ax + bx into x(a+b). Or they are taught you can do the same things to both sides of an equation, as long as you do the same thing to each side.Then they are given equations to solve, which seem to use a bunch of those manipulations or principles. And finally they are given problems in words which seem to have something to do with equations and manipulations. I write the above the way I did because much of algebra seems rather arbitrary to students who do not understand the individual manipulations and principles (in algebra overall, or in a particular chapter or unit) or who do not understand their point. Some of these students will not be able to remember the manipulations well enough to do them very well; others will be able to use them rather mechanically to solve problems of a type they have been trained to solve, even though they don't really understand why one goes about those particular mechanics other than that they give you the answer the teacher likes. For both of these types of students, new problems will be particularly difficult. What is actually occurring is that it turns out there are certain (kinds of) logical, sensible, reasonable principles and manipulations that tend to be useful in solving certain kinds of problems that are the typical algebra problems, or, to put it perhaps better -- there are certain (kinds of) logical principles and manipulations that tend to be useful in solving the sorts of problems that algebra lends itself to solving. That is why students are taught these particular manipulations and ideas. It is important for students to see the logic and the sense in the principles they are taught, not just to learn the rules as some sort of arbitrary recipes. The principles themselves are logical, not arbitrary, although the way they are stated, the order in which they are introduced, and the particular ones chosen for a particular book or chapter may have been quite different. One of the important aspects taught in algebra is precision of expression, so that one can learn to express in numerical, usable form ideas or problems that normally occur first in words. The example I gave above is one such case, where I was entering checks into a ledger and needed to figure out how much of the amount on the check was for sales tax and how much was the price of the object. Another case might occur in something like baseball where a batter might want to know how many hits he may need in his next 10 at bats to raise his average to a certain level. Or you might want to know how much money you need to take on a certain car trip in order to pay cash for gasoline. Or you might want to compute how much interest you paid on your mortgage last year versus how much of what you paid went for principle. Solving these problems generally requires your being able to express the problem in numbers related to each other in some way, and then knowing how to go about manipulating the numbers. Some of the concepts apply not just to math, but to language in words. I was driving home tonight listening to a news program on the radio in which they were talking about celebrating Dr. Seuss's birthday in many schools, and in one school, a chef had prepared "green eggs and ham" in honor of the book by that name. Well, I was familiar with the book, and had read it many times to my own children. However, I was surprised when the news reporter asked the chef, after he had explained how he made the eggs green, how he had made the ham green. I was surprised because it never occurred to me that the ham was supposed to be green. I thought Green Eggs and Ham meant Ham and Green Eggs; I thought the "Green" went just with the "Eggs", not with the ham too, or not with the Eggs-And-The-Ham. To put it in math-like terms, I thought the title and story were about (Green Eggs) and Ham, not about Green (Eggs and Ham) or Green Eggs and Green Ham. When I mentioned it to my younger daughter, she put another interpretation to it -- Green Ham-and-Eggs, that is a greenish mixture of ham and eggs, not just Green Ham with Green Eggs. So now I am not sure at all what Dr. Seuss really meant, because he didn't use parentheses in the story or the book title and he didn't write about the individual components.... So part of algebra is learning the language of how to write down consistently precisely what you mean when you are trying to express or represent something numerically; it is about learning a precise language. As you learn to do this, you should be thinking about what a given numerical expression might mean if you write it one way versus another. If you do that, then numerical expressions will begin to take on meaning for you and not just be a bunch of symbols you are trying to manipulate. And if you understand their meaning, you will be able to figure out ways to manipulate them when you cannot remember by rote how to do something. For example, if you go to add 1/a to 1/b, you might be tempted to think it will come out to 2/(a+b), but if you understand that 1/a is a fraction, and that 1/b is a fraction with a different denominator, you can check to see whether you can add fractions that way by looking at fractions you know, say adding 1/2 to 1/4. You know that will be 3/4, so the question is whether your inclined way to do it will also give you three fourths. However, you will see that it gives you 2/6, which is 1/3 and is not anything near 3/4. That way you know your inclined way of adding 1/a and 1/b is not right. If you weren't thinking about what 1/a and 1/b meant, you might have gone ahead and just made the erroneous combination. At a more complex level, suppose you are doing one of those problems where it takes one guy 3 days to do a job by himself, another guy 2 days, and a third guy a day and a half, and they want to know how long it will take them all working together to do the job. If you get an answer of more than a day and a half, you know something is wrong, because that means that when the fastest guy has help, it takes him longer to do the job than it does when he is working alone. (Now, of course, some people DO slow you down when they try to help you, but that is not the intent of problems like these.) So you not only want to think about your problems and your answers in numerical terms, but what those numerical terms mean in your own language. Another tool that tends to crop up repeatedly in working problems in an algebraic way is multiplication across or through parentheses -- expressions of the sort (a+b)(c+d), or even more complicated by having more components or more multipliers. You need to be able to do these sorts of multiplications quite often in order to be able to get to the specific quantities of a certain variable (or unknown) and the quantities of non-variables. E.g., if you have some problem that starts out being expressed as 8(x + 3) - 4(x - 21)=5(x-1) + 3(4x - 2), you will likely need to multiply all that out in order to figure out how many X's equal how much. But, on the other hand, there will be times you will want to be able to factor expressions into components in order to work with them. For example, if you have (X2 - 49)/(X + 7) = 14, you can figure out pretty easily that X = 21 because any expression of the form (A2 - B2) can be factored, as you normally would be taught in an algebra class, into (A + B)(A - B), which means that the above expression will factor into (X + 7)(X - 7)/(X + 7) = 14 And that means that you can then divide the (X + 7) in the numerator by the (X + 7) in the denominator and end up with just X - 7 = 14, which means X must be 21. And if you work out (212 - 49)/(21 + 7), you will get (441 - 49)/(28), which is 392/28, which is 14, as the original equation stated. So by factoring you made it easy to calculate something that would otherwise be difficult to see or figure out. Algebra courses also often teach about the relationship between graphs, or certain kinds of lines and curves and shapes (that appear on graphs), and numerical expressions or representations of those things. I am not sure whether it is true or not, but it may be helpful to think of many branches of math as being potentially able to represent or express certain important characteristics of phenomena of all kinds in numerical and/or logical terms. Basically what you want to do when studying algebra is to make sure you understand 1) what expressions, equations, formulas, and manipulations really represent and why they are able to represent what they do, and to make sure you understand 2) how to do the sorts of manipulations they give you, AND how and why those manipulations work. And you want to ask your teacher how those representations and manipulations will likely be useful later when you get to actually working real problems, or at least the sorts of problems expressed in ordinary language in the algebra class. Then you also want to have practiced sufficient representations and manipulations sufficiently to be able, not only to understand them but, to do them fairly quickly and automatically. Otherwise what will tend to happen to you in an algebra class is that you will just try to memorize sequences of equations and their manipulations that don't really make any sense to you, but which you can memorize -- UNTIL you get too many to be able to retain or UNTIL you have to figure out WHICH MANIPULATION is the one you need at a particular time. It is one thing, for example, to be able to work out problems involving (A2 - B2) when they come at the end of a chapter teaching about (A2 - B2); it is quite another thing to be able to recognize something in that form and realize the form can be useful to you three chapters later in the book when you haven't been working specifically with that form and aren't looking just for it. Part of the reason students tend to memorize aspects of algebra that they instead ought to be trying to understand logically is that they wasted time at the beginning of algebra trying to understand "conventions" that did just need to be memorized instead of being understood logically. How mathematicians understand the use of parentheses (or their absence) is a matter of convention that just has to be learned by memory, but the consequences of that choice have to be understood logically as you practice doing different manipulations, such as adding fractions with different denominators. For example, you cannot logically add 2/3(a + b) to 3/3a + b to get 5/3a + b, because the denominators are not the same even though they look similar. Suppose, for example, that a = 4 and b = 6. The first fraction then is 2/30 and the second fraction is 3/18. And their sum is neither 5/18 nor 5/30. So, if you have a problem such as 2/4(a + 4) + 3/(3a + 2) = 7/10 and you are trying to solve to find out what "a" is, you have to know how to add the two fractions together first. That is why algebra books give you many exercises (sometimes far too many) to practice calculating or "simplifyng" manipulations such as adding fractions with unlike denominators. The manipulations may or may not be useful for solving any given problem. It will sometimes seem as though the manipulations or practice calculations have no point other than to torture students with homework. But they have a point in that they tend to be the general kinds of calculations one will need to be able to do to (easily) solve different kinds of typical problems (on tests and in real life) that require algebra to solve. So what students need to do in general in algebra courses is: 1) Learn the symbols and conventions of the language by memory and practice. This is not a matter of logic. However, understanding the need and use for the symbols and conventions sometimes is a matter of logic -- seeing what sorts of distinctions and differences necessitate the symbols and conventions. 2) Learn to do various kinds of calculations using the conventions. These are a matter of logic and understanding, prior to practicing them to help you use them better. 3) Learn to solve equations, normally by using the logical manipulations and calculations in a logical and creative manner to isolate the unknown variable on one side of the equation and its eqivalent on the other. This is a matter of insight, logic, creativity, and sometimes luck. But insight, creativity, and luck can be improved many times by practice and understanding. There is an analogy to much of this in learning computer languages, or even in building web pages with HTML codes. It is one thing to learn HTML codes or functions you can make the computer do in a given programming language, but it is quite another to see how you can build elaborate web pages or create very complex functions and utilities by simply utilizing a few simple codes or functions in ingenious combinations. Rick Garlikov (Rick@Garlikov.com) There are two ways to get this -- the short way of just following a rule (either the rule that when you multiply a negative by a negative, you get a positive; or the rule that when you subtract a negative number, that is the same thing as adding the number), and the longer way where you understand what you are doing -- which is to realize that in the above case you are subtracting (double) a-number-that-is- going-to-be-made-smaller-by 7-first. Let's look at an example in numbers first: Suppose you have 20 things and someone thinks he wants to buy 9 of them. If he does, you would have 11 left, since 20 - 9 would be 11. Now suppose someone else comes along and wants to buy some of those things but for some reason he says "I want 7 less than the last guy bought". Well, he wants 9 - 7 then, or 2. There are at least two ways you could figure out how many you will have left after this purchase: 1) you could just say, he is buying 2, and since I have 11, I will have 11 - 2 left, or 9. Or 2) you COULD say (but you probably wouldn't) that what you will have left will be 11 - (9 - 7), since (9 - 7) is in numbers what the guy told you in words that he wanted -- seven less than the last guy bought. Hence, you are subtracting 9 from the 11, BUT you are adding back the seven the guy did not want to take from you. In essence he is subtracting seven less than the first guy, so if you subtract the same amount the first guy took, you will be subtracting 7 too many. Either way it should come out the same, because either way you figure it out, it will still be that you will have 9 things left. And since, in the equation they gave you they double the quantity after they subtract something from it, it would be like the second guy's saying he wanted to have twice as many things as seven less than the other guy, which, of course is a stupid way to talk. But suppose he and his brother each have the same number of kids and that he and his brother are trying to keep up with the Joneses who have seven more kids than each of them has. So he wants to buy the same things for his kids and for his brother's kids that the Joneses buy. So he goes everywhere Jones does, and any time Jones buys something for each of his kids, he wants to buy the same number of things for his own kids and for his brother's kids. So he always tells the sales person, "whatever that guy bought, I want to buy seven fewer -- but after you figure out how much that is, I need you to double it, since I am buying the same amount for my brother as I am buying for myself." This is represented by 2(Jones' purchase - 7), and it will come out to be twice what Jones purchased, minus 14. So, if you were keeping a running inventory of what you had left, and you started with, say, 100 of these things, Jones would leave you with an inventory of (100 - Jones'purchase) and the next guy's purchase would leave you with that amount minus the following amount: 2(Jones'purchase - 7) and if you play around with some numbers, you will see that always ends up where the second purchase is 14 less than the first purchase, and therefore leaves you with 14 more items left in your inventory than if the second guy had simply bought twice what Jones did. (Return to the main text.) The equation we have arrived at is 9 - 12X + 30 = 5X - 12X + 14 Notice that 12X is subtracted on both sides of the equal sign. This means that the same amount is being taken away from both sides and therefore the rest of what is left on either side will still be equal. So instead of adding 12X to both sides, we could actually just eliminate subtracting 12X from both sides, and either way, arrive at: 9 + 30 = 5X + 14, which is to say that 39 = 5X + 14. So if we didn't add the 14 to the 5X, we would have 14 less than the 39, which would be 25; meaning that 25 = 5X, which is just to say that some quantity multiplied by 5 will give 25. And, of course, that quantity is 5. So X = 5. (return to the text) Factoring & "Multiplying Out" By "multiplying out" an expression, I simply mean taking an expression such as a(x + y) and doing the multiplication which is indicated so that you get ax + ay. Or, if we were to take an expression such as 5(15x - 4y), you would get 75x - 20y. Or if we had (3x + 2)(4x - 5), that would give us, when we "multiply it out" 12x2 - 15x + 8x - 10 or (combining the "x's")12x2 - 7x - 10. "Factoring" just means going in the opposite direction; that is, dividing a quantity into factors or components which, when multiplied together, would give you that quantity. The factors of 10 then would be 5 and 2. Factors of ax + ay would be a and (x + y) so that when you "factor" ax + ay, you get a(x + y). From the paragraph above, if you factor 12x2 - 7x - 10, you get (3x + 2)(4x - 5). Multiplying out expressions is pretty much just a mechanical procedure where you multiply each of the terms times the other terms and then combine the "like" or similar terms -- numerical quantities, quantities with the same variables to the same power, etc.; but factoring takes some insight, and often a great deal of luck in seeing combinations. For example, it is not easy to see that the above expression 12x2 - 7x - 10 even factors, let alone see what the factors are. If you have been doing "factoring problems" in a text book chapter, you start to see patterns that the author has begun to use, or that are stereotypical in textbooks, but those are not usually in your mind when you are working real problems later and get into an expression that is factorable but not obviously so. (return to text) Sometimes you can do a problem without having to go through lots of manipulations because you can see the answer right off. Physicist Richard Feynman, when he was in high school, answered a difficult algebra problem immediately during a math tournament, without doing ANY algebra or math at all. It was something of the sort where a rowing team during practice is rowing upstream against a current that is moving 4 mph relative to the shore. They are making progress relative to the shore at the rate of 1.5 mph. The hat of the guy in the back of the boat falls off into the river without his realizing it, and it floats downstream with the current. After 15 minutes they realize they have lost the hat, and immediately begin rowing back downstream to retrieve the hat. If they row with the same strength or power they were rowing upstream, now that they have the current going with them, how long will it take them to retrieve the hat? Feynman saw immediately that it was 15 minutes because he realized that all the rates relative to the shore were irrelevant to the result, just as when you drive west on an open stretch of level road for an hour and then drive back at the same rate, it doesn't take you longer to go one direction rather than the other, even though the earth is turning eastward at the rate of approximately 1000 mph (near the equator). I found out, through a different, counter-intuitive, "trick" problem one time that not only is the circumference of any circle six and a quarter times its radius, but that when you increase the radius of any circle any amount, you thereby increase the size of its circumference by roughly 6.25 times that amount. Therefore, if you tell me that you added 10 inches to the radius of a dime, or 10 inches to the radius of the universe (assuming it is round, which may not be true, of course), I know that you have increased the circumference of each by the same amount -- roughly 62.5 inches. Of course, in an algebra course, teachers won't tend to accept such reasoning, and want to see a "mathematical proof" -- which can be given for both of these cases; but I am simply saying that in real life, one does not necessarily need to solve what look like algebra problems in an "algebraic way". The idea in real life is to solve problems however you can. Algebraic manipulations -- particularly standard cookbook manipulations -- are just one way to solve certain kinds of problems. Feynman himself seemed to hold that the algorithmic or cookbook types of rules one learns in algebra class are really just rules for people to follow who don't really understand mathematical thinking. I wouldn't go quite that far, but I would say that following such rules is only one way to solve many (apparently) mathematical problems. (Return to text.) These are what are usually called "word problems" because they are logical/numerical problems expressed in ordinary language. They are attempts at giving you some practice in solving problems the way they supposedly appear in real life, since real life problems don't appear already set up in formulas or equations. However, unfortunately, real life problems also don't appear formulated as structured as word problems do; and they don't appear at the end of a unit so that you get an arbitrary, circumstantial, clue to what is expected. (return to text) Languages are "conventions" because what words or phrases or marks on paper mean is what people decide they mean or what they happen to grow to mean. There are private conventions, such as secret codes, and public conventions such as ordinary languages. There are also private conventions for individuals. For example, if you are measuring and sawing wood, you might mark the length of the wood to be cut by putting your mark even with the end of your measuring tape, or you might put the mark just outside the measuring tape. Either way is fine, as long as you know when you go to cut the wood, which way you chose to make the mark. If you made your mark even with the end of the measuring tape but cut the wood inside of that mark because you thought you had made the mark on the outer edge of the tape, your wood will be a fraction shorter than you intended. So it is important to remember what your mark really means. You can do this by remembering how you do things each time you do them, even if you do them differently each time. Or, usually easier, you choose a way to do it every time and then do it that way each time, and there is less to remember. You have developed a convention for yourself. In math and science, ambiguities of ordinary verbal language (such as in the "Green Ham and Eggs" case) are tried to be eliminated by developing and improving as necessary, precise symbols that have very specific meanings. This is intended to prevent confusion in communicating to others what you are doing. But it also helps you keep straight yourself what you are doing, by not having to remember each time what you meant by using a specific symbol. Conventions have something of an arbitrary nature, however, though once developed they might have some sort of logic or psychological sense of appropriateness or seeming reasonableness of their own. They are arbitrary in that we could have used any symbol to designate what we want to designate. And in some cases how we use them is arbitrary. For example, in algebra, "3x + 1" is understood by convention to mean the quantity that is one more than the product of 3 times the variable "x", rather than the product of three times the number which is one larger than x. If "x" were 8, "3x + 1" is 25 in the way the convention or language of algebra is used because it is 3 times 8, which is 24 and then 1 is added to give 25. But if there were no such convention, someone might take it to be equivalent to 27, because they thought it meant 3 times the sum of eight and one, which would be 3 times 9. In algebraic notation, that is to say that "3x + 1" just is designated to mean the same thing as "(3x) + 1" rather than "3(x + 1)". Without that convention "3x + 1" would be ambiguous and possibly mean different things to different people, or you might use it one way when setting up a problem and then mistakenly think it meant something else when working the problem -- as when you accidentally forget to keep the parentheses when going from one step to the next while solving a problem and then get the wrong answer. In algebra, sometimes they state conventions in ways that make it sound like they are a conclusion to some sort of logic rather than merely an arbitrary convention or choice that was once made. This confuses students who are trying to understand "why" something is the way it is when, in fact, there is no logical reason, because it is simply a convention. For example, using the "x" below to mean simply the multiplication symbol (not an unknown variable) some teachers at the beginning of algebra will ask students what the answer is to something like 3 + 5 x 8 - 2 x 3 Many students might say it is 186 because they just did the steps in the order they were given: 3 + 5 is 8, then 8x8 is 64, and subtracting 2 gives 62, and then multiplying that by 3 is 186. That is certainly logical. But the teacher will often say, "No, the answer is 37" and give as the reason that "Because in algebra, you always do the multiplications and divisions first and then do the additions and subtractions." So the problem becomes 3 + 40 - 6, which is 37. When stated that way, it leaves many students asking "Why?" in the sense of how that works. But it doesn't "work" in the sense of being a matter of logic. It is only true because that is the convention that was established. It could have been established that you do calculations in order unless there are parenthesis grouping quantities together, but it just wasn't. Neither way is necessarily better than the other, but once one way is picked, if you want to communicate with others, you need to use the conventions they understand. It is like driving on the right or left side of the road. It is not that there is some reason for one side's being better than the other -- if we are going to choose, as a society, from the very beginning; but once a choice is made, it is better to abide by the choice so you don't run into others. Sometimes conventions are not as clear as they ought to be. Crosswalks, for example, in some places mean that pedestrians already walking in them have the right of way and cars need to stop for them. But in some places, they mean that cars have to stop for pedestrians on the curb at a crosswalk who have not yet even stepped into the street. That is a very dangerous ambiguity for pedestrians who think the crosswalk means they can step off the curb without even stopping or looking if approaching drivers think it means there is no reason to slow down because the pedestrian will surely stop walking when he gets to the curb and wait till there are no cars approaching before he begins to cross the street. But conventions, once established, also have a resulting logic that is not arbitrary. For example, because the English drive on the left side of the road, and Americans drive on the right side of the road, the way they each have to make right or left turns from two-way streets onto two-way streets in their own countries is different. When Americans turn right, they stay near the curb. When they turn left, they have to "swing wide" to get to the right side of the street onto which they are turning. The English have to do just the opposite, hugging the curb lane to make left turns and swinging wide to the outside lane to make right turns. That is a logical result of choosing which side of the road to drive on, even though the choice itself had no logic but was simply a matter of convention. Moreover, there is another logical result of the convention. Although we are taught to look both ways before crossing a street, we tend to look one way, toward the traffic approaching on the curb side, as we step off the curb; and we look the other way as we get to the center of the street. In America, one generally then looks left before stepping off the curb, and right once one gets to the middle of the street. In England, that can put you in front of a bus, because the traffic next to the curb is coming from your right, not your left; and the traffic on the far side of the center line is coming from your left not your right. The English have the same problem in reverse when they are in America. That is a very difficult habit to overcome when visiting the other country and walking across streets. But the reason you have to look the way you do as you cross a street is a logical result of the side of the road the country chose to have drivers use. So conventions which are arbitrary, nevertheless can have consequences that logically depend on them. (Return to text.)
Secondary Solutions Our collaborative textbooks will engage your students. One way to motivate students is to deliver math instruction in a collaborative learning environment. This approach helps students spend more time being active learners during class periods as they interact with their peers to solve problems together. We use real-world situations in our math problems, which helps students to see how math is relevant in their daily lives. And our math problems are designed to emphasize connections between verbal, numeric, graphic and algebraic representations. Carnegie Learning develops and publishes textbooks to support a collaborative classroom. Our classroom activities address both mathematical content and process standards. Students develop skills to work cooperatively to solve problems. Additionally, they improve their reasoning, sense making and communication skills. Our consumable textbooks provide an opportunity for extended investigations, analysis and alternate solution paths. Each student is given a text that they can write in whether it is taking notes, highlighting key data in a problem, solving a problem, or writing complete sentences to describe problem solving strategies program has changed my life in that I am no longer intimidated by math. I'm no longer afraid to ask for help. And it's given me a more positive outlook in learning in my college career. Because if I can do this, I can do anything.
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Editorial Reviews From The Critics This textbook reviews the mathematical symbols and operations of algebra, and reinforces function and graphing concepts for future courses. The authors cover polynomial, rational, radical, exponential, and logarithmic equations, and both linear and nonlinear systems. The eighth edition introduces functions and graphs of linear equations earlier in the text. Annotation c. Book News, Inc., Portland, OR (booknews.com) Booknews New edition of a text that overlaps between typical beginning and intermediate algebra texts. Lial (American River College) and Hornsby (U. of New Orleans) have organized the 14 chapters to accommodate the early introduction of functions and graphing lines in a rectangular coordinate system, thus providing students with important concepts that will be an integral part of later mathematics courses. Subsequent chapters cover linear equations, lines and graphing, lines and inequalities, sequences and series, and other related
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The word "advanced" in the title of this book can be interpreted in two ways. On the one hand, the book discusses topics in linear algebra (canonical forms, bilinear and sesquilinear forms, matrix Lie groups, etc.) that are rarely taught in an introductory course. On the other hand, even when discussing topics that are usually considered elementary, the book does so in a theoretical, sophisticated way, generally eschewing the kind of routine calculations that are so common in introductory linear algebra books in favor of carefully defined terms and precise statements (and proofs) of theorems, often presented at a fairly high level of generality. This approach is evident even in the very first chapter, on vector spaces and linear transformations. Vector spaces are not assumed finite-dimensional, and are defined over an arbitrary field rather than the field of real or complex numbers. The term "field" is not defined in the text, thereby making it clear even from page 1 that the author assumes that the reader has some background in abstract algebra. Zorn's Lemma is also assumed, and used to prove the existence of a basis for an arbitrary vector space V. Likewise, the author's discussion of the fact that two bases for V have the same number of elements also does not assume finite-dimensionality (though things are simplified somewhat by not distinguishing between cardinalities of infinite sets). This chapter also discusses dual (and double dual) spaces and the dual T* of a linear transformation T. After a chapter addressing coordinates and the matrix of a linear transformation, (including discussion of change of basis and the matrix of the dual transformation), the book moves to determinants, which are initially given a somewhat nonstandard axiomatic geometric definition: axioms are given for the concept of a "volume function" which associates to every n x n matrix a real number (representing the volume of the "parallelogram" spanned by the columns of the matrix). It is shown that a volume function exists and is unique up to scaling, and the determinant of a square matrix A is defined to be the image of A under that volume function (scaled, of course, so that the volume of the unit n-cube is 1). This definition is immediately followed by two sections, giving a more traditional characterization of determinants and setting out the basic facts about them. The chapter then concludes with three sections discussing topics not generally seen in elementary courses: the first discusses determinants and invertibility of integer matrices, the second discusses orientation in real vector spaces (via a detour through the topology of the general linear group in which the connected components of the group GLn(R) are characterized; knowledge of the topological ideas is assumed), and the third discusses (without proof) some basic facts about Hilbert matrices. This approach to determinants reflects a fairly common theme: the author frequently gives nonstandard definitions of topics and then proves the equivalence to the usual definition. For example, to define the product of two matrices A and B (of appropriate sizes) the author takes the composition of the linear transformations defined by A and B and defines AB to be the matrix corresponding to this composition. Likewise, the transpose of a matrix A is defined as the matrix corresponding to the dual of the transformation induced by A. Whether any enhanced motivation and insight given by this approach justifies the departure from standard definitions is, of course, a matter of individual taste. The next two chapters address the structure of linear transformations via eigenvalues and canonical forms. The first of these chapters provides a very succinct and efficient development of eigenvectors and generalized eigenvectors (developed in tandem), the minimal and characteristic polynomials of a matrix, diagonalizability and triangularizability, and then culminates in a section relating these concepts to the theory of linear differential equations. The next chapter (the longest and, I thought, most difficult) addresses the Jordan and rational canonical forms of a matrix. (The approach here is by invariant subspaces; in an appendix, the author discusses the module-over-a-PID approach to this topic.) An algorithm for computing the Jordan form of a matrix (whose characteristic polynomial is given as the product of linear factors) is provided, as are several very helpful, rather non-trivial, examples, worked out in some detail. It would have been nice, though, to see more applications of the material in this chapter; for example, it would not have taken much additional exposition to prove the interesting result that any square matrix is similar to its transpose, but this does not appear. Chapters 6 and 7 discuss, respectively, forms (bilinear, sesquilinear, quadratic) and their classification, and inner products on real and complex vector spaces. Unlike many books on quadratic forms (e.g., Lam's Introduction to Quadratic Forms Over Fields) the author here does not adopt the blanket assumption that char F ≠ 2. The discussion of inner products in chapter 7 addresses many familiar topics (Gram-Schmidt, normal and unitary operators, spectral theorem), done clearly and succinctly, with attention paid to the infinite-dimensional situation and nice applications to analysis and topology given. A final section discusses singular values; consistent with the author's strong belief that linear algebra "is about vector spaces and linear transformations, not matrices" (about which, more later) the standard decomposition A = U∑VT does not, however, appear; everything is phrased in terms of eigenvalues of transformations. The final chapter is entitled "Matrix Groups as Lie Groups". Recent years have seen the publication of a number of books (Stillwell's Naive Lie Theory being an excellent example) that attempt to make the rudiments of Lie theory accessible to a broader audience by working with matrix groups rather than general Lie groups, thereby exposing the reader to the ideas of Lie theory in a concrete (but reasonably general) setting, letting linear-algebraic arguments replace more difficult manifold-theoretic ones. Given that this is a book on linear algebra, I expected, when I saw the title of this chapter, that it was intended to do the same. However, the chapter begins with the definition of a Lie group (the author assuming knowledge of the definition of differentiable manifold and other facts about differential topology) and consists primarily of the definitions of various classical matrix groups and proof that they are Lie groups. Aside from the fact that many people who have studied differentiable manifolds probably have already seen most or all of these examples, this chapter seems like a lost opportunity to showcase the utility of linear algebra in learning something about Lie theory, perhaps by talking about the exponential of a matrix and the Lie algebra corresponding to a matrix group. I enjoyed reading this book and more than once found myself admiring the exposition, but I am not sure I know just who its intended audience is. Since there are no exercises at all, it seems not to be intended as a text; the fact that a number of terms are given non-standard definitions may also limit its value in this regard. The book's value as a reference may be limited by the choice of topics. As noted earlier, the author firmly believes that linear algebra is not about matrices; he says so both in the preface and the body of the text. People are of course entitled to their opinion as to whether linear algebra is best approached from the operator-theoretic or matrix-theoretic viewpoint, but it seems a bit odd to baldly assert as fact a statement like this, particularly given that (a) much of the area of numerical linear algebra is concerned with matrices, (b) many people do research in matrix theory and consider themselves linear algebraists, and (c) journals like Linear Algebra and its Applications run lots of articles about matrices. In any event, a number of matrix-oriented topics (Perron-Frobenius, Rayleigh-Ritz, Courant-Fischer, Gershgorin) that are covered in some graduate linear algebra courses are not mentioned in this book at all, thereby making this book less attractive as a potential resource for graduate students preparing for qualifying examinations. However, students preparing for exams that do not cover these topics, or mathematicians not specializing in linear algebra who want a concise reference for the topics that are covered, might well find this book worth a serious look. Mark Hunacek teaches mathematics at Iowa State University. After near-simultaneous acquisitions of both a PhD and a wife, he solved the "two body problem" in his family by going to law school and then becoming an Assistant Attorney General for the state of Iowa while his wife pursued a career as a mathematics professor. He is happy to report, however, that he has now retired from the practice of law and returned to the fold of mathematics teaching (but he also teaches a course in engineering law for old time's sake.)
This page covers content that you need to learn for the Welsh Board (WJEC) Foundation GCSE in Mathematics. If you are entered for GCSE Foundation, you can achieve up to a grade C. You will sit the papers at the end of your course. This may be in November or in June (usually in Year 11, but you may sit it early in Year 10). There are two papers, each one hour and 45 minutes long. Paper 1 is the non-calculator paper, and Paper 2 is the calculator paper. Each paper is out of 100 and each is worth 50% of your mark. If you are studying Higher, it is expected that you will also be able to do all of the topics on the Foundation list. GCSE Foundation Topic List by Grade Check the list of topics below to find out what you need to learn for each grade. If you are aiming for a C, you will need to know it all! Topics with stars at the start do not come up very frequently (but make sure you learn them in case they do!). Grade G Topics Number Rounding to the nearest whole number. Rounding to the nearest 10, 100 and 1000. Identifying fractions and percentages from a shaded diagram. Calculating simple fractions of quantities. Ordering decimals. Ordering, reading and writing whole numbers using place value. Writing simple fractions as ratios. Algebra Using coordinates in one quadrant. Reading from simple real-life graphs. Finding the next term in a simple linear sequence. Shape Finding perimeters, areas and volumes by counting squares or cubes. Drawing and naming 2D shapes. Measuring and drawing lines. Drawing circles using compasses. Naming parts of a circle. Drawing lines of symmetry on a diagram. Reflecting a shape in a given line of symmetry. Making accurate drawings of given shapes. Choosing appropriate (metric) units for measurement. Data Finding median and mode (single digits only). Drawing and interpreting bar charts. Drawing and interpreting line graphs. Drawing and interpreting pictograms. Making tables (e.g. tally tables), lists and charts from discrete data. Being able to choose the most likely outcome from a given set of outcomes. Interpreting bills and timetables. Grade F Topics Number Multiplying a three digit number by a two digit number. Dividing a three digit number by a two digit number. Calculating simple percentages of quantities. Calculating fractions of quantities. Understanding the order of operations (BIDMAS). Rounding to a given number of decimal places. Understanding place value. Finding squares, cubes and roots. Finding factors of a number. Converting between fractions, decimals and percentages. Using negative numbers in context. Algebra Finding terms in a linear sequence. Recognising non-linear number sequences. Using coordinates in four quadrants. Using simple formulae. Solving simple equations (such as 3x = 18 or x + 3 = 5). Deriving simple expressions. Shape Estimating lengths. Using simple scale drawings. Naming, measuring and drawing angles. Naming polygons. Identifying lines of symmetry. Identifying rotational symmetry. Using the fact that the angle sum on a straight line is 180 degrees. Identifying faces, edges and vertices. Data Working out simple probabilities. Listing all possible outcomes for one event. Estimating probability from diagrams and charts. Finding the range (and comparing two distributions). Finding mean and mode. Interpreting pie charts. Using bar charts to compare two sets of data. Images on this website, unless otherwise credited, are in the public domain or provided by Classroom Clipart. Unless otherwise stated, all other work on this website is the intellectual property of C. Norledge. Feel free to download and photocopy resources I have created, but please do not alter or redistribute without prior permission. All rights reserved.
This work is an introduction to mathematical analysis at an elementary level. Emphasis is given to the construction of national and then real numbers, using the method of equivalence classes and of Cauchy sequences. The text includes the presentation of: sequences of real numbers, infinite numerical series, continuous functions, deriviatives and Ramon-Darboux integration. There are also sections on convex functions and on metric spaces, as well as an elementary appendix on logic, set theory and functions.
Math Advantage Product Information Advantage™ provides an interactive learning experience and the tools students need to gain learning confidence and improve their grades. Help your child build a solid academic foundation with Math Advantage, a complete student resource center that combines lessons, exercises and quizzes with additional learning resources to support and motivate your child in reaching his or her full academic potential. The ADVANTAGE™ Approach to Effective Learning: ENGAGE: Interactive learning experience engages the student REINFORCE: Standards-driven lesson plan reinforces classroom learning SUPPORT: Study aids & reference tools support the learning experience MOTIVATE: Brain-building games add fun to studying Student Benefits Learn At Your Own Pace Build Critical Skills Identify Problem Areas Review Lessons As Needed Pre-Algebra Get a head start in Algebra with an engaging introduction to algebraic symbols, variables and expressions. Mixed Numbers Ratios & Proportions Scientific Notation Order of Operations Formulas & Substitution Algebra I & II Develop a firm understanding of algebraic concepts and learn how to apply them in solving complex problems. Expressions & Equations Absolute Values Lines, Slopes & Intercepts Proportions & Inequalities Polynomials & Functions Geometry Master Geometry at your own pace with detailed lessons and practice exercises that reinforce learned skills. Reasoning & Equality Lines & Angles Circles & Triangles Quadrilaterals Transformations Trigonometry Improve your knowledge of trigonometric functions, identities and more through interactive lessons and exercises that teach the fundamentals. Complex Numbers Functions & Equations Pythagorean Theorem Laws of Sines Laws of Cosines Statistics & Probability Learn how to collect, analyze and present complex data in a clear and concise manner. Mean, Median & Mode Standard Deviation Sampling Theory Correlation & Regression Plots & Graphs Calculus Develop a clearer understanding of Calculus with the help of simplified explanations and detailed examples. Limits & Continuity Derivatives Sequences & Series Common Graphs Functions & Equations PLUS: Brain-Building Games and iPod® Study Materials! * The Advantage Money Back Guarantee If your grade-point-average within the core subjects does not improve from one report card to the next after using the Advantage products, return this product within 180 days of the date of purchase and we will gladly refund your money OR if for any reason you are not completely satisfied with this product, return this product within 30 days of the date of purchase and we will refund your money. See complete details inside the box.
Introduction to Fitting Things In Spaces: If you aren't the greatest at maximizing closet space, you may have some direct experience being frustrated by this one. It will often come in handy to know how much room you are working with, and how much of a certain object or material can possibly go there. Sample Problem Shin is building a shelf to put over his desk and hold his books. Each book is of an inch thick. Okay, they're issues of Vogue, but same difference. The board Shin is using is 2 ft long. How many "books" can Shin fit on the shelf? This problem can be turned into an inequality. We're turning it into an inequality rather than an equation, because we might have a little space left over on the shelf. Let x be the number of "books" on the shelf. We'll stop putting quotes around "books" now, since it's exhausting. Paying attention to units, we see the shelf is 24 inches long. Taking this information and writing it in symbols, we find that Now that we have this inequality, we can forget about books for the time being and solve the inequality. To do this, we multiply both sides by to find that and simplify to find that x ≤ 32 Now we need to think about books again. Sorry. It'll all be over soon. This answer means Shin can fit up to 32 books on his shelf. Okay, you can stop thinking about books now. We told you it would fly by. Algebra could also be used to figure out how many cars you can fit in a parking lot, how many boxes of cereal you can fit on a shelf, how many airplane runways you could fit on a piece of land, or how many full-sized marshmallows you can fit in your mouth without choking. Don't try this at home. In the next section we will be dealing a lot with specific practical applications of algebra. In the meantime, rest assured that algebra is useful.
98102350Precalculus Engineers looking for an accessible approach to calculus will appreciate Young s introduction. The book offers a clear writing style that helps reduce any math anxiety they may have while developing their problem-solving skills. It incorporates Parallel Words and Math boxes that provide detailed annotations which follow a multi-modal approach. Your Turn exercises reinforce concepts by allowing them to see the connection between the exercises and examples. A five-step problem solving method is also used to help engineers gain a stronger understanding of word problems
Mathematics - Algebra (529 results) The purpose of this book, as implied in the introduction, is as follows: to obtain a vital, modern scholarly course in introductory mathematics that may serve to give such careful training in quantitative thinking and expression as well-informed citizens of a democracy should possess. It is, of course, not asserted that this ideal has been attained. Our achievements are not the measure of our desires to improve the situation. There is still a very large "safety factor of dead wood" in this text. The material purposes to present such simple and significant principles of algebra, geometry, trigonometry, practical drawing, and statistics, along with a few elementary notions of other mathematical subjects, the whole involving numerous and rigorous applications of arithmetic, as the average man (more accurately the modal man) is likely to remember and to use. There is here an attempt to teach pupils things worth knowing and to discipline them rigorously in things worth doing.<br><br>The argument for a thorough reorganization need not be stated here in great detail. But it will be helpful to enumerate some of the major errors of secondary-mathematics instruction in current practice and to indicate briefly how this work attempts to improve the situation. The following serve to illustrate its purpose and program:<br><br>1. The conventional first-year algebra course is characterized by excessive formalism; and there is much drill work largely on nonessentials. Florian Cajori's A History of Mathematics is a seminal work in American mathematics. The book is a summary of the study of mathematics from antiquity through World War I, exploring the evolution of advanced mathematics. As the first history of mathematics published in the United States, it has an important place in the libraries of scholars and universities. A History of Mathematics is a history of mathematics, mathematicians, equations and theories; it is not a textbook, and the early chapters do not demand a thorough understanding of mathematical concepts. The book starts with the use of mathematics in antiquity, including contributions by the Babylonians, Egyptians, Greeks and Romans. The sections on the Greek schools of thought are very readable for anyone who wants to know more about Greek arithmetic and geometry. Cajori explains the advances by Indians and Arabs during the Middle Ages, explaining how those regions were the custodians of mathematics while Europe was in the intellectual dark ages. Many interesting mathematicians and their discoveries and theories are discussed, with the text becoming more technical as it moves through Modern Europe, which encompasses discussion of the Renaissance, Descartes, Newton, Euler, LaGrange and Laplace. The final section of the book covers developments in the late 19th and early 20th Centuries. Cajori describes the state of synthetic geometry, analytic geometry, algebra, analytics and applied mathematics. Readers who are not mathematicians can learn much from this book, but the advanced chapters may be easier to understand if one has background in the subject matter. Readers will want to have A History of Mathematics on their bookshelves. The present work contains a full and complete treatment of the topics usually included in an Elementary Algebra. The author has endeavored to prepare a course sufficiently advanced for the best High Schools and Academies, and at the same time adapted to the requirements of those who are preparing for admission to college.<br><br>Particular attention has been given to the selection of examples and problems, a sufficient number of which have been given to afford ample practice in the ordinary processes of Algebra, especially in such as are most likely to be met with in the higher branches of mathematics. Problems of a character too difficult for the average student have been purposely excluded, and great care has been taken to obtain accuracy in the answers.<br><br>The author acknowledges his obligations to the elementary text-books of Todhunter and Hamblin Smith, from which much material and many of the examples and problems have been derived. He also desires to express his thanks for the assistance which he has received from experienced teachers, in the way of suggestions of practical value. Bringing to life the joys and difficulties of mathematics this book is a must read for anyone with a love of puzzles, a head for figures or who is considering further study of mathematics. On the Study and Difficulties of Mathematics is a book written by accomplished mathematician Augustus De Morgan. Now republished by Forgotten Books, De Morgan discusses many different branches of the subject in some detail. He doesn't shy away from complexity but is always entertaining. One purpose of De Morgan's book is to serve as a guide for students of mathematics in selecting the most appropriate course of study as well as to identify the most challenging mental concepts a devoted learner will face. "No person commences the study of mathematics without soon discovering that it is of a very different nature from those to which he has been accustomed," states De Morgan in his introduction. The book is divided into chapters, each of which is devoted to a different mathematical concept. From the elementary rules of arithmetic, to the study of algebra, to geometrical reasoning, De Morgan touches on all of the concepts a math learner must master in order to find success in the field. While a brilliant mathematician in his own right, De Morgan's greatest skill may have been as a teacher. On the Study and Difficulties of Mathematics is a well written treatise that is concise in its explanations but broad in its scope while remaining interesting even for the layman. On the Study and Difficulties of Mathematics is an exceptional book. Serious students of mathematics would be wise to read De Morgan's work and will certainly be better mathematicians for it. This text is prepared to meet the needs of the student who will continue his mathematics as far as the calculus, and is written in the spirit of applied mathematics. This does not imply that algebra for the engineer is a different subject from algebra for the college man or for the secondary student who is prepared to take such a course. In fact, the topics Avhich the engineer must emphasize, such as numerical com)utations, checks, graphical methods, use of tables, and the solution of specific problems, are among the most vital features of the subject for any student. But important as these topics are, they do not comprise the substance of algebra, which enables it to serve as part of the foundation for future work. Rather they furnish an atmosphere in which that foundation may be well and intelligently laid. The concise review contained in the first chapter covers the topics which have direct bearing on the work which follows. No attempt is made to repeat all of the definitions of elementary algebra. It is assumed that the student retains a certain residue from his earlier study of the subject. The quadratic equation is treated with unusual care and thoroughness. This is done not only for the purpose of review, but because a mastery of the theory of this equation is absolutely necessary for effective work in analytical geometry and calculus. Furthermore, a student who is well grounded in this particular is in a position to appreciate the methods and results of the theory of the general equation with a minimum of eii ort. The theory of equations forms the keystone of most courses in higher algebra. The chapter on this subject is developed gradually, and yet with pointed directness, in the hope that the processes which students often perform in a perfunctory manner will take on additional life and interest. Isaac Todhunter's Algebra for Beginners: With Numerous Examples is a mathematics textbook intended for the neophyte, an excellent addition to the library of math instructionals for beginners. Todhunter's textbook has been divided into 44 chapters. Early chapters highlight the most basic principles of mathematics, including sections on the principal signs, brackets, addition, subtraction, multiplication, division, and other topics that form the foundation of algebra. Simple equations make up the large majority of the material covered in this textbook. Later chapters do introduce quadratics, as well as other more advanced subjects such as arithmetical progression and scales of notation. It is important to note that Todhunter sticks very much to the basics of algebra. The content of this book lives up to its title, as this is very much mathematics for beginners. The content is provided in an easy to follow manner. This book could thus be used for independent learning as well as by a teacher. A great deal of focus has clearly been given to providing examples. Each concept is accompanied by numerous sample questions, with answers provided in the final chapter of the book. The example questions are every bit as important as the explanations, as one cannot begin to grasp mathematical concepts without having the opportunity to put them into practice. The basics of algebra are explained in an easy to follow manner, and the examples provided are clear and help to expand the knowledge of the learner. If given a chance, Isaac Todhunter's Algebra for Beginners: With Numerous Examples can be a valuable addition to your library of mathematics textbooks. The orientalists who exploited Indian:-histC Ty a Ul literature about a century ago were not always perfect in their methods of investigation and consequently promulgated many errors. Gradually, however, sounder methods have obtained and we are now able to see the facts in more correct perspective. In particular the early chronology has been largely revised and the revision in some instances has important bearings on the history of mathematics and allied subjects. According to orthodox Hindu tradition the Surya Siddhanta, the most important Indian astronomical work, was composed over two million years ago! Bailly, towards the end of the eighteenth century, considered that Indian astronomy had been founded on accurate observations made thousands of years before the Christian era. Laplace, basing his arguments on figures given by Bailly considered that some 3, 000 years B.C. the Indian astronomers had recorded actual observations of the planets correct to one second; Playfair eloquently supported Bailly sviews ;Sir William Jones argued that correct observations must have been made at least as early as 1181 B.C.; and so on; but with the researches of Colebrooke, Whitney, Weber, Thibaut, and others more correct views were introduced and it was proved that the records used by Bailly were quite modem and that the actual period of the composition of the original Surya Siddhanta was not earliar than A.D.400. It may, indeed, be generally stated that the tendency of the early orientalists was towards antedating and this tendency is exhibited in discussions connected with two notable works, the Sulvasutras and the Bakhshali arithmetic, the dates of which are not even yet definitely fixed. In preparing this work the author has been prompted by many reasons, the most unportant of which are: The dearth of short but complete books covering the fundamentals of mathematics. The tendency of those elementary books which begin at the beginning to treat the subject in a popular rather than in a scientific manner. Those who have had experience in lecturing to large bodies of men in night classes know that they are composed partly of practical engineers who have had considerable experience in the operation of machinery, but no scientific training whatsoever; partly of men who have devoted some time to study through correspondence schools and similar methods of instruction; partly of men who have had a good education in some non-technical field of work but, feeling a distinct calling to the engineering profession, have sought special training from night lecture courses; partly of commercial engineering salesmen, whose preparation has been non-technical and who realize in this fact a serious handicap whenever an important sale is to be negotiated and they are brought into competition with the skill of trained engineers; and finally, of young men leaving high schools and academies anxious to become engineers but who are unable to attend college for that purpose. Therefore it is apparent that with this wide. The theory of linear associative algebras (or closed systems of hypercomplex numbers) is essentially the theory of pairs of reciprocal linear groups (52) or the theory of certain sets of matrices or bilinear forms (53). Beginning with Hamilton's discovery of quaternions seventy years ago, there has been a rapidly increasing number of papers on these various theories. The French Encyclopedia of Mathematics devotes more than a hundred pages to references and statements of results on this subject (with an additional part on ordinary complex numbers). However, the subject is rich not merely in extent, but also in depth, reaching to the very heart of modern algebra.<br><br>The purpose of this tract is to afford an elementary introduction to the general theory of linear algebras, including also non-associative algebras. It retains the character of a set of lectures delivered at the University of Chicago in the Spring Quarter of 1913. The subject is presented from the standpoint of linear algebras and makes no use either of the terminology or of theorems peculiar to the theory of bilinear forms, matrices, or groups (aside of course from 52-54, which treat in ample detail of the relations of linear algebras to those topics).<br><br>Part I relates to definitions, concrete illustrations, and important theorems capable of brief and elementary proof. A very elementary proof is given of Frobenius's theorem which shows the unique place of quaternions among algebras. The remarkable properties of Cayley's algebra of eight units are here obtained for the first time in a simple manner, without computations. Other new results and new points of view will be found in this introductory part.<br><br>In presenting in Parts II and IV the main theorems of the general theory, it was necessary to choose between the expositions by Molien, Cartan and Wedderburn (that by Frobenius being based upon bilinear forms and hence outside our plan of treatment). Bertrand Russell was a British logician, nobleman, historian, social critic, philosopher, and mathematician. Known as one of the founders of analytic philosophy, Russell was considered the premier logician of the 20th century and widely admired and respected for his academic work. In his lifetime, Russell published dozens of books in wildly varying fields: philosophy, politics, logic, science, religion, and psychology, among which The Principles of Mathematics was one of the first published and remains one of the more widely known. Although remembered most prominently as a philosopher, he identified as a mathematician and a logician at heart, admitting in his own biography that his love of mathematics as a child kept him going through some of his darkest moments and gave him the will to live. With his book The Principles of Mathematics, Russell aims to instill the same deep seated passion for mathematics and logic that he has carefully cultivated in the reader. He adeptly explores mathematical problems in a logical context, and attempts to prove that the study of mathematics holds critical importance to philosophy and philosophers. Russell utilizes the text to explore the some of the most fundamental concepts of mathematics, and expounds on how these building blocks can easily be applied to philosophy. In the second part of the book, Bertrand addresses mathematicians directly, discussing arithmetic and geometry principles through the lens of logic, offering yet another unique and groundbreaking interpretation of a field long before considered static. This book affords new insight and application for many basic mathematical concepts, both in roots of and application to other fields of scholarly pursuit. Russell uses his book to establish a baseline of mathematical understanding and then expands upon that baseline to establish larger and more complex ideas about the world of mathematics and its connections to other fields of personal interest. The Principles of Mathematics is a very captivating glimpse into the logic and rational of one of history's greatest thinkers. Whether you're a mathematician at heart, a logician, or someone interested in the life and thoughts of Bertrand Russell, this book is for you. With an incredible amount of information on mathematics, philosophy, and logic, this text inspires the reader to learn more and discover the ways in which these very disparate fields can interconnect and create new possibilities at their intersections. This tract is intended to give an account of the theory of equations according to the ideas of Galois. The conspicuous merit of this method is that it analyses, so far as exact algebraical processes permit, the set of roots possessed by any given numerical equation. To appreciate it properly it is necessary to bear constantly in mind the difference between equalities in value and identities or equivalences in form; I hope that this has been made sufficiently clear in the text. The method of Abel has not been discussed, because it is neither so clear nor so precise as that of Galois, and the space thus gained has been filled up with examples and illustrations.<br><br>More than to any other treatise, I feel indebted to Professor H. Weber's invaluable Algebra, where students who are interested in the arithmetical branch of the subject will find a discussion of various types of equations, which, for lack of space, I have been compelled to omit.<br><br>I am obliged to Mr Morris Owen, a student of the University College of North Wales, for helping me by verifying some long calculations which had to be made in connexion with Art. 52. "The education of the child must accord both in mode and arrangement with the education of mankind as considered historically; or, in other words, the genesis of knowledge in the individual must follow the same course as the genesis of knowledge in the race. To M. Comte we believe society owes the enunciation of this doctrine - a doctrine which we may accept without committing ourselves to his theory of the genesis of knowledge, either in its causes or its order." If this principle, held also by Pestalozzi and Froebel, be correct, then it would seem as if the knowledge of the history of a science must be an effectual aid in teaching that science. Be this doctrine true or false, certainly the experience of many instructors establishes the importance of mathematical history in teaching. With the hope of being of some assistance to my fellow-teachers, I have prepared this book and have interlined my narrative with occasional remarks and suggestions on methods of teaching. To intelligently perform his work, an artizan must have a knowledge of Elementary Mathematics. When he comes to appreciate this fact for himself the workman generally finds that even the arithmetic he learnt at school has left him, and that he remembers little more than four simple rules and the multiplication table. Teachers soon discover that though anxious to learn, a student of this kind does not wish to lose contact with the practical requirements of the workshop, - he is impatient of "pure" mathematics, - so the question arises how to teach him mathematics enough, by dealing with the calculations themselves which he is actually called upon to make at his work.<br><br>The plan which is found most successful is a compromise. It is useless to say that all students ought to learn the broad principles of mathematics first, and apply them afterwards. Experience has proved that most artizans will not attend classes where the authorities decide that this is the only course.<br><br>To meet the difficulty classes in Workshop Arithmetic, Workshop Calculations and Practical Mathematics, have grown up, and it is to provide for young workmen beginning to attend one of these classes that this little book has been prepared. This new Dover edition first published in 1958 is an unabridged and unaltered republication of the first edition which was originally entitled Memorabilia Mathematica or The Philomath's Quotation-Book. The present collection of Exercises, gathered from many sources, is one which has accumulated through several years, and consists of papers set weekly or bi-weekly to boys of all ages during that time. They serve to recall back work, and keep boys always ready for the examination. The First Series contains 261 papers, about half the total number, and commences with exercises in Arithmetic suitable to boys who have gone through the First Four Rules, Simple and Compound, and are beginning Fractions; and Algebraical Exercises consisting chiefly of Numerical Values, Addition, and Subtraction. From these onward, the exercises rise in difficulty by careful gradations, reaching Cube Root and Compound Interest in Arithmetic, and Quadratic Equations in Algebra, at the end of the First Series.<br><br>The Second Series is a continuation of the First, and includes problems in Higher Algebra, Logarithms, Trigonometry, and easy Mechanics, and Analytical Geometry. The reader will find in the widely known memoir of Hilbert on the Foundations of Geometry various algebras of segments, independent of one or of another group of axioms, the purpose of these algebras being, in Hilberts case, to show the mutual independence of his set of axioms. More recently, in an excellent book, Schur fhas taken up von Staudt scalculus of projective segments (Wurfrechnung) in order to develop it analytically and to build upon it a complete system of metrical, euclidean and non-euclidean, geometry. This is admirably done in 4 and 5 of his work. Schur bases his definitions of equality, of addition and multiplication of projective segments, upon the correspondence known as prospectivity, and, at first, avails himself only of the axioms of connection and of order Schur spostulates I. to 8.; for the further development of the subject, however, he has recourse 5 to the axioms of congruence or of motion, postulates 9. to 13., and completes his investigation by adding an independent, 14 th postulate concerning the use of compasses. The result is a most charming and lucid structure of the complete system of non-euclidean geometry (of an isotropic three-dimensional space of any constant curvature), the last touch to this true masterpiece being given in Schur sclosing section by adding the archimedean postulate.2. The purpose of the present investigation (intended originally as a paper, but ultimately shaped into the form of a little book) is a more modest and much more restricted one, viz. to construct, D.Hilbert, Grundlagen der Geometric, Gottingen, 1899 ;translated byE. T.Townsend, Chicago, 1910. fF. Schur, Grundlagen der Geometric, Teubner, 1909.P.V.A. The present work is intended as a sequel to our Elementary Algebra for Schools. The first few chapters are devoted to a fuller discussion of Ratio, Proportion, Variation, and the Progressions, which in the former work were treated in an elementary manner; and we have here introduced theorems and examples which are unsuitable for a first course of reading.<br><br>From this point the work covers ground for the most part new to the student, and enters upon subjects of special importance: these we have endeavoured to treat minutely and thoroughly, discussing both bookwork and examples with that fulness which we have always found necessary in our experience as teachers.<br><br>It has been our aim to discuss all the essential parts as completely as possible within the limits of a single volume, but in a few of the later chapters it has been impossible to find room for more than an introductory sketch; in all such cases our object has been to map out a suitable first course of reading, referring the student to special treatises for fuller information.<br><br>In the chapter on Permutations and Combinations we are much indebted to the Rev. W. A. Whitworth for permission to make use of some of the proofs given in his Choice and Chance. It was, in fact, rather hastily compiled during a seaside holiday, and I had neither time nor opportunity for adequately treating the practical side of graphical work. Consequently all questions dealing with statistics and physical formulae were deliberately omitted to enable me to present the analytical aspect of the subject in sufficient detail within the limits of a few pages. The present edition has been very considerably enlarged. The additions are of two kinds: first, a further development of the illustrations arising out of graphs of known functions; and secondly, the application to practical questions in which the graph has to be obtained by plotting a series of values determined by observation or experiment. The subject is practically inexhaustible; but it is hoped that a student who has worked intelligently through the following pages will have added something useful and interesting to his algebraical knowledge, and will find himself sufficiently equipped to pursue the study further in the laboratory or workshop. I am indebted to several friends for advice and suggestions. In particular, I wish to express my thanks to Mr.D. Rintoul of Clifton College, and to my former pupil Mr. E.A. Price of Winchester. H.S. Hall. January, 1903. The transition from the traditional algebra of many of our secondary schools to the reconstructed algebra of the best American colleges is more abrupt than is necessary or creditable. This lack of articulation between the work of the schools and the colleges emphasizes the need of a fuller and more thorough course in elementary algebra than is furnished by the text-books now most commonly used. It is with the hope of supplying this new demand that an American edition of Charles Smiths Elementary Algebra is published; a work whose excellencies, as represented in former editions, have been recognized by able critics on both sides of the Atlantic. In the rearrangement of the work and in its adaptation to American schools many changes have been made, too many to be noted in a short preface, and a considerable amount of new subject-matter has been introduced. The following are innovations of some importance: Chapter I., consisting of a series of introductory lessons, is wholly new, and Chapter XIII. is partly new and partly transferred from Chapter XXVIII. of the second edition. The work on Algebra of which this volume forms the first part, is so far elementary that it begins at the beginning of the subject. It is not, however, intended for the use of absolute beginners. The teaching of Algebra in the earlier stages ought to consist in a gradual generalisation of Arithmetic; in other words, Algebra ought, in the first instance, to be taught as Arithmetica Universalis in the strictest sense. I suppose that the student has gone in this way the length of, say, the solution of problems by means of simple or perhaps even quadratic equations, and that he is more or less familiar with the construction of literal formulae, such, for example, as that for the amount of a sum of money during a given term at simple interest Then it becomes necessary, if Algebra is to be anything more than a mere bundle of unconnected rules, to lay down generally the three fundamental laws of the subject, and to proceed deductively in short, to introduce the idea of Algebraic Form, which is the foundation of all the modern developments of Algebra and the secret of analytical geometry, the most beautiful of all its applications. This text differs widely from that marked out by custom and tradition. It treats the various branches of mathematics more with reference to their unities and less as isolated entities (sciences). It seeks to give pupils usable knowledge of the principles underlying mathematics and ready control of them. These texts are not an experiment; they were thoroughly tried out in mimeograph form on hundreds of high school pupils before being put into book form. The scope of Books I and II does not vary greatly from that covered in algebras and geometries of the usual type. However, Book I is different in that arithmetic, algebra, and geometry are treated side by side. The effect of this arrangement is increased interest and power of analysis on the part of the learner, and greater accuracy in results. Some pupils like arithmetic, others like algebra, still others like geometry; the change is helpful in keeping up interest. The study of geometry forces analysis at every step and stage; consequently written problems and problems to be stated have no terrors for those who are taught in this way. For several years mathematical associations have urged that all work should be based upon the equation. In accordance with this view we have made the demonstrations in this book largely algebraic, thus making the demonstration essentially a study in simultaneous equations. In this method of treatment, we have found it advantageous not to hurry the work. Pupils gain power, not in solving many problems, but in analyzing and tio?oxt 3 xaAwafcaxs.- ing the principles of a few. Thi 8 work was commenced sixteen years ago at the earnest solicitation of numerous teachers, who were dissatisfied with the textbooks then in use. That they were not alone in their opinion is evidenced by the number of new treatises, or revisions of old ones, printed since that time, and now used in the schools of this country. The crudeness of even the best Algebras of a quarter-century ago was mainly owing to the fact that, as a rule, mathematicians neglected the elementary branches for the more attractive fields of Higher and Applied Mathematics; hence blunders and inconsistencies were allowed which otherwise would not have been tolerated. The wonderful progress made in the Natural Sciences, and the extended use of Algebra in the treatment of Geometrical Magnitudes, have finally called the attention of educators to the necessity of improving the elementary treatises, and more rigidly limiting the meaning of the signs. That this agitation comes none too soon is evident to every thoughtful teacher, and can be readily seen by auy one who compares the various text-books used in our schools. Note the following inconsistencies: In some text-books now before me, 6 : 7 equals f;in others, 6 : 7 equals. In some, 6 -f 4 X 2 = 20;in others, 6 -- 4 X 2 = 14.Of course, the meaning and use of a sign depend upon agi eement, but it is of extreme importance that we do agree in such matters. In the same work, too, statements incompatible with each other are made; thus, a -i-bc and a -i-b Xc are said to have different values, and yet be and bXc are, in all woi ks, said to have one and the same meaning. Since a-h be and a -ib Xe differ only in She use of bXc for be, it is plainly necessary that one or the other of these two statements be changed. One of the objects in writing this book is to urge the adoption of the following law for Numerical Values; viz.,(l) Find the value of each term separately; thus, 6-f-4X 2 = 6 -f8= 14. (2)In finding the m, lue of a term, begin at the Right and use the signs in their oi der; thus, 6-f-4x 2 = 6-r-8= f.In other words, the jm tion of the term to the left of the division sign is the Dividend, and the part to the right is the divisor. eBook Shop MathematicsAdvanced Shop Mathematics; Prepared in the Extension Division of the University of Wisconsin by Earle B. NorrisVol. 2 This volume presents the second half of the instruction papers in Shop Mathematics as developed and used in the Extension Division of the University of Wisconsin. In it the authors have endeavored to present such of the principles of algebra, geometry, trigonometry and logarithms as have been found to be of practical value in the shop, showing some of the better known applications and making the presentation as practical as seemed possible. Experience in the teaching of this course for over five years shows that it has been successful in developing in the student ability to apply the principles to his own shop problems and in giving him a good mathematical preparation for advanced technical study.<br><br>It is here presented in the belief that it will be found suitable for home study and for use as a text in trade schools, technical high schools and continuation schools.<br><br>The authors are indebted to Mr. Herbert J. Lehmann, Assistant in Applied Mathematics in the University Extension Division, for many valuable suggestions and criticisms; also to the authors and publishers of Van Velzer and Slichter's logarithm tables for permission to use their plates. Academic and University Algebras. The first 24 fpages of the Higher Algebra are the same as the corresponding pages of the Academic Algebra. The work on pages 249 to 305 of the latter has been rewritten with reference to the new matter, and 71 pages have been added to the book; and it is now put forth as a complete preparatory text, containing all the topics required for admission to any of the Colleges, Universities, or Scientific Schools of the country. The new matter is contained principally in the following chapters: XXVI. Inequalities. XXVII. The Theory of Limits; Interpretation of the- a a-, 0 forms-, , and 0 0 Xxix. Variation. XXXII. Harmonical Progression. XXXIV. The Theorem of Undetermined Coefficients. XXXV. The Binomial Theorem; Fractional and Negative Exponents. XXXVII. Compound Interest and Annuities. XXXVIII. Permutations and Combinations. XXXIX. Continued Fractions. There is also given in connection with the chapter on Logarithms, a discussion of Logarithmic and Exponential Series.
Additional Product Information Features/Benefits Emphasis on learning objectives and outcomes--Every section begins with a list of learning objectives called What You Should Learn. Each objective is restated in the margin at the point where it is covered. Why Should You Learn It provides a motivational explanation for learning the given objectives. Detailed, titled examples to develop concepts--Each example has been carefully chosen to illustrate a particular mathematical concept or problem-solving technique. The examples cover a wide variety of problems and are titled for easy reference. Many include detailed, step-by-step solutions with side comments that explain the key steps of the solution process. Real-world applications--Identified by an icon, a wide variety of real-life applications are integrated throughout the text in examples and exercises, demonstrating the relevance of algebra in the real world. Many of the applications use current, real data. Straightforward problem-solving approach--The text provides many opportunities for students to sharpen problem-solving skills. In both the examples and the exercises, students are asked to apply verbal, numerical, analytical, and graphical approaches to problem solving. The authors' five-step strategy for solving applied problems begins with constructing a verbal model and ends with checking the answer. Plentiful exercises and tests--Graded exercise sets are grouped into three categories, offering a diversity of computational, conceptual, and applied problems to accommodate many learning styles. Detailed solutions to odd-numbered exercises are in the Student Solutions Guide; answers to odd-numbered exercises are in the back of the text. In-text learning aids--Definitions and rules are highlighted, Study Tips offer suggestions for studying algebra and point out common errors, and Technology Tips point out where the use of a graphing calculator is helpful in visualizing concepts and solving the problem. What's New Emphasis on study skills and self-responsibility--Each chapter opener presents a study skill essential to success in mathematics, followed by a Smart Study Strategy that offers concrete ways that students can help themselves with the skill. These chapter openers were written by noted study skills expert, Kimberly Nolting. Quotes from real students who have successfully used the strategy appear in It Worked for Me! Later in the chapter, a Smart Study Strategy note points out an appropriate time to use the strategy. Concept Checks--Each exercise set is preceded by four non-computational exercises that check students' understanding of the main concepts of the section. These exercises could be completed in class to make sure that students are ready to start the exercise set. Checkpoints--Each example is followed by a checkpoint exercise. After working through an example, students can try the checkpoint exercise in the exercise set to check their understanding of the concepts presented in the example. Interactive chapter summaries--The What Did You Learn? section at the end of each chapter has been reorganized and expanded to promote interactivity and better help students prepare for exams. The Plan for Test Success provides a place for students to actively plan their studying for a test; it also includes a checklist of things to review. Students can check off chapter Key Terms and Key Concepts as they are reviewed. A space to record assignments for each section of the chapter is also provided. Cumulative review exercises--Each exercise set (except those in Chapter 1) is followed by exercises that cover concepts from previous sections. This serves as a review for students and also helps them connect old concepts with new concepts. Best Buy Packages Other Popular Packages Choose the textbook packaged with the resources that best meet your course and student needs. Contact your Cengage Learning representative for more informationBy Gerry Fitch, Louisiana State University, this guide includes detailed ,step-by-step solutions to all odd-numbered exercises in the section exercise sets and in the review exercises. It also includes detailed step-by-step solutions to all Mid-Chapter Quiz, Chapter Test, and Cumulative Test questions. By Gerry Fitch, Louisiana State University, this manual is available online and includes Chapter and Final Exam test forms with answer keys, individual test items and answers for chapters 1-10 and notes to instructors including tips and strategies on student assessment, cooperative learning, classroom management, study skills, and problem solving. The annotated instructor's edition contains answers in place for exercise sets, review exercises, Mid-Chapter Quizzes, Chapter tests, and Cumulative tests. It also includes annotations at point of use that offer strategies and suggestions for teaching the course and point out common student pitfalls handy manual contains detailed, step-by-step solutions to all odd-numbered exercises in the section exercise sets and in the review exercises. In addition, it also includes detailed step-by-step solutions to all Mid-Chapter Quiz, Chapter Test, and Cumulative Test questions interpretMeet the Author About the Author Ron Larson
This course targets students majoring in both computational and biological sciences, broadly defined to include mathematical, computer science, bio-medical and environmental majors. The goal of this course is to give students an understanding of the biological-mathematical interface, and how mathematics contributes to the study of biological phenomena. Biological systems have a very high level of complexity and practically every phenomenon is the result of complex interactions between various levels of organization. To apply modeling (both mathematical and experimental models), we always simplify the natural system by making both implicit and explicit assumptions, and this course teaches students to see the hidden assumptions and understand their role in the results of model applications. The course introduces general mathematical methods in biology, such as scaling, approximations of stochastic and individual-based biological models by differential equations, and linearization and stability analysis, using both classic and recent examples. The course covers fundamental and applied models operating at different organization levels, from processes inside individual cells to those that form ecosystems. Specific examples include: dynamics of infectious diseases (flu epidemics and AIDS), natural recourse management (fisheries), forest dynamics, interacting species (resource competition, predator-prey, and host-parasite models), spatial models, enzyme kinetics, chemostat theory, and bioremediation. In this course biology students learn to formulate their specific questions in a mathematical way, while mathematics students learn what constitutes biologically relevant questions, and how to accept the high level of uncertainty that exists in biological research. A substantial part of the course will use analytical methods in concert with computer simulations, using the Mathematica software.
linear programming problems worksheet? Possible Answer Discussion of Linear Programming to precede worksheet: Linear Programming ("Planning") is an application of mathematics to such fields as business, industry, social science, economics, and engineering
Here are topics for which you may want to hone your skills: -Equations and inequalities -Linear equations and functions -System of linear equations and inequalities -Matrices and Determinants -Quadratic functions -Polynomials and polynomial functions -Powers roots and radicals -Exponential and Lo
Subject: Mathematics (9 - 12) Title: Now, where did THAT come from? Deriving the Quadratic Formula Description: Generally, teachers expect students to memorize the quadratic formula and to know that you use it after exhausting all other means of solving a quadratic equation, i.e. as a last resort. This technology-based lesson is designed to assist students with deriving the formula on their own. Students must first be familiar with complex numbers and the process of "completing the square." This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project. Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: Family Ties: Parabolas Description: This lesson allows students to manipulate the parameters while using the vertex form of the equation of a parabola to see the effects on the graph. The spreadsheet can be altered for other functions.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project. Subject: Business, Management, and Administration (9 - 12), or Mathematics (9 - 12) Title: What's The Real Cost of That Car? Description: This is a Commerce and Information Technology lesson plan. A project requiring research, critical thinking and complex decision-making about factoring all the costs of purchasing a large ticket item... a car. Subject: Finance (9 - 12), or Mathematics (9 - 12) Title: Liquidity for Success Description: This lesson will input values to calculate financial ratios and intepret the information derived from the calculations. This is a Commerce and Information Technology lesson plan. Thinkfinity Lesson Plans Subject: Mathematics,Science Title: Modeling Orbital Debris ProblemsAdd Bookmark Description: In this lesson, from Illuminations, students examine the problem of space pollution caused by human-made debris in orbit to develop an understanding of functions and modeling. The lesson gives students an opportunity to use spreadsheets, graphing calculators, and computer graphing utilities. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
This courses uses the 2011 edition of the Jurgensen, Brown, and Jurgensen textbook, ... Brown, and Jurgensen, Geometry. Houghton Mifflin, 2011. Teachers use other texts for supplementary ideas, such as Discovering Geometry by Michael Serra, and also current mathematical This course use the 2000 edition of the Jurgensen, Brown, and Jurgensen textbook, Geometry, published by Houghton Mifflin. ... This text matches both the 2000 edition of the National Council of Teachers of mathematics curriculum standards and the 2000 edition of the Massachusetts State Ray Jurgensen, Richard Brown, and John Jurgensen Students and Grade Levels ... Geometry, Pupil's Edition ... provide service to teachers. This service is available from 8 a.m. to 5 p.m. CST, Monday through Friday. Page 4
Follow Us Applied Mathematics Mathematics is an essential part of scientific development. By itself, mathematics is a subject of great depth and beauty. But mathematics is also crucial in the development of natural sciences, engineering and social sciences. At UC Merced, several professors focus on interdisciplinary, applied mathematics. Their focus is in solving real-world problems using modeling, analysis and scientific computing. Related Topics Arts and Culture Computing Sensing Gaming and Robotics Earth and Environment Economy and Markets Evolution and Genomics Human Health Math and Science Education Physics The first new American research university in the 21st century, with a mission of research, teaching and service.
Introduction to Technical Mathematics - 5th edition Summary: Introduction to Technical Mathematics, Fifth Edition, has been thoroughly revised and modernized with up-to-date applications, an expanded art program, and new pedagogy to help today's students relate to the mathematics they are learning. The new edition continues to provide a thorough review of arithmetic and a solid foundation in algebra, geometry, and trigonometry. In addition to thousands of exercises, the examples in this text include a wealth of applications from ...show morevarious technological fields: electronics, mechanics, civil engineering, forestry, architecture, industrial engineering and design, physics, chemistry, and computer science. ...show less 8.1 The Distributive Property and Common Factors 8.2 Factoring Trinomials 8.3 Factoring General Trinomials 8.4 The Difference Between Two Squares 8.5 The Sum and Difference of Cubes Summary Review Exercises Test17106
4. R Bhatia, Pinching,trimming,truncating and averaging of matrices, paper available on the course website. ------------------------------------------------------------ Useful preparation for the course "Numerical ranges (classical and higher-rank) with applications to quantum information theory" , to be given by John Holbrook during the second week, might include some familiarity with:
Introduction to Ordinary Differential Equations 9780486659428 ISBN: 0486659429 Pub Date: 1989 Publisher: Dover Pubns Summary: A thorough, systematic 1st course in elementary differential equations for undergraduates in mathematics and science, requiring only basic calculus for a background, and including many exercises designed to develop students' technique in solving equations. With problems and answers. Index. Landin, Joseph is the author of Introduction to Ordinary Differential Equations, published 1989 under ISBN 9780486659428... and 0486659429. Five hundred forty four Introduction to Ordinary Differential Equations textbooks are available for sale on ValoreBooks.com, one hundred twenty nine used from the cheapest price of $2.38, or buy new starting at $9.14
numerical evaluations.[ understand the meaning of an equation, be able to perform numerical evaluations.[Collapse Summary] Summary:This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Algebraic Expressions and Equations" and contains many exercise problems. Odd problems are accompanied by solutions. provides an exercise supplement for objectives of proficiency exam for the chapter "Algebraic Expressions and Equations".[Collapse Summary] Summary: ... by solutions.[Expand Summary]. The problems in this exam are accompanied by solutions.[Collapse Summary] Summary: ... solve equations.[Expand Summary] the multiplication/division property of equality, be able to solve equations of the form ax = b size 12{ ital "ax"=b} {} and x a = b size 12{ { {x} over {a} } =b} {} and be able to use combined techniques to solve equations.[Collapse Summary] Summary: ... {} .[Expand Summary] meant by the solution to an equation and be able to solve equations of the form x + a = b size 12{x+a=b} {} and x − a = b size 12{x - a=b} {} .[ - b).[ be able to expand (a + b)^2, (a - b)^2, and (a + b)(a - b).[Collapse Summary]
Mathematics Mathematics The Gonzaga Prep mathematics department believes the study of mathematics leads students to a deeper understanding of the patterns of God's creation and provides a language to uniquely describe those patterns. Students experience mathematics through active, guided discovery through which they learn important mathematical concepts and procedures which promote innovative thinking, varied problem solving strategies, inductive and deductive reasoning and critical thinking skills. Through the study of mathematics students fully realize their own unique gifts and academic potential, prepare themselves for further educational opportunities, and develop cognitive skills to promote justice in an ever changing world. Algebra I This course introduces concepts such as linear and quadratic equations, graphing, polynomial, factoring, and problem solving. An honors section is available for those with teacher recomendation. Course Outcomes Algebra I B: This is the first year of a two year sequence. I the first year students will cover 2/3 of the standard Algebra 1 curriculum. The course content includes review of essential arithmetic skills, explores and develops algebraic thinking and concepts, in addition to practicing and applying algebra skills in a variety of problem solving situations. Course Outcomes Geometry B: This course is a semester of geometry and a semester of algebra. The geometry portion of the course introduces students to geometry vocabulary. In addition to the study of proofs, as applied to plane figures, symbolic logic is introduced. The algebra portion of the course is a continuation of Algebra B. Students will learn how to graph polynomials, factoring, and problem solving. Prerquisite: Algebra I B Course Outcomes Geometry: This course introduces students to geometry vocabulary, postulates, and theorems. In addition to the study of proofs, as applied to plane figures, symbolic logic is introduced. The curriculum includes a significant review of algebra and applications of algebra to analytic geometry. An honors section is available for those with teacher recommendation and have an appropriate score on the honors placement exam. Prerequisite: Algebra I. Course Outcomes Algebra II/Trigonometry: This curriculum advances the students' algebraic skills by focusing on the conic graphs and polynomial graphs, logarithmic and exponential functions, as well as trigonometric functions. The topics prepare the student for pre-calculus analysis. An honors section is available for those with teacher recommendation. Prerequisite: Geometry. Course Outcomes UW Pre-Calculus: This course is offered by the University of Washington. It is Math 120 at the UW. It is a pre-calculus course with an emphasis on science and engineering. This is a problem solving based course with many "real world problems." Course Outcomes Pre-Calculus: The fourth course in the regular sequence includes advanced concepts in equations, graphing and trigonometry. The students will be introduced to sequences, series, probability and elementary calculus. An honors section is available to those with teacher recommendation. Prerequisite: Algebra II/Trig Course Outcomes AP Statistics: A course for students planning to study the humanities or social sciences in college. This course will address the analysis of data, central tendencies, variance, sampling, inference from samples, linear regression, and correlation as well as probability distributions. Many examples from the social sciences will be presented. Graphing calculators will be used extensively. Prerequisite: Algebra II/Trig Course Outcomes Advanced Placement Calculus: This course will provide a college level treatment of differential and integral calculus. Trigonometric, logarithmic and exponential functions will be explored. Problem solving skills in areas of exponential growth, related rates and maximum/minimums will be introduced. Students who have successfully completed this course are recommended to take the Advanced Placement Exam for college credit. Prerequisite: Pre-Calculus. Course Outcomes
Problem- Solving Strategies (Paperback) Problem- Solving Strategies Book Description A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week," thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market. Popular Searches The book Problem- Solving Strategies by Arthur Engel (author) is published or distributed by Springer [0387982191, 9780387982199]. This particular edition was published on or around 1997-12-31 date. Problem- Solving Strategies has Paperback binding and this format has 406 number of pages of content for use. This book by Arthur Engel
Saul Stahl When reviewing a book on modern algebra the issue is not only how good the book good is, but also for whom it is good. This book is an excellent book for an upper-level, undergraduate, one or two semester course, in modern algebra, for a typical University student population that is not especially strong in proofs. What I particularly like about the book is the following. Doable Exercises: The strongest point of the book is the richness and diverse flavor of over 1000 exercises. There are proof exercises but most exercises are non-routine computations or verifications. The issue with general proof exercises is that weak students can attempt them and get nowhere, thus wasting time and encouraging them to give up. An exercise that has thinking aspects but is based on non-routine computation or verification can be done with enough work even by a weak student. This stimulates and motivates. An illustration of the computational-verification flavor of the exercises is afforded by the first section in the chapter on group theory which has 37 exercises. 10 of them are of the form "compute the group of symmetries of x1/x2 + x3/x4" 12 of them are of the form "compute the product and find the axes and angles of the rotations of the following two rotations of the tetrahedron in Figure 9.3: A = (1 2 3) and B = (2 4 3)" 3 of them ask about the dihedral group Dn (e.g. how many elements does the group have; how many have order 2, etc.) 4 of them are of the form "Describe the vertex symmetries of the cube in Figure 9.5" 6 of them are "verification proofs", for example, "show that all even permutations form a group" 2 of them are more serious proofs, for example, "Prove that for every positive integer k there is a polygon whose group of vertex symmetries contains k elements." Exercise Richness: The text excels in both quantity and quality of exercises. The exercises have a rich diversity of color as the following examples illustrate. The book has a standard appendix on mathematical induction. There are 18 exercises; a) there are routine exercises such as proof of the sum of squares or cubes of the first n integers; b) there are also inequality proofs such as "prove (by induction!) that 2n > n2 for n > 4" ; c) there are number theory exercises such as "prove (by induction!) that 11n+2+122n+1 is divisible by 133" ; and there are d) geometric and e) integral exercises. The exercises on polynomials are enriched by many exercises requesting factorizations over finite fields. History: The author wrote this book from the historical point of view. This can indeed be exciting to a student interested in what mathematics is like. I myself found it interesting to see original excerpts from the masters such as al-Khwarizmi (solution of the quadratic equation), Cardano (solution of the cubic), Abel (unsolvability of the quintic), Galois (foundations of Galois theory) and of course Cayley (enumeration of groups by looking at permutation groups). I believe the real strength in using a historical approach is the wealth of computational examples it invites. This is felt throughout the book where exercises challenge students to apply the theory to solve equations of degree 3 or 4 over the complex and finite fields as well as factorizations over rings over the integers. Modern Look: The book has all the characteristics of many modern textbooks: a) accompanying diagrams, b) adequate illustrative examples in each section, c) chapter summaries, d) a list of new terms at the end of each chapter, e) chapter review exercises, f) supplementary chapter exercises, g) solutions to odd number exercises, h) appendices covering induction and logic in adequate depth, i) a modest bibliography and a j) neat collection of one-paragraph biographies of about two dozen mathematicians. Semester Coverage: The book has 14 chapters and 60 sections (each with several dozen exercises) making it usable for either a one or two semester course. The section lengths are just right for coverage in one day. The book uses an example-abstract approach vs. an abstract axiom-example approach. This means, for example, that the definition of group is delayed a few weeks into the semester. Personally, I prefer such an approach and I think the students, exposed to an axiomatic approach for the first time, find it easier. Non-standard Applications: Every author tries to include non-standard applications, that is, applications of modern algebra not found in almost all other text books. This book emphasizes a) the 15 puzzle, b) the RSA algorithm, c) Dedekind ideal theory, and (as already mentioned) the historically motivated d) solvability of equations and e) geometric constructibility. I have never seen another modern algebra book with a presentation of the quadratic reciprocity law. True to the book's spirit, both the historical (mathematical theorem with the second most proofs) and aesthetic (the golden theorem) aspects of quadratic reciprocity are mentioned. The law is presented with accompanying diagrams and computational exercises showing the theorem's power. Of course, instructors who wish to can comfortably omit teaching the "Number Theory" chapter. I found two topics lacking in the book. The Beautiful Cayley Counting Theorem: At this I was surprised, since the Cayley theory lends itself to many clever and combinatorial computational exercises that would be consistent with the book's goals. This is not a serious omission, however, unless the student target population consists of Chemistry majors. I would recommend to the author to include an additional chapter in edition 3 or 4. The Sylow Theorems: I and many colleagues prefer to omit this topic anyway. Russell Jay Hendel, RHendel@Towson.Edu, holds a Ph.D. in theoretical mathematics and an Associateship from the Society of Actuaries. He teaches at Towson University. His interests include discrete number theory, applications of technology to education, problem writing, actuarial science and the interaction between mathematics, art and poetry.
Using the Calculator on the GED Math Test This section of the GED Mathematics web-based training module has provided you with basic information about the Casio fx-260 Solar Scientific calculator. Students will be allowed to use this calculator on Part I of the GED Mathematics Test. A calculator will be provided for each examinee. Students cannot use their own calculators or those that they have used in your classroom. The teaching of basic calculator use is important, not only for the GED Mathematics Test, but also for use in real-life situations. However, it is important to remember that a calculator is merely a tool. Students will need to be proficient in the different math content areas. Calculators do not teach skills; they merely aid in the speed and accuracy of computations. You may wish to print copies of this page for your students. The calculator directions are reprinted with permission of the GED Testing Service (c) 2001. You have now completed the Calculator section. If you're working straight through, click "Next" to go to the Grid Formats section, or click on one of the modules in the navigation bar on the left to go to another section that interests you.
All the fantastic features that have made other Teaching Textbooks are so popular are included in the new Math 5. Designed for independent students, the Teaching Textbooks learner will discover a wealth of instruction written directly to them, clear examples, fun hand-drawn illustrations, highlighted important concepts, and of course, step-by-step solutions to every problem. Plus, a 5-10 minute interactive lecture is included for every lesson, and includes a print summary that reinforces the key concepts to remember. Automated grading, non-required additional practice problems, lectures and step-by-step audiovisual solutions to every homework and quiz problem make for a thorough and easy to use curriculum for both parent and student. Consistent review and real-world illustrations help reinforce both concepts taught, as well as the relevance of what they're learning. product has great features Date:August 20, 2013 Wendy Location:Macon, GA Age:35-44 Gender:female Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5 This is the best teaching method for math for homeschoolers. I've used teaching textbook since pre-algebra and was thrilled to see that teaching textbook was available starting in the 3rd grade. My youngest son loves it...he's been using since 3rd grade and now is on the 5th grade....Thank you! Share this review: 0points 0of0voted this as helpful. Review 2 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 Date:July 25, 2013 Glory Location:Kamloops,Canada Age:35-44 Gender:female My Son loves this program so much! He can work independently. The program would be a good fit for several types of learners. He used to complete one math lesson a week, now he completes up to three in one day. We will continue to buy this curriculum. Share this review: 0points 0of0voted this as helpful. Review 3 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 Easy to use, and it works! Date:December 23, 2012 Rafismom Location:Minneapolis, MN Age:55-65 Gender:female Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5 I had previously tried non-curriculum, and 4 other curricula for my son. He had learned to say "I can't" in school and had particular difficulties in math. This curriculum, which we began using at the "third grade" level and have continued with, has worked well. We supplement with the word problem materials from Critical Thinking Publications, and with the online drill program of Reflex math - and my son wants to do his math first!. As he has difficulty with the physical acct of writing we use this on a split screen with the MathPad Plus program, to work out the problems. This means I don't really need the book, but I get it anyway so I can review what is coming up first. Concerns that it is "not at grade level" don't matter to me, as we are working at several grade levels, catching up on math by completing 1.5 levels per year, and I don't care what level the program says it is -- only that my son is learning the skills. I have no intention of putting him back in school , so the level just is irrelevant. Share this review: +5points 5of5voted this as helpful. Review 4 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 5th Grade Teaching Textbooks Date:November 5, 2012 PamperedPumpkinWe LOVE Teaching Textbooks!! Three weeks ago we made the decision to remove our son from the public school system, and start home schooling. Math is not my best subject, and I didn't want to hold him back. With such huge pressure falling on my shoulders, I researched curriculum for 3 days. What a blessing to have found such a fantastic program. We are both learning to actually "enjoy" math time! Gone are the tears and 3 hour homework battles. Thank You so much for creating such an awesome program, and easing some of the pressure! Now if only they would create programs for the other subjects! :) Share this review: +1point 1of1voted this as helpful. Review 5 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 The BEST math curriculum ever!!!! Date:October 29, 2012 Kristin C. Location:Dallas, TX Age:35-44 Gender:female Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5 We have used about 4 of the levels now and have NOTHING negative to say! It is an amazing program that I recommend to ALL of my friends and any homeschooler I meet! It allows our kids to work independently and they have gained sooo much self-confidence. We have many learning disabilities in our home...some with major auditory & visual processing disorders, as well as fetal alcohol effects, and they ALL do amazing with this program. I don't know how, but it works with all 5 of our kids that have used it, and I am so thankful for it! On a side note...we only buy the CD's alone...the workbooks etc are optional & we have never needed them (saves money). And it is VERY simple to reuse the CD for another child...I am computer illiterate & have called the customer service a few times when forgetting how to 'erase' a CD for a new student to use, and they have always been so wonderful!! It is worth every penny to purchase this program!! (just wish they would make other subjects!!) Share this review: +2points 2of2voted this as helpful. Review 6 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 Date:September 17, 2012 9yr old twins Location:Baton Rouge, LA Age:45-54 Gender:female Love it -- It makes math so much more fun and kids look forward to it and they also like the bonus points. Share this review: 0points 0of0voted this as helpful. Review 7 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 4out of5 Very user friendly for student! Date:August 16, 2012 Christine Location:Waterloo, IA Age:35-44 Gender:female Quality: 5out of5 Value: 4out of5 Meets Expectations: 5out of5 The program is very easy to use and my daughter loves it! I love how it checks her work and I can see the results easily. I don't see a need yet for the printed book or answer book. Next time I will just get the discs! Love it! Share this review: 0points 0of0voted this as helpful. Review 8 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 Date:May 8, 2012 homeschool mom Location:Lancaster, Pa. Age:35-44 Gender:female Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5 This math program has saved my sanity! Some say it is below grade level so I put my gifted 5th grader in Math 6th and he has done well and gets his work done in no time flat. He does 2 lessons a day and does not complain at all. (This is after 2 years of struggling to get 1 lesson done a day! When I asked him what the difference was he said his previous math curriculum bored him to tears!) My daughter always struggled with math before but she loves Teaching Textbooks! She loves that she can listen to the lectures by herself. If she forgets how to do something she will go back to the lecture that explains it and listen again. Also, the fact that the program lets her know if she did a problem wrong right away has been a HUGE help! (This ensures that she is doing it correctly and not learning something incorrectly and then having to RELEARN it again the correct way after I grade her papers) We love this program! :) Share this review: +1point 1of1voted this as helpful. Review 9 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 Great Math program Date:April 11, 2012 Farmermom Location:Elma, Wa Age:35-44 Gender:female Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5 I started my kids on this math after struggleing with other math program a friend told me about this and it has worked great for all my kids Share this review: 0points 0of0voted this as helpful. Review 10 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 Wonderful Product Date:February 10, 2012 BeckyE Location:PA Age:35-44 Gender:female Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5 My daughter has always struggled with math. I have used many different types of math programs, and this seems to be the perfect fit for us. She really likes it. She actually wants to do math!! I will continue using Teaching Textbooks for my daughter and will be purchasing it for my sons next school year also. Share this review: 0points 0of0voted this as helpful. Review 11 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 3out of5 Not on grade level shown Date:February 8, 2012 Persi Location:NC Age:35-44 Gender:female Quality: 5out of5 Value: 4out of5 Meets Expectations: 2out of5 This kit is great if you want your child to gain independence skills, or if he's struggling with math. It's fun and easy to use. However, it is below the grade level shown. In addition, it's not organized by topics, so it's very difficult to supplement with other materials. Problem solving is limited. We're half way through the school year, and my son hasn't learned much of anything new. I'm searching for a new curriculum now. Share this review: +3points 3of3voted this as helpful. Review 12 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 Excellent program Date:January 7, 2012 kabob86We took our daughter out of public school at the end of last year in 4th grade. She was struggling, getting 10% on math tests and average 2 out 4 on her report card. We did Teaching Textbooks Grade 4 over the summer and caught her up so she could start 5th grade in September. She has gained confidence and now she is getting 90%-100% on her daily work and tests as well on this program. This program is made her more motivated as well. Her frustration level is diminished and she now knows she can do Math! We will use Teaching Textbooks through high school! Share this review: 0points 0of0voted this as helpful. Review 13 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 This product meets our needs Date:December 17, 2011 peaceful momI am so happy to have purchased this math set. I was a little hesitate to purchase it because of the price. This is our third math program we are trying for our 6th grade son. My son is a different child now. He now loves doing math and now I don't have to tell him to do his math. He does the computer and workbook everyday. This program is the BEST for my son. If you have a struggling math student, then I recommend Teaching Textbooks to you. Share this review: +1point 1of1voted this as helpful. Review 14 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 1out of5 Not at appropriate grade level Date:September 15, 2011 Sandy Location:Castle Rock, CO Gender:female Quality: 1out of5 Value: 4out of5 Meets Expectations: 1out of5 This math program has an excellent method of presenting and teaching the information from the CD's. My kids liked it for awhile. However, I have found for grades 4 - 7 (at least) that it falls a year behind of Saxon and other reliable homeschool math curriculum, and is not very challenging. My kids became bored about half-way through the book. If your child must take a standardized test under your state's homeschool law, he/she may have trouble with the math portion. Share this review: +4points 4of4voted this as helpful. Review 15 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 Date:September 9, 2011 wenluel Quality: 5out of5 Value: 4out of5 Meets Expectations: 5out of5 I love how this product has EVERYTHING your child needs to learn how to be a self-starter for this subject. All the teaching, help, solutions, and support are right there! Share this review: 0points 0of0voted this as helpful. Review 16 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 Wow! Date:August 5, 2011 Rebecca Blaise Location:Northern NY Age:35-44 Gender:female Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5 My daughter used to hide when it was time for math! Now she asks to do it. She loves seeing her progress, as do I. This curriculum is great! If you want to see a demo, the company has a website with a great demo feature for each grade level. I just can't enough good about it! Be sure to have your child take the placement test before selecting a grade level. BTW, I am a homeschooling mom of three and have been schooling since 1998. We have also done Algebra 2 by Teaching Textbooks and my eldest says that now she REALLY understands math. You can't get a better recommendation than that. Share this review: +1point 1of1voted this as helpful. Review 17 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 Date:June 13, 2011 jndean Quality: 5out of5 Value: 4out of5 Meets Expectations: 5out of5 Math is a chore in our house, usually. Now my children fight over who will do their math first. Share this review: +1point 1of1voted this as helpful. Review 18 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 very engaging Date:April 26, 2011 heather Location:Sumter, SC Age:35-44 Gender:female Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5 You will never need to remind your student to get their math lesson done. They will be reminding you. Share this review: +1point 1of1voted this as helpful. Review 19 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 1out of5 Date:August 31, 2010 Lisal Mcdonald The CDs did not work in our Mac computer. We ordered Mac CDs but they did not work. We talked with TT and they determined that the CDs weren't formatted correctly or that we were send Window's CDs by mistake. We had to exchange them with IT. Two years in a row this has happened. Share this review: -13points 1of15voted this as helpful. Review 20 for Teaching Textbooks Math 5 Kit (Windows & Macintosh) Overall Rating: 5out of5 Date:August 30, 2010 Momto4LittleLambs After I tried many different math products in our homeschool experience (to include nice programs like math SOS, Horizons), we decided to try this. It is outstanding. The ease of use for both the student, and the teacher is great. The "grade book" is very well laid out, and shows you so much information on the students progress. Math time was a hard time for one of my children, and this gave a new perspective as it is on the computer. I do tend to think it is somewhat on the lighter side, and not an advanced grade level program (it does not claim to be advanced...it clearly states it is a basic math program), but math is founded on basic principals and I want my children to be grounded in them, so this works for us. (You can always add "specials" to your math time, like a Keys To... workbook (a personal favorite) or the like to "kick it up a notch" from time to time!)Despite the price, or even if you go for just the books, I am pleased with this program, in fact I am planning to put another child in Teaching Textbooks very soon!
In recent years the mathematics department at Virginia Commonwealth University has seen an increase in the number of students enrolling in calculus who are likewise enrolled in chemistry courses. Some of this increase can be attributed to the addition of a school of engineering and a forensic science program. Calculus textbooks have long had applications in physics, economics, biology and statistics but lacking in chemistry based problems. This project, in part, is to address this discrepancy. Many individuals who take courses in calculus seem to lack an adequate understanding of where and how calculus might be applicable to their future. This is probably due, in part, to the fact that most exercises in traditional calculus programs are tied to equations which are furnished by either the textbook or the instructor. The student often dismisses or overlooks how this might apply in a world where formulas and equations are now handed to them. This project addresses the concepts in calculus through tables of data which students are very likely to encounter rather than through given equations. Parameters Because scheduling is a priority and roadblock in creating any new program, this project attempts to limit any and all such impeding factors. To facilitate this no constraints are applied to the students who might participate in the program other than that they be "calculus ready students" in the traditional sense. No background in chemistry is assumed, no particular major or curriculum is required, the project can be carried out in any or all calculus classes - no perquisites beyond that of meeting the requirements to enroll in calculus is needed. One of the goals of this project is to insure that students participating are not exposed to less or different material than that covered in our other calculus classes. The problems are in a laboratory format and are included as an addendum to particular assignments. These labs parallel the existing curriculum. Realizing that some students may feel intimated by the fact that the exercise (labs) are not traditional calculus problems, students are allowed and encouraged to work with a partner. If a student works with a partner, each partner is required to turn in a lab of their own with their partners name included. The intent is that the student's final grade is neither inflated nor impacted downward through participation in the project. One point is added to the final test for the year for each lab completed. This, in reality, increases the individual's average by a maximum of 0.8 percent. Realizing that some students might be inclined to turn in a lab based on their partner's work, bonus questions worth one point each are added to tests and quizzes throughout the semester. Thus students need to have some understanding of the lab results in order to answer these questions successfully. Through these bonus questions individuals can add an additional 0.8 percent to a semester average. Hence, active participation could add 1.6 percentage points to the final grade which could affect borderline grades. No grades, however, are affected adversely - which is the intent of the program. (A discussion of this will be included in the results portion of this document.) Assessment Six labs were assigned during throughout the course of the semester. (Eight were prepared but due to the newness of the study, it was decided to err on the side of too few rather than too many. Titles of Laboratories Fahrenheit vs Celsius Temperature Scales (As Inverse Functions) Average and Instantaneous Rate of Change (the Derivative) in a Chemical Reaction Conditions Leading to Optimization (Maximum/Minimum) Through Chemistry * Related Rates and the Chain Rule Applied to the Ideal Gas Law and Arterial Blood Flow * * These labs were not included (due to time constrains in the initial semester) but should be in the future. Graphs of results Graph A - Number of Students who participated in Lab (out of 35 students) Graph B - Number of Students who picked up Bonus Points per Lab (out of 35 students) Graph C - Number of Students whose grade improved due to Labs (out of 35 students). Graph D - Final Grade Distribution of Class (class of 35 students) Graph A Graph B Note: No bonus questions were associated with Lab 6 Graph C Graph D Summary The motivation for the assessment portion of the project is not to actually measure the affect on student grades; in fact, improving student grades is not a goal of this project. Points are assigned to each lab in the same manner they are assigned to most class assignments - to motive student participation. The student scores are really most critical as a vehicle to determine whether students are willing participants to see if the level of the labs are proper for the students' background establish a baseline with respect to length of labs and if they can be completed in a timely fashion. try and establish whether this project merits further field testing and if so, what fine tuning needs to be done to incorporate it into the curriculum. Projects Future Considering the fact that not a lot of preliminary work was done to mentally prep students for the incorporation of the labs into the course, I was well pleased. Student participation was at the minimum what I had hoped for; and, as expected, students with the higher averages were more inclined to put forth a much more concerted effort to do their best. The number of students who attempted the last lab was much less than for the others and may be attributed to the fact that it came just prior to exams. I believe part of the success of the pilot labs was the fact that they (the labs) were prepared prior to the project which meant that most of tedious work was done in advance leaving time during the project for instructor energy to be focused towards motivation of the students and insuring that the curriculum paralleled the labs. The following labs have been written since this trial was conducted in Calculus I and will be added to the curriculum as time permits: Related Rates and the Chain Rule Applied to the Ideal Gas Law and Arterial Blood Flow Conditions Leading to Optimization (Maximum/Minimum) Through Chemistry The following labs have been written which are appropriate to the Calculus II curriculum: Exponential Grow and Decay Models Calculating the Center of Mass (Center of Data Values) for the Product in a Chemical Reaction Using Numerical Integration Note - If this project is continued into Calculus II (which is the intent), students will not be required to have participated in the program in Calculus I - in fact - if they have, it will be merely coincidental. Addendum Attached (PDF) to this report is an example of one of the labs used in this project.
More About This Textbook Overview Exploring the Real Numbers helps readers understand the real number system. Stevenson brings readers up to date with the study of the nature of real numbers, and provides a sense of the historical journey that has led to our current knowledge of the subject. Presents many interesting topics that arise during study of the real numbers. Offers 21 exploratory projects, encouraging readers to pursue concepts beyond the book. Includes over 100 carefully worked examples. Features abundant exercises throughout. For anyone interested in learning more about some of the very different and often beautiful aspects of mathematics. Rings of Factors. Sums of Consecutive Numbers. Measuring Abundance. Inside the Fibonacci Numbers. Pictures at an Iteration. Eenie Meenie Miney Mo. Factoring with the Pollard r Method. Charting the Integral Universe. Triangles on the Integral Lattice. The Gaussian Integers. Writing Fractions the Egyptian Way. Building Polygons with Dots. The Decimal Universe of Fractions, I. The Decimal Universe of Fractions, II. The Making of a Star. Making Your Own Real Numbers. Building 1 the Egyptian Way. Continued Fraction Expansions of x1/2N. A Special Kind of Triangle. Polygon Numbers. Continued Fraction Expans
Calculus AB: First-Time (math 1247) This course will consider topics typically included in the first year of a college-level calculus course. It will cover elementary functions, limits, and differential and integral calculus. Time will be set aside for discussion related to how to best set up a high school AP Calculus course. Methods, teaching materials and facility with the graphing calculator will be emphasized. Students will be actively engaged in problem solving, lesson design and discussion of the AP program. Course Objectives: Students in this course will: understand that Calculus is the mathematics of change and apply this principle to describe and predict the behavior of changing quantities. be able to calculate an amount (cost, distance, etc.) given a rate of change using integral calculus. understand and apply the Fundamental Theorem of Calculus. develop activities that will help their students understand the principles of calculus. understand and apply the concept of limit in developing the derivative and the integral. recognize the components of a strong AP curriculum in calculus develop strategies to help their students succeed in the AP program understand the components of the graphing calculator which students are required to know for the AP Calculus exam. demonstrate proficiency in solving both multiple-choice and free-response AP problems. Rose Gundacker taught AP Calculus, both AB and BC, for twenty years at Rosemount High School. She has been involved in the grading of AP exams since 1998 as a reader, table leader, question team member, and question leader. She has been a College Board* consultant since 1999, conducting summer workshops and one-day workshops throughout the Midwest. She is presently teaching Calculus part time at the University of St. Thomas in St. Paul. Summer Academic Programs The Summer Writing Program emphasizes a writing process approach, teaching you how to compose academic papers similar to those you will write in college. The program is designed for college-bound students with strong reading and writing abilities. The Carleton Summer Science Institute will help students learn to think and write like a scientist by doing science. CSSI students, faculty, and Carleton undergraduate research assistants will engage in classroom and hands-on research related to faculty and student interests. The Summer Quantitative Reasoning Institute is designed to give high school sophomores and juniors a substantial college-level experience in how social scientists think about the world, measure important variables of study, prepare research, and present their findings. Students will examine theories in three core disciplines - Economics, International Relations and Psychology. Students will learn how to systematically approach problems like a computer scientist as they engage in classroom learning, hands-on lab activities, and collaborative guided research directed by Carleton faculty and mentored by undergraduate research assistants. The program will culminate with a Research Symposium where students will demonstrate the results of their collaborative guided research project. The world is a complicated place—a tangle of languages and cultures and market forces. We've devised the Summer Language and Global Issues Institute to show how these entities are intertwined. While giving students an experience of language immersion in French or Spanish, we also provide an introduction to a global topic (this year: immigration) that reveals how language, culture, religion, history, economics and politics converge to influence the flow of populations. The Summer Humanities Institute is a three week program in which students develop and present interdisciplinary, guided research projects in History (including art historical topics) or literature and theater, and acquire tools and techniques of research, interpretation, and presentation essential to achieve the goal of humanistic research: to understand with depth and complexity the nature of human thought, action, and expression. The Summer Teaching institute is a week-long workshop for teachers of existing or proposed Advanced Placement, enriched, or accelerated classes in grades 7-12. Since 1980, Carleton has hosted more than 4500 teaches from over 520 schools nationwide.
Use of Logtables: The logarithm of a number consists of two parts: Characteristics : Integral part of log. Mantissa : Fractional or decimal part of log. To find characteristic (i) The characteristic of the log of a . number >1. is . Maths is a subject which is a part and parcel of our day to day life whether it is buying vegetables or going ... LogTables Logarithms 345 Antilogarithms 347 . TARGET Publications Std. XI Sci.: Perfect Maths - II 1 Sets, Relations and Functions Maths revision for algorithmic analysis The course will assume familiarity with a small range of standard ... The use of logtables is now a thing of the past but logarithms are still important in computer mathematics because 1+log 2!"n#$ is the Selecting Times Tables 23 Selecting in Basic Mode 23 Selecting in Advanced Mode 24 Selecting Topical Content 26 ... In all editions of Ultimate Maths Invaders, you can log in by either double-clicking the user or by selecting the user and clicking the Next button. Note: The Add User Discrete Maths 7. Discrete Maths SECTION B (Do 1 out of 4) 8. Further Calculus You can start studying any section you wish but it is advisable to start with Algebra and Trigonometry as these areas contain the fundamentals that are ... PAGE 6 & 7 OF THE TABLES r C b a c h C b a h h r r h r lMaths Find out your families favourite ... stick them in your learning log. Write a letter to Santa persuading him that you have been good this year. Think about different ways to begin ... Practice your times tables for BIG MATHS. MATHS LEARNING CENTRE Level 3, Hub Central, North Terrace Campus The University of Adelaide, ... We use log as an abbreviation for the word logarithm. ... bases 10 and e were listed in tables. As you can imagine, it was a herculean task constructing by hand, they used a tool called logarithm tables to do these multiplications. The logarithm tables basically ... This value of r is called log 10 x. Then, if you had to multiply x and y, you first found log 10 x and log 10 y. It turns out that log 10 (xy) = log 10 MathsLogTables No new books required for ordinary level. History: (1)The United States and the World (1945 – 1989) Folens (2)The Pursuit of Sovereignty and the Impact of Partition (1912-1949) Vincent Foley Folens Geography: Exam ... project using a PC maths package, making use of variable place arithmetic. The story that unfolds is remarkable: some parts, though well-documented, ... examples - using his logtables - that the operations of addition and well as learning about the slide−rule and logtables your grandfather might have used to make calculations 'Mathematics Galore' 'Mathematics Galore' 1. ... areas of maths a long way from normal curriculum courses the book lacks the gradual building up of ideas and a loglog = b log eometric series un = ar − 1 ... These tables concern tests of the hypothesis that a population correlation coefficient ρ is 0. The values in the tables are the minimum values which need to be reached by a sample correlation JF Maths, JF TP JF TSM, SF TSM Michaelmas Term 2007 Course 121 Monday, December 10 Luce Hall 14 ... but you may not use logtables. Page 2 of 2 XMA1212 1. Make a table listing the min, inf, max and sup of each of the following sets; write DNE for all quantities which fail to exist. You need not ...
26Algebra is accessible and engaging with this popular text from Charles "Pat" McKeague! ELEMENTARY AND INTERMEDIATE ALGEBRA is infused with McKeague's passion for teaching mathematics. With years of classroom experience, he knows how to write in a way that you will understand and appreciate. McKeague's attention to detail and exceptionally clear writing style help you to move through each new concept with ease. Real-world applications in every chapter of this user-friendly book highlight the relevance of what you are learning. And studying is easier than ever with the book's multimedia learning resources, including CengageNOW for ELEMENTARY AND INTERMEDIATE ALGEBRA, a personalized online learning companion.
SM6E Points of Inflexion Part 2. This video fleshes out the theory of the last video, Part 1 on Points of Inflexion with some practical examples of working through the maths associated with them. 18 more words SM6E. Points of Inflexion Part 1. This video introduces and examines points of inflexion and their behaviour. It was prepared for Year 12 Specialist Mathematics students in the State of Victoria, Australia. SM6C Derivatives of Inverse Circular Functions. This video was prepared for students of Specialist Mathematics, a Year 12 subject which is fully prescribed by the Victorian Curriculum and Assessment Authority in the State of Victoria, Australia. SM6B. Derivatives where x is a function of y. This video was prepared for students undertaking Specialist Mathematics in Year 12. This subject is fully prescribed by the Victorian Curriculum and Assessment Authority in the State of Victoria, Australia. SM3B Compound and Double Angle Formulae. This video explores and uses Compound and Double Angle Formulae for Circular Functions. The video was prepared for students undertaking Specialist Mathematics in Year 12, a science and engineering mathematics subject which is fully prescribed by the Victorian Curriculum and Assessment Authority in the State of Victoria, Australia.
Highlights of Calculus - Videos Prof. Gilbert Strang 작성 설명 Highlights of Calculus is a series of videos that introduce the fundamental concepts of calculus to both high school and college students. Renowned mathematics professor, Gilbert Strang, will guide students through a number of calculus topics to help them understand why calculus is relevant and important to understand. 이름 설명 등록일 가격 1 VideoGil Strang's Introduction to Highlights of Calculus Gil Strang gives an overview of his video series Calculus for MIT's Highlights for High School program. Designed to give an easier introduction to calculus. Calculus finds the relationship between the distance traveled and the speed — easy for constant speed, not so easy for changing speed. Professor Strang is finding the "rate of change" and the "slope of a curve" and the "derivative of a function." The second half of calculus looks for the distance traveled even when the speed is changing. Finding this "integral" is the opposite of finding the derivative. Professor Strang explains how the integral adds up little pieces to recover the total distance.
Material Type: Textbooks (245) Advanced Algebra II provides three complementary resources for teachers and students that ... (more) Advanced Algebra II provides three complementary resources for teachers and students that combine to provide a friendly, easy-to-understand explanation of Algebra II concepts. The main text, "Activities and Homework", consists of a series of worksheets for both in-class group work as well as homework assignments. The concepts behind those activities are described in detail in the "Conceptual Explanations" text. The third book, the "Teacher's Guide", provides instructors with guides and suggestions for presenting these materials. Over a period of time, I have developed a set of in-class assignments, homeworks, and lesson plans, that work for me and for other people who have tried them. If I give you the in-class assignments and the homeworks, but not the lesson plans, you only have ⅔ of the story; and it may not make sense without the other third. So instead, I am giving you everything: the in-class assignments and the homeworks (the Homework and Activities book), the detailed explanations of all the concepts (the Conceptual Explanations book), and the lesson plans (the Teacher's Guide). Once you read them over, you will know exactly what I have done. This digital textbook was reviewed for its alignment with California content standards. (less) This is the Conceptual Explanations part of Kenny Felder's course in Advanced ... (more) and the "Advanced Algebra II: Teacher's Guide" collections (coming soon) to make up the entire course. (less) Ahlan wa Sahlan: Functional Modern Standard Arabic for Intermediate Learners: Instructor's Handbook by Mahdi Alosh can be used by anyone who is an Arabic teacher or would like to become one, whether Ahlan wa Sahlan is used in the classroom or not. It includes tips on teaching from how to create the right kind of atmosphere in the classroom to specific drills used with Ahlan wa Sahlan. The example drills in the book can be generally applied to any language-learning textbook. (less) This second edition of book two in the Ahlan wa-Sahlan Modern Standard ... (more) This second edition of book two in the Ahlan wa-Sahlan Modern Standard Arabic textbook series has been revised and expanded to include communicative activities and grammar, an updated and expanded audio program, a companion website, and a new full-color design. Book two is designed to bring students up to the high-intermediate level upon completion. A glimpse of the culture of Cairo, Jordan, and Syria is included in the book. (less) This site contains dialogues in modern standard Arabic from the Al-Kitaab (including ... (more) This site contains dialogues in modern standard Arabic from the Al-Kitaab (including Alif Baa) textbook series. There are 74 recordings, grouped by category, and accompanied by transcripts, translations, and vocabulary sheets. Beside each recording are notes stating which module in the textbook series the recording goes with. (less) A work in progress, CK-12's Algebra I Second Edition is a clear ... (more) A work in progress, CK-12's Algebra I Second Edition is a clear presentation of algebra for the high school student. Topics include: Equations and Functions, Real Numbers, Equations of Lines, Solving Systems of Equations and Quadratic Equations. (less) CK-12's Texas Instruments Algebra I Teacher's Edition Flexbook allows an Instructor to teach students to better utilize a graphing calculator in understanding the fundamental concepts of algebra. (less) Anatomy and Physiology is a dynamic textbook for the yearlong Human Anatomy ... (more) Anatomy and Physiology is a dynamic textbook for the yearlong Human Anatomy and Physiology course taught at most two- and four-year colleges and universities to students majoring in nursing and allied health. There are 29 chapters organized by body system, and written at an audience-appropriate level. The online book provides students with links to surgical videos, histology, interactive diagrams, and cadaver imagery at critical junctures. (less) This is a blogspot through which the author has gathered a number ... (more) This is a blogspot through which the author has gathered a number of videos, PDF files, and articles to teach basic Arabic. There is information on how to install Arabic on a windows computer, vocabulary lists including the days of the week and Arabic phrases, an article on the history of Arabic grammar, information on the alphabet and how to read and write it, an Arabic keyboard, recorded conversations, links to the Madinah Books, and more. The majority of the information given is accompanied YouTube videos and written explanations. (less) Arabic complete is a website that offers Arabic Revisited, a free ebook that is a step-by-step guide complete with audio pictures available for Kindle, iPad, iPhone, iPod touch, Blackberry, and Android. The site further includes 80 podcasts, 7,000 audio recordings, and grammar lessons. Many of the lessons include a recorded dialogue that offers a transcription and translation of the dialogue. Classical Arabic, Modern Standard Arabic, and Egyptian dialect lessons are offered for students who are at an advanced and intermediate level. (less) This textbook is designed for beginning students in Arabic and focuses on ... (more) This textbook is designed for beginning students in Arabic and focuses on formal grammar. It tackles grammar from a classical standpoint and relies on highly technical terminology. The textbook includes exercises based on passages from classic Arabic literature as well as brief anecdotes. Two glossaries are appended at the end of the text. The filesize is 16 MB. (less) This is a textbook for beginning Arabic language learning. The textbook is ... (more) This is a textbook for beginning Arabic language learning. The textbook is divided into twelve lessons. Each lesson focuses on an activity and common theme to introduce the basics of Arabic. Each lesson starts with a short video, which you'll be asked to watch. To help you understand the video, each lesson also includes a transcript (in English), a list of vocabulary (with audio clips), and language and grammar notes. (less)
Algebra I Unit 10 (Pace 1106) In Algebra I Unit 10, students will learn solve word problems involving averages, percents, interest, perimeter, area and volume of geometric figures, monetary value, two-digit numerals, and bodies in motion. The character trait is temperance. This unit is one unit in a series of twelve colorful independent study mastery-based units of instruction and includes direct instruction to the student as well as all necessary quizzes and tests. Throughout the twelve Algebra I Paces your student will: Learn basic algebraic concepts (definitions, signs, and expressions), introduced in a carefully structured way to make the learning material understandable. Learn principles for logically solving, transposing, and canceling algebraic equations. Work with monomial and polynomial expressions. Work with algebraic addition, subtraction, multiplication, and division. Work with complex fractions: reducing, simplifying, and solving word problems. Learn algebraic graphing-linear equations, consistent, inconsistent, and dependent in word problems. Encounter quadratic equations, factoring, positive and negative numbers, averages, percents, interest, ratios, and proportions, and translate word problems to algebraic equations. Learn and implement the Pythagorean theorem. *Twelve DVDs reinforce this course.
$ 210.79 This is a comprehensive exposition of topics covered by the American Mathematical Society's classification "Global Analysis", dealing with modern developments in calculus expressed using abstract terminology.... $ 252.99 This book provides a comprehensive coverage of the fields Geometric Modeling, Computer-Aided Design, and Scientific Visualization, or Computer-Aided Geometric Design. Leading international experts have contributed,... $ 10.99 Linear models, normally presented in a highly theoretical and mathematical style, are brought down to earth in this comprehensive textbook. Linear Models examines the subject from a mean model perspective, defining... $ 116.29 LearningExpress's 20 Minutes a Day guides make challenging subject areas more accessible by tackling one small part of a larger topic and building upon that knowledge with each passing day. Practical Math Success... $ 74.99 Collecting, analyzing, and extracting valuable information from a large amount of data requires easily accessible, robust, computational and analytical tools. Data Mining and Business Analytics with R utilizes... $ 84.99 In How Math Explains the World, mathematician Stein reveals how seemingly arcane mathematical investigations and discoveries have led to bigger, more world-shaking insights into the nature of our world. In the... $ 10.79 The book could be a good companion for any graduate student in partial differential equations or in applied mathematics. Each chapter brings indeed new ideas and new techniques which can be used in these fields....
lack. I have gone through ESL/ES...It shows what is to come in Algebra by introducing the variable in formulas involving geometric shapes and ratios and solving one-step linear equations. Elementary Math delves into the factoring of the numerator and the denominator of fractions and into the properties of exponents. It works on the Pythagorean Theorem and uses said theorem to compute the length of an unknown side.
You might want to edit the second paragraph. The imperative voice can be grating to some readers. The second request is also somewhat broad... – danielSep 1 '12 at 1:55 The question is very broad. Many people have strong preferences, sometimes based on which program they have experience with. If you don't pose a more specific problem, I suspect there isn't a good answer. – Ross MillikanSep 1 '12 at 3:20 5 Answers I have heard that Sage is probably the best program there is for two subjects, number theory and graph theory. See this question on a Sage specific forum, with exact quote from the answer by kcrisman: "If you are doing graph theory or serious number theory, you shouldn't even be asking the question of which package to use." In other words. If you are doing graph theory or serious number theory, there is no question that Sage is the best. It is open source and has many other open source programs built in. It's free, which is much better than Maple or Mathematica. It also uses Python which is a main-stream language so as you work in you are developing a skill that is helpful in other places. You can easily program new functions if you like, and can even contribute them to future versions of Sage if you want. Here is an algebraic number theory book and elementary number theory book written by the creator of Sage. Both books have Sage code in them. Here is a cryptography book with a Sage appendix.
On selecting a constituent part of MU the "Overview of publishing activities" page will be displayed with information relevant to the selected constituent part. The "Overview of publishing activities" page is not available for non-activated items. This book presents methods of solving problems in three areas of classical elementary mathematics: Equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are immediately followed by carefully worked out examples of increasing degrees of difficulty, and by exercises which range from routine to rather challenging problems. While this book emphasizes some methods that are not usually covered in beginning university courses, it nevertheless teaches techniques and skills which are useful not only in the specific topics covered here. There are approximately 330 examples and 760 exercises.
Calculus: Single Variable (Coursera) This course provides a brisk, entertaining treatment of differential and integral calculus, with an emphasis on conceptual understanding and applications to the engineering, physical, and social sciences. Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences.
Summary: Mathematics 211A Fall 2001 Instructor: Professor R. Alperin; Office: Duncan 239; Telephone: 924-5066; E-mail: alperin@mathcs.sjsu.edu Text: Projective Geometry by P. Samuel, Springer-Verlag Course: Projective Geometry The main goal of this course is to introduce the students to the ideas of projective geometry, transformations and relations to conics. This is founda- tional material useful for the modern study of varieties, for example. Moreover, methods of projective geometry are important in understanding other impor- tant geometries and related combinatorial structures, and also algorithms used in computer graphics. There will be a second semester of this course which will cover the parts of the text not covered in this first semester and also other aspects related to algebraic curves, especially cubic and quartic curves. Curves have been extremely useful in modern aspects of error correcting codes, besides being fascinating geometrical quantities. Your final grade is based on the point total on two (take home) tests and homework. Homework will be assigned each class. Students must prepare a notebook of homework assignments which will be collected as announced.
Product Details Published: 2003 Isbn: 1-885581-45-9 Pages: 193 Math is an important part of everyday life and an integral part of the skills necessary to become certified in the safety profession. Many who pursue certification have long since completed their college math courses and have not actively pursued the math skills they once had. Background Math provides the basics necessary to successfully negotiate the math included on the certification exams, as well as a handy primer for those who already have their credentials. Topics include: Calculator selection and use, including BCSP rules for calculators, strategies for examinations and hierarchy for operations Fractions, reciprocals, proportions, rounding and absolute value Exponents, roots and logarithms and antilogs Systems of measurement, including English, metric, conversions and dimensional analysis Notation, both scientific and engineering Algebraic properties and simple equations, including variables, commutation, associative and distributive properties, order of operations, rules of equations, multiplying polynomials, and solving equations
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Mathematics Placement Mathematics Placement Exam Information All students at Saint Mary's College of California are required to take an appropriate mathematics or computer science class as part of their liberal arts experience. In order for you to be successful in your mathematics and science classes you need to be in a college level mathematics class for which you are prepared. In order to enroll in a mathematics course at SMC you must satisfy the Mathematics Placement Requirements. ∫: What's New The math department is seeking applications for the Brother Dominic Barry Math Scholarships to be awarded to in-coming freshmen in 2013! Find out more about our scholarships and sign up for the scholarship competition HERE! October 18, 2011 ∑: Featured Math Fun Nature or Nurture? A podcast on where our "Number Sense" comes from: Numbers, by Radiolab The mathematical physicist, John Baez, blogs about math and physics in Environmental Science Azimuth
Mathematics for Economists Book Description: Mathematics for Economists, a new text for advanced undergraduate and beginning graduate students in economics, is a thoroughly modern treatment of the mathematics that underlies economic theory. An abundance of applications to current economic analysis, illustrative diagrams, thought-provoking exercises, careful proofs, and a flexible organization-these are the advantages that Mathematics for Economists brings to today's classroom
007877344X 9780078773440 Geometry, Study Guide and Intervention Workbook:The Study Guide & Intervention Workbook contains two worksheets for every lesson in the Student Edition. Helps students: Preview the concepts of the lesson, Practice the skills of the lesson, and catch up if they miss a class. Tier 2 RtI (Response to Intervention) addresses students' needs up to one year below grade level. Back to top Rent Geometry, Study Guide and Intervention Workbook 1st edition today, or search our site for textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Glencoe/McGraw-Hill.
MAPLE: Mastery Achievement Personalized Learning Engagement Developmental Math The MAPLE format requires 80% Mastery Achievement of each topic and will employ Personalized Learning which will increase student Engagement with the material and the instructor. All students will begin by taking an initial assessment over numerous concepts. If the student shows mastery on this overall assessment, the student will be allowed to take an assessment on another set of concepts without completing assignment covering those topics. If the student does not show mastery on this group of topics, they will take assessments on smaller groups of topics. If the student shows 80% mastery on an assessment on a topic, the student will be allowed to continue to the next topic immediately. If a student scores less than 80% on a topic, the student will be required to do the lesson for that topic and take another assessment. The student must continue working on the topic until an 80% or higher is scored on the assessment. Benefits to the student Ability to complete all Developmental Math courses in as little as one semester, thus saving the student time and money Ability for the student to master topics that will be required to successfully complete College Level Math courses Ability for the student to bypass topics mastered in previous courses, thus allowing time for new topics Ability to access learning materials 24/7 Ability for the student to continue the course the next term at the topic last completed, if a minimum amount of topics are mastered Ability for the student to attend alternate class times in addition to their scheduled time Ability for the student to receive one-on-one attention from instructors each class meeting
In this activity students view and analyze images of ramps and steps to see if they conform to the requirements of the Americans with Disabilities Act. Students measure horizontal and vertical distances and compute the... Created by David Smith for the Connected Curriculum Project, this module develops a graphical representation for a differential equation that reveals the nature of solutions, even when formulas for those solutions are Murray Bourne developed the Interactive Mathematics site while working as a mathematics lecturer at Ngee Ann Polytechnic in Singapore. The site contains numerous mathematics tutorials and resources for students and...
... More hosted by Wolfram Research, Inc., and is offered as a free service to the mathematics community. Technical Requirements: Basic browser. A Java-enabled browser provides enhancements but site is fully viewable without Java. Much of the material is powered by "Live Graphics 3D" which produces images similar to those in Mathematica. Discussion for Eric Weisstein's World of Mathematics Jessica Lynn (Other) Like a great interactive online textbook for math, one could easily get lost clicking from link to link. I bookmarked this page for further use. The visuals are great, the content is crisp and the information is easily accessible. This would be a great resource for teachers or for anyone looking for help with a math project. 9 years ago jason miller (Student) Although I am new to Merlot, this isn't the first time I've been on mathworld. I have used this site before for research on a mathematics paper. Just for fun I checked out how diverse this site is and was even more impressed with it. I will bookmark it for future use. A good tool for instructors and students alike. Easy to use, and well organized. 10 years ago Barbra Bied Sperling (Staff) The giant of Mathematics reference tools on the net. It was such an amazingly exhaustive catalogue of mathematics concepts, with superior illustrations, that it was also published in print. An absolutely phenomenal contribution by one person, comparable in scale to a mathematician's life's work. Used in course 11 years ago Christopher Taylor (Student) The sheer volume of material here is staggering. This site certainly outlines pretty much anything the average mathematics student could want to know. I spent a good twenty minutes just looking around, making sure that everything I could want to know was there. Like those hard to remember formulae from high school geometry, for example, because who can remember those when they need them...in their college math classes. Anyway, this site was very dense, from a materials stand-point, but never difficult to navigate. I would highly recommend it to anyone without a textbook handy. It has pretty much everything you could be looking for. 12 years ago Ben Flores (Student) The most outstanding math site I have ever visit, so easy to use an so much to see, I will have to get back to it with more time, I learn that usually Physicis use the term sphere to mean the solid ball, but mathemathicians give a total different meaning, and that is the outer surface of a bubble.
Description This well-respected text gives an introduction to the theory and application of modern numerical approximation techniques for students taking a one- or two-semester course in numerical analysis. With an accessible treatment that only requires a calculus prerequisite, Burden and Faires explain how, why, and when approximation techniques can be expected to work, and why, in some situations, they fail. A wealth of examples and exercises develop students' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. The first book of its kind built from the ground up to serve a diverse undergraduate audience, three decades later Burden and Faires remains the definitive introduction to a vital and practical subject. Contents Mathematical Preliminaries and Error Analysis \| Solutions of Equations in One Variable \| Interpolation and Polynomial Approximation \| Initial-Value Problems for Ordinary Differential Equations \| Direct Methods for Solving Linear Systems \| Iterative Techniques in Matrix Algebra \| Approximation Theory \| Approximating Eigenvalues \| Numerical Solutions of Nonlinear Systems of Equations \| Boundary-Value Problems for Ordinary Differential Equations \| Numerical Solutions to Partial Differential Equations Additional ResourcesCompanion WebsiteRelated TopicsCalculus and Analysis
The irresistibly engaging book that "enlarges one's wonder at Tammet's mind and his all-embracing vision of the world as grounded in numbers." --Oliver Sacks, MD THINKING IN NUMBERS is the book that Daniel Tammet, mathematical savant and bestselling author, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates... more... Maths is everywhere, often where we least expect it. Award-winning professor Steven Strogatz acts as our guide as he takes us on a tour of numbers that - unbeknownst to the most of us - form a fascinating and integral part of our everyday lives. In The Joy of X , Strogatz explains the great ideas of maths - from negative numbers to calculus, fat... more... All the math basics you'll ever need! It's not too late to learn practical math skills! You may not need to use quadratic equations very often, but math does play a large part in everyday life. On any given day, you'll need to know how long a drive will take, what to tip a waiter, how large a rug to buy, and how to calculate a discount. With The... more... This text embodies at advanced and postgraduate level the professional and technical experience of two experienced mathematicians. It covers a wide range of applications relevant in many areas, including actuarial science, communications, engineering, finance, gambling, house purchase, lotteries, management, operational research, pursuit and search.... more... Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-application of functions was at the heart of Russell's paradox. This led Russell to introduce type theory in order to avoid the paradox. Since, the twentieth century has seen an amazing number of theories concerned with types... more... Rod structures are widely used in modern engineering. These are bars, beams, frames and trusses of structures, gridwork, network, framework and other constructions. Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics... more...
Algebra 1 is a key program in our vertically-aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments
....New. Brand new. We distribute directly for the publisher. Proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into six chapters: Geometry and Algebra; Trigonometry, Calculus and Analytic Geometry; Inequalities; Integer Sums; Sequences and Series; and Miscellaneous. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics883857007
ForThe second edition preserves the book's clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions. Review from the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably."—MATHEMATICAL REVIEWS Book Description:SPRINGER VERLAG GMBH 01/02/2014, 2014. Hardback. Book Condition: New. New Book. This item is printed on demand. Shipped from US This item is printed on demand. Bookseller Inventory # IJ- New York, NY, 2013. Book Condition: New. Language: english. For three decades, this classic has been a must-have textbook for transitional courses from calculus to analysis, celebrated for its clear style and simple proofs. This edition adds material on the irrationality of pi, the Baire category theorem and more. Bookseller Inventory # 26436985
The overriding mission of this site is to effectively accomplish the following: ................................ o Aid the students in their efforts to successfully negotiate and complete the basic courses in Chemistry, Physical Science, Physics, and Process Technology(PTEC). Inasmuch as these basic level science courses require a level of preparedness in basic mathematics, the student should consult their advisor to ensure that the prerequisites have been satisfied. If uncertain, it is strongly suggested that the student complete the relevant sections in basic mathematics(marked with a yellow check below[i.e., ]). In essence, by following this approach, the student will reduce, if not eliminate, most anxiety. o Provide a valuable resource for scientists and engineers of all stripes. This will, therefore, be an evolutionary effort. Hence, as needed, improvements, modifications, additions, and etc, will be an on-going process. As humankind, we must keep in mind that wise application of science and technology can lead to a better world. The following individual study modules are evaluation/assessment aids which will aid the student/individual to both review and adequately determine their respective level of preparation in basic mathematics. The following two(2) refresher/review/practice sections provide some introductory practice activity for those students/interested individuals who are either taking or plan to take a science course. These sections are also good practice for those who may simply be curious!
ACT Math Formula Pages "Cheat Sheets" for three major ACT Math Topics Quickly review for the ACT Math test using 1-page formula sheets. These pages contain important equations for each topic along with short examples to show how the equations are used in ACT Math problems. Download the first two formula pages for FREE. ACT Formula Page:TRIGONOMETRY ($5) The Trigonometry Formula sheet covers right triangles, trig ratios, identities, trig equations, and more. The Trig problems on the ACT are considered some of the harder math problems, so they generally show up near the end of the test. This ACT formula sheet summarizes important equations, definitions, graphs, and examples to help you quickly review Trig for the ACT Math test. $5 IMPORTANT!!After completing your payment in Paypal, stay on that screen and look for the linkReturn to MathOnTimeto access the file. NOTE: Each of the formula pages above is a 1-page pdf. You'll need the (free) Adobe Reader to view and print the files. Tips for printing the ACT Math Formulas & Tips pages 1. You may want to print in color to better see the organization of each page. However, if you only have access to a gray-scale printer, you'll be able to see all the ACT Formulas & Tips just fine. 2. Each of these files should print as a single page. If you have trouble with the edges cutting off, look for a "shrink to fit" option for your printer. Be sure to check out MathOnTime's ACT Math practice test,ACT Math Made EASY. This VIDEO practice test provides a fast and low-cost way to prepare for the ACT Math test.
IowaInformation and Communications Technologies Tutorials Mon, 17 Dec 2012 09:41:07 -0600Foundational Subjects Tutorials Information and Communications Technologies Center (ICT) presents this collection of links to a number of online tutorials. The tutorials fall under the categories of mathematics, physics, electronics, ethics and general science. These resources would be helpful in a variety of classroom settings and many instructors and students would benefit from the collection.Wed, 28 Nov 2012 09:28:31Loci: Constructing Mathlets Quickly Using LiveGraphics3D Mathematical Association of America (MAA) has developed a vast set of educational materials for mathematics teachers, and many of them can be found on their well-thought out website. This particular resource is an article by Jonathan Rogness and Martin Kraus, and the piece offers an explanation of how to use a Java applet called LiveGraphics3D to speed up the process of creating interactive graphics. Visitors can use this piece to learn how to accurately describe and create animations that illustrate various mathematical principles and objects. The piece is divided into eighteen short sections, including "Moving Lines and Polygons", "Advanced Examples", "Future Directions", and "Occlusions of Objects". It's a fine resource overall, and it will probably inspire interested parties to explore the other articles archived here.Thu, 22 Sep 2011 03:00:05 -0500CAUSEweb Resources Consortium for the Advancement of Undergraduate Statistics Education (CAUSE) was part of an initiative created by the American Statistical Association, and their website was designed to "support and advance undergraduate statistics education in four target areas resources, professional development, outreach, and research." With monies from the National Science Foundation, they created CAUSEweb, where they provide this set of resources for members of the undergraduate statistics education community. The resources are divided into eleven categories, including "analysis tools", "datasets", and "curriculum". "Curriculum" has 350 resources, including searchable databases of 1000 test questions for an introductory statistics course and a demonstration site that addresses nonprobability sampling. The "lecture examples" shouldn't be missed, as visitors can use these resources to complement their existing lectures and class presentations. The site is rounded out by a listing of their review criteria and editorial standards for determining which resources make the cut for inclusion here.Mon, 12 Sep 2011 03:00:04 -0500Carnegie Foundation for the Advancement of Teaching: Statway by the Carnegie Foundation for the Advancement of Teaching, the Statistics Pathway (Statway) is focused on providing educational resources on statistics, data analysis, and quantitative reasoning. The hope is that the Statway program will help students "understand the world around them and the math they can use right now." On the site, interested parties can take advantage of resources related to this mission, including the "Problem Solution Exploration Papers". These papers are designed to measure student success in community college developmental mathematics and to help identify problems of practice for potential future work. Visitors can also view materials from their recent summer institute, including presentations made by content specialists and others. The site is rounded out by the "Readings, Reports, Essays" area which includes some primers on improving developmental mathematics education.Sat, 19 Mar 2011 15:49:12 -05 Online: Classroom Capsules and Notes Mathematical Association of America (MAA) provides a range of high-quality educational resources for educators all across the United States and the world. Recently, they completed digitizing over 114 years of their short classroom materials, and they are now available right here. On the homepage, visitors can look over "Featured Items" to get started, and then they can type in keywords to look for specific items. Recently featured items have included "Proof without Words: Geometric Series", "Museum Exhibits for the Conics", and "The Birthday Problem Revisited". Visitors should also check out the "Tips on Searching" area to help out with their exploration of this archive. Educators will find that the site is worthy of several visits, and this material can be used to illuminate a wide range of mathematical topics and concepts.Fri, 19 Nov 2010 13:33:24 -0600
2013-2014 CCGPS Mathematics Unit Frameworks Teacher and Student Editions of the 2013-2014 CCGPS Mathematics Unit Frameworks were posted on July 1, 2013, to GeorgiaStandards.Org and Learning Village. These unit frameworks reflect the thoughtful collaboration and dedication of mathematics teachers, coaches, and supervisors from across the state of Georgia. Please refer to the release date of July 1, 2013, on the footer of the documents to insure you have accessed the most recent version. 9-12 CCGPS Mathematics Overview In high school (grades 9-12) the standards are organized by conceptual categories, the overarching ideas that describe strands of content in high school, domains/clusters, which are groups of standards that describe coherent aspects of the content category, and standards, which define what students should know and be able to do at each grade level. These standards include skills and knowledge – what students need to know and be able to do, as well as mathematical practices – habits of mind that students should develop to foster mathematical understanding and expertise. The high school standards are organized around five conceptual categories: number and quantity, algebra, functions, geometry, and statistics and probability. The high school standards call on students to practice applying mathematical ways of thinking to real world issues and challenges; they prepare students to think and reason mathematically. The high school standards set a rigorous definition of college and career readiness, not by piling topic upon topic, but by demanding that students develop a depth of understanding and an ability to apply mathematics to novel situations, as college students and employees regularly do. Standards indicated with a (+) are beyond the college and career readiness level but are necessary to take advanced mathematics courses such as calculus, advanced statistics, or discrete mathematics. The high school standards emphasize mathematical modeling—the use of mathematics and statistics to analyze empirical situations, understand them more fully, and make better decisions. For example, the standards state: "Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data." The CCGPS Mathematics framework units were developed under a grant from the U. S. Department of Education. However, the contents do not necessarily represent the policy of the U. S. Department of Education, and users should not assume endorsement by the Federal Government.
Weehawken MathCalculus is used extensively in numerous fields: business, physics, biology, medicine, engineering. Its ability to deal with change makes it a useful tool for describing the constantly changing world. Without calculus, modern science and technology would not exist
The Barron's Painless book series just took Pre-Algebra to the next level, fun! Test your knowledge and then test your skill...it's the ultimate Pre-Algebra and arcade game challenge 5 3 3 2 2 1 8Prepare to achieve the ACT scores you need to get into your top choice schools. Get ready for the test day with this most comprehensive app on ACT Math : Pre-Algebra 400 questions across 40 subtopics. ~~~~~~~~~~~~~~~~~~~~~~~~~ Features include: • HIGHEST QUALITY and QUANTITY Over 400 questions and 40 revision notes in all just for Pre-Algebra. High quality content written by experienced ACT tutors. • MOCK TEST Mixed questions from all topics. • REVIEW WITH• REVISE BY TOPIC 1. Basic Number and Arithmetic Addition and Subtraction with Negative Numbers Using Integer Properties Negative Numbers Multiplying and Dividing with Negative Numbers Order of Operations and PEDMAS Place Value and Ordering Numbers Approximation of Roots and Exponents Multiplication and Division Problems The Number Line Disclaimer: ACT is a registered trademark of ACT Inc. ACT Inc neither sponsors nor endorses this product or any of its content. There may be a possibility of some bugs, inaccuracies or typographical errors for which the owner cannot be held liable.Test yourself on: Addition, Subtraction, Multiplication, Division, Negative Numbers, Decimals, Percents, Fractions, Order of Operations, Exponents and Square roots. Get the steps to solve these problems in real time as you take the test. Solution steps use the actual values in the test questions to show how to get the answer. You can take any of the six standard tests provided and save the results to see what types of problems give you trouble. You can also use the Test Builder to create tests that contain 20 questions of whatever type(s) you choose. Test Builder results can also be saved and reviewed planeREAL TEACHER TAUGHT LESSONS Pre-Algebra This course teaches students to expand number sense to understand, perform operations, and solve problems with rational numbers. Pre-Algebra is taken by students as a first introduction to the concepts and skills needed to be successful in Algebra and higher math. Chapter 10 Area and Volume 10.1 Area of a Parallelogram 10.2 Area of a Triangles and Trapezoids 10.3 Area of Circles 10.4 Space Figures 10.5 Surface Area of Prisms and Cylinders 10.6 Surface Area of Pyramids, Cones and Spheres 10.7 Volume of Prisms and Cylinders 10.8 Problem Solving - Make Model 10.9 Volume of Pyramids, Cones and Spheres And 4 more chapters with 8 lessons each Chapter 11 Right Angles in Algebra Chapter 12 Data Analysis and Probability
Buy Used Textbook Buy New Textbook eTextbook Instant Online Access 180 day digital rental $75.99 More New and Used from Private Sellers Starting at $121Ideal for lecture-format courses taught at the post-secondary level, ELEMENTARY ALGEBRA, Ninth Edition, makes algebra accessible and engaging. Author Charles "Pat" McKeague's passion for teaching mathematics is apparent on every page. With many years of experience teaching mathematics, he knows how to write in a way that you will understand and appreciate. His attention to detail and exceptionally clear writing style help you to move through each new concept with ease, and real-world applications in every chapter highlight the relevance of what you are learning.
... read more Customers who bought this book also bought: Our Editors also recommend: Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller Remarkable puzzlers, graded in difficulty, illustrate elementary and advanced aspects of probability. These problems were selected for originality, general interest, or because they demonstrate valuable techniques. Also includes detailed solutions. Probability Theory: A Concise Course by Y. A. Rozanov This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, and more. Includes 150 problems, many with answers. Elements of the Theory of Markov Processes and Their Applications by A. T. Bharucha-Reid Graduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. Appendixes. Bibliographies. 1960 edition.Foundations of Probability by Alfred Renyi Taking an innovative approach to both content and methods, this book explores the foundations, basic concepts, and fundamental results of probability theory, plus mathematical notions of experiments and independence. 1970 edition as those who wish to attain a thorough knowledge in the field. Based on the author's lectures at the University of Budapest, this text requires no preliminary knowledge of probability theory. Readers should, however, be familiar with other branches of mathematics, including a thorough understanding of the elements of the differential and integral calculus and the theory of real and complex functions. These well-chosen problems and exercises illustrate the algebras of events, discrete random variables, characteristic functions, and limit theorems. The text concludes with an extensive appendix that introduces information theory. Bonus Editorial Feature: Alfred Renyi: The Happy Mathematician Alfred Renyi (1921–1970) was one of the giants of twentieth-century mathematics who, during his relatively short life, made major contributions to combinatorics, graph theory, number theory, and other fields. Reviewing Probability Theory and Foundations of Probability simultaneously for the Bulletin of the American Mathematical Society in 1973, Alberto R. Galmarino wrote: "Both books complement each other well and have, as said before, little overlap. They represent nearly opposite approaches to the question of how the theory should be presented to beginners. Rényi excels in both approaches. Probability Theory is an imposing textbook. Foundations is a masterpiece." In the Author's Own Words: "If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy." "Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?" — Alfred Rényi
Modern Algebra: An Introduction 1 rating: 3.0 A book by John R. Durbin This book presents an introduction to modern (abstract) algebra covering the basic ideas of groups, rings, and fields. The first part of the book treats ideas that are important but neither abstract nor complicated, and provides practice in handling … see full wiki Effectively usable text in modern or abstract algebra With the exception of material such as encoding that requires a computer for the most complex problems; the area called modern algebra has not changed in decades. In fact, this is an area where the inclusion of a computer in the early work is detrimental rather than beneficial. Modern algebra is also known as abstract algebra for good reason, to understand it you have to be able to process symbols abstractly. Therefore, I tend to score modern algebra books lower if there is significant dependence on a computer. That is not an issue with this book; computer involvement is kept to a minimum. First courses in modern algebra are now fairly fixed in terms of coverage and this one is in no way a deviant. Proofs of the most important basic concepts are present but not in overwhelming numbers. The style of presentation is to introduce one concept, illustrate it with examples and then have a series of exercises, some of which are answered in an appendix. The final three chapters cover:
Engineering Mathematics by K.A. Stroud ... This is one of the reasons Engineering Maths is so popular as incomplete explanations often hinder learning more than help. The one thing I would stress is that this book really can only be considered as the first half of a two part set. I don't know about other Engineering courses but ... Read review category books comics magazines about speedy hen ltd by continuing with this checkout and ordering from speedy hen you are accepting our current terms and conditions details of which can be found by clicking here content note tables graphs country of publication united states date of publication 10 03 2011 edited by a k haghi format hardback genre level 1 adult non fiction specialist genre level 2 engineeri Great Value, Very clear, easy to understand, You can pass exams, earn more money, buy more beer You might not find it useful but everyone I know does "As someone studying for an engineering degree this book has proved invaluable. it starts at the basic components of A-Level Mathematics and works it way through a large portion of the maths needed for a first year engineering course. The book is divided into programmes so it works similarly to a lectured course. it directs the reader to answer certain questions and achieve the correct answers before progressing. it seems like an overly-simplistic ..." Read review "...form of Maths, Physics or Engineering in your degree then I highly recommend that you purchase this book! Maths comes into so many things and covers a very wide range of topics but for the basic things and a wide range of what you will study in your first few years at university this book has it well covered. Unlike other books that I have looked at, this book does not assume that you have gained an A or A* at A-level Further mathematics or mathematics. ..." Read review "1236 PAGES As an Engineering student I own several maths text books but this beauty is by far the best. This book differs from most maths textbooks in that it is easy to read and understand. It is designed for people who use maths.. but not "true mathematicians" .. which is why its so great!! If you're really awesome at maths (550+ / 600 in Further Maths without working) you could probably cope with something harder and poncier! If you see maths ..." Read review "...maths student. If your an Engineering student, Chemist, Physicist, Cybernetician etc etc this book is perfect for you. It contains vast amounts of useful and accessible knowledge. What I mean by accessible is that this book requires no prior research. It takes topics and breaks them down into constituent parts and takes you through very slowly. Asking you little questions throughout and giving you the answers. It then moves on to the more complex ..." Read review Those with superior maths/further maths skills may find it less helpful "As a 3rd year Mechanical Engineering student at UCL I have found this textbook to be the most useful textbook in my study and revision arsenal. Although engineers are required to cover and learn a great deal of math concepts, they must more importantly be able to apply them in everyday problems with confidence. This is where this particular book is heads and shoulders above the rest. Instead of assuming that the reader is already a master of ..." Read review
Using the author's considerable experience of applying Mathcad to engineering problems, Essential Mathcad introduces the most powerful functions and features of the software and teaches how to apply these to create comprehensive calculations for any quantitative subject. The simple, step-by-step approach makes this book an ideal Mathcad text for professional engineers as well as engineering , science, and math students. Examples from a variety of fields demonstrate the power and utility of Mathcad's tools, while also demonstrating how other software, such as Excel spreadsheets, can be incorporated effectively. A companion CD-ROM contains a full non-expiring version of Mathcad 14 (North America only). The included software is for educational purposes only. Mathcad is the industry-standard software for engineering calculations. Its easy-to-use, unitsaware, live mathematical notation, powerful capabilities, and open architecture allow engineers and organizations to streamline critical design processes
TI-84 Plus Silver Step-by-Step Instructions PDF (Acrobat) Document File Be sure that you have an application to open this file type before downloading and/or purchasing. 0.1 MB PRODUCT DESCRIPTION Basic instructions for the TI84-Plus that include: descriptions of menu keys; how to create lists and then use the list to find measures of central tendency; how to graph lines; how to change the viewing window. Instructions include screen captures at each step so students can make sure they are doing the right thing. 2009, Sashaa Murphy Average Ratings Comments & Ratings Product Questions & Answers Be the first to ask Sashaa Murphy
More About This Textbook Overview This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from Editorial Reviews From the Publisher 'This is a textbook that demonstrates the excitement and beauty of geometry ... richly illustrated and clearly written.' Extrait de L'Enseignement Mathématique '... this is a remarkable and nicely written introduction to classical geometry.' Zentralblatt MATH '... could form the basis of courses in geometry for mathematics undergraduates. It will also appeal to the general mathematical reader.' John Stone, Times Higher Education Supplement 'It conveys the beauty and excitement of the subject, avoiding the dryness of many geometry texts.' J. I. Hall, Mathematical Association of America 'To my mind, this is the best introductory book ever written on introductory university geometry ... readers are introduced to the notions of Euclidean congruence, affine congruence, projective congruence and certain versions of non-Euclidean geometry (hyperbolic, spherical and inversive). Not only are students introduced to a wide range of algebraic methods, but they will encounter a most pleasing combination of process and product.' P. N. Ruane, MAA Focus '... an excellent and precisely written textbook that should be studied in depth by all would-be mathematicians.' Hans Sachs, American Mathematical
Teach Algebra: Write Exprssns - MAT-960Teach Algebra: Write/Simplifying Expressions - Teaching the first ideas of Algebra is extremely important to give students the foundation that they will need to succeed in math courses for years to come. This course, and the accompanying AIMS lessons, will help any teacher build a strong foundation in Algebraic principles using hands-on activities. Primarily focused on the Common Core standard 6.EE, these lessons use four big ideas along with activities, video demonstrations and animations to reinforce the concepts. Teachers will also reflect on the lessons based on concepts from the National Board for Professional Teaching Standards in an effort to bridge content and pedagogy
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There are specific 'practical' problems but there is much more development of the ideas … [The authors] have shown how to write a serious yet lively look at algebra."—The American Mathematics Monthly "Were 'Algebra' to be used solely for supplementary reading, it could be wholeheartedly recommended to any high school student of any teacher … In fact, given the long tradition of mistreating algebra as a disjointed collection of techniques in the schools, there should be some urgency in making this book compulsory reading for anyone interested in learning mathematics."—The Mathematical Intelligencer This text, which is intended to supplement a high school algebra course, is a concise and remarkably clear treatment of algebra that delves into topics not covered in the standard high school curriculum. The numerous exercises are well-chosen and often quite challenging. The text begins with the laws of arithmetic and algebra. The authors then cover polynomials, the binomial expansion, rational expressions, arithmetic and geometric progressions, sums of terms in arithmetic and geometric progressions, polynomial equations and inequalities, roots and rational exponents, and inequalities relating the arithmetic, geometric, harmonic, and quadratic (root-mean-square) means. The book closes with an elegant proof of the Cauchy-Schwarz inequality. Topics are chosen with higher mathematics in mind. In addition to gaining facility with algebraic manipulation, the reader will also gain insights that will help her or him in more advanced courses. The exercises, which are numerous, often involve searching for patterns that will enable the reader to tackle the problem at hand. Many of the exercises are quite challenging because they require some ingenuity. Some of the exercises are followed by complete solutions. These are instructive to read because the authors present alternate solutions that offer additional insights into the problem. This book inspires even those with minimal interest in mathematics. If you are passionate about math, this is a must for you. The book is simply a refresher for high school algebra. It contains numerous gems that you could hardly find in a standard algebra text. If you are a teacher, you would have learned much to improve your teaching style and knows how to make your math classes more interesting...overall, a key source to keep on your bookshelf Well, H. Wu on his page and N.F Taussig here have written quite good reviews, so I guess I can't really add anything new. Still, I feel the need to praise this book some more. Could it be used for a main text or should it be just a supplement? I don't know, but there is much more mathematics contained in these 149 pages than in any standard 500 page high school text on the market today. That's the unsurprising result of accomplished mathematicians writing a math book. Sure, some topics are missing. You won't find 3 or 4 chapters devoted to the several "different" ways to graph a line. There aren't fifty problems in a row that start with "suppose Sam rows upstream at 5 miles per hour and it takes her seven times as long as..." Unfortunately, there isn't even a treatment of complex numbers, the only omission that seems wrong. You will find several interesting and serious topics that would be dangerous to bright students who insist they hate math, or rather what they've been told is math. Imagine their initial embarrassment when they find out that they can enjoy the subject! Maybe more importantly, imagine their relief when they realize that there IS a reason why we "FOIL", there IS a reason why negative times negative is positive, there IS a reason why we say a^(-1)=1/a, and it's not because "the teacher said so" or "that's just the rule" (ok, it is the rule, but now you'll see why). And there's no attempt to sneak anything by the reader. The authors are quick to acknowledge any gaps in their reasoning, and to assure the reader that in the future he or she will fill them. It's this honesty and attention to rigor without being too formal or dry that give this book some extra charm. It moves smoothly from basic arithmetic (which everyone should still read if only to learn a different way of explaining it to a student/younger sibling/child) all the way to proofs, both algebraic and visual when possible, of some important inequalities. Cauchy's inductive proof, first for powers of two and then filling in the gaps, of the AM-GM inequality is here, as is the standard proof of Cauchy-Schwarz by the discriminant of a polynomial. Go to your local high school and look at its algebra book. I doubt that's in there. I bought this book for my daughter (10 years old) and we read it together. We went very slow and I supplement it with a work book. She likes it. I was impressed by the beauty of this book. It might be a little too slim for a textbook but every kid who wants to learn algebra should read it. More than teaching algebra it shows what math should be: simple and beautiful. My daughter's math textbook is 5 pounds and I can't even stand looking at it. I understand that not every is enthusiastic about math and not everyone can feel the beauty of math. But you don't have to make math so ugly. Learning math with a 5 lb textbook is simply terrifying but if your kid goes to public school you probably have no choice. Let you kid read a good book like this one, as early as possible, before he(she) grows a life time aversion to math. The material in the book, the knowledge, its great and wonderful. The style with which the information is presented is beautiful because it does so in the form of questions but in the process of answering the questions is how you obtain the information; the book makes you think. The way with which the book is bound is another story though. My book started coming apart after only a few days, the pages are glued with no string to hold the pages together at all; they easily rip at the binding and from what I notice is that there is no way around it. It just spontaneously happening while I was trying to hold the pages open in a way so that the book is full open. It is getting 4 stars because of the information and not five because of the binding. this isn't a primary algebra book; I would most definitely recommend it to use as a supplement along with any other text though because it is great in that role.
int... read more Customers who bought this book also bought: Our Editors also recommend:Sets, Sequences and Mappings: The Basic Concepts of Analysis by Kenneth Anderson, Dick Wick Hall This text bridges the gap between beginning and advanced calculus. It offers a systematic development of the real number system and careful treatment of mappings, sequences, limits, continuity, and metric spaces. 1963 edition. Product Description: introductory section by the author reviews the roles of sets, relations, and functions. Subsequent chapters explore real numbers, the limit concept, useful theorems, continuity, differentiability, and integrability. The author focuses on real-valued functions of a real variable. Considerations of complex numbers appear only in optional supplements to certain chapters, as well as in the final two chapters, which consist of in-depth explorations of sequences of functions and Fourier series. Each chapter features several helpful exercises
MATH R116 - College Trigonometry Course description: This course is designed to give calculus-bound students a solid foundation in trigonometric functions. Emphasis will be placed on the trigonometric functions and their graphs, radian measure, trigonometric identities and equations, inverse trigonometric functions, complex numbers in trigonometric form, and DeMoivre's Theorem. Special topics in trigonometry, such as solving right triangle applications, law of sines, law of cosines, parametric equations, vectors, polar coordinates, and curves in polar form are also included. See a counselor for more information on IGETC or CSU GE-Breadth certification. Some transfer information: Credit for MATH R116 can be transferred to several universities; the chart below shows a few of the possibilities. For more complete transfer information, see a counselor at the Transfer Center or visit ASSIST online.
algebra book requires a different type of reading than a novel or a short story. Every sentence in a math book is full of information and logically linked to the surrounding sentences. You should read the sentences carefully and think about their meaning. As you read, remember that algebra builds upon itself; for example, the method of factoring that you'll study don page 188 will be useful to you on page 697. Be sure to read with a pencil in your hand: Do calculations, draw sketches, and take notes. 1. VOCABULARY: you'll learn many new words in algebra. 2. SYMBOLS: algebra, and mathematics in general, has its own symbolic language. You must be able to read these symbols in order to understand algebra. 3. DIAGRAMS: throughout this book you'll find many diagrams. They contain information that will help you understand the concepts under discussion. 4. DISPLAYED MATERIAL: throughout this book important information is displayed in gray boxes. This information includes properties, definitions, methods, and summaries. 5. READING AIDS: throughout this book you will find sections called Reading Algebra. These sections deal with such topics as independent study and problem solving strategies. 6. EXERCISES, TESTS, AND REVIEWS: each lesson in this book is followed by Oral and Written Exercises. Lessons may also include Problems, Mixed Review Exercises, and optional Computer Exercises. Answers for all Mixed Review Exercises and or selected Written Exercises, Problems, and Computer Exercises are given at the back of this book. Within each chapter you will find Self-Tests that you can use to check your progress. Answers for all Self-Tests are also given at the back of this book. Each chapter concludes with a chapter Summary that lists important ideas from the chapter, a Chapter Review in multiple-choice format, and a Chapter Test. Lesson numbers in the margins of the Review and Test indicate which lesson a group of questions covers.
Student Explorations in Mathematics - National Council of Teachers of Mathematics (NCTM) An official journal of the NCTM, Student Explorations in Mathematics publishes resources for teachers and teacher educators at grades 5-10. Each issue develops a single mathematical theme or concept in such a way that fifth grade students can understand the first one or two pages, and so that high school students will be challenged by the last page. The content and style of the notes are intended to interest students in the power and beauty of mathematics and to introduce teachers to some of the challenging areas of mathematics within the reach of their students. Article downloads are free to individual members who subscribe to SEM. Read submission guidelines and browse back issues. more>> Adventures in Statistics - Scavo, Petraroja A Web unit preprint of a paper by teachers Tom Scavo and Byron Petraroja that describes a mathematics project involving fifth grade students and the area of classrooms, including measurement, graphing, computation, data analysis, and presentation of results; ...more>> Algebra 4 All A community of educators sharing resources and supporting one another in the practice of teaching algebra: lesson sharing, applets for students and teachers, discussion forum, blogs, media, and other content related to the functions-based approach to ...more>> The Algebra Survival Kit - Josh Rappaport A kit that includes a 520-page handbook covering the main content areas of Algebra 1 in accordance with the NCTM Standards. Sections are tabbed, and pages are written in flash card format with questions on the front and answers on the back. Also, a poster, ...more>> Algorithmic Vectorial Geometry - Jean Paul Jurzak In French. The author writes: "This work studies vectorial geometry under a new aspect which allow to solve most of the exercises of vectorial geometry without the traditional support of a drawing. For students, teachers, and informaticians." ...more>> Alive Maths/Maths à Vivre - Nathalie Sinclair Hands-on, interactive "microworlds," in which students investigate patterns and relationships, pose questions, play with the variables, and solve problems: Play with Lulu on a grid; practice triangle reflections; play with fractions and decimal patterns ...more>> Analysis & Knowledge - Sanford Aranoff Download data analysis software, such as Patterns, which analyzes and charts trends in stock market using Andrews concepts. See also this former Rutgers University physics professor and current high school educator's thoughts on teaching and help file ...more>> AngryMath - Daniel R. Collins Blog by an adjunct math lecturer at Kingsborough Community College who believes that "Math is a battle. It is a battle that feels like it must be fought ...," and for whom "math isn't beautiful or fun, but it is powerful, and that's what we need from ...more>> Avances de Investigación en Educación Matemática The official publication of the Spanish Society for Research in Mathematics Education (SEIEM, Sociedad Española de Investigación Matemática) welcomes contributions in either Spanish or Portuguese. Freely download PDFs of past articles,b's law - Brian Lawler Blog begun March, 2011, by a professor of math education at California State University San Marcos. Posts, which "try to disrupt," have included "continued reaction to tracking," "The Problem of the Skateboarder Problem in IMP," "A Deconstruction of Learning ...more>> CalculusABC.com - Chris Watson A site for calculus teachers to share questions they've written and discuss issues relating to the field. Sort multiple choice questions according to calculator use and representation type (verbal, numerical, analytical, or graphical). With web forums ...more>> Constructing Math Instruction - Chris Robinson Blog by teacher "averse to binary thinking that refuses to countenance all the complexities of the minefield that is the real classroom." Posts, which date back to December, 2012, have included "Number Sense and My Students"; "Analyzing Student Questions"; ...more>> The Cow in the Classroom - Ivars Peterson (MathLand) Math Curse by Jon Scieszka and Lane Smith spoofs the types of word problems that educators and textbook writers invent to dress up arithmetic exercises and, supposedly, to demonstrate the relevance of math to everyday life. Canadian economist and humorist ...more>> Daniel Willingham From the author of Why Don't Students Like School? and When Can You Trust the Experts? (subtitled: "How to tell good science from bad in education"). See, in particular, Willingham's articles, such as "Why transfer is hard," "Why students remember or ...more>> Developing Function Sense with SAQs - Judah Schwartz A work in progress, this is an online book on the philosophy of teaching functions in middle and high school algebra. He has come to believe "that approaching algebra through the study of functions using symbolic and graphical representations simultaneously ...more>> Double Division - Jeff Wilson Double Division is a method for doing manual division that reinforces the principles of division and gives students success with a less frustrating alternative. The online calculator shows and explains each step. Feedback from teachers who've used theEASI Street to Science, Engineering, and Math (SEM) Equal access to software and information: an NSF-sponsored project to collect and disseminate information on tools that make these fields more accessible to professionals with disabilities. Online workshops, Webcasts, links to programs for the visually ...more>> Educational Aspirations "Ramblings from a 21st century educator" who specializes in differentiating math and seeks to make the subject "more engaging and relevant to students' lives." Blog posts, which date back to July, 2011, have included "Measuring Student Growth," "Twitter ...more>> Edward Burger Journal publications, Thinkwell textbooks, and other professional activities of the Francis Christopher Oakley Third Century Professor of Mathematics, formerly Baylor University's Robert Foster Cherry Professor for Great Teaching. Burger, who co-authoredThe Exponential Curve - Dan Greene A blog by a math teacher at Downtown College Prep charter high school (San Jose, California), where the students "... are primarily Latino, are far below grade level in their math and reading skills, and will be the first in their families to go to college. ...more>> Finding Ways to Nguyen Students Over - Fawn Nguyen Nguyen blogs mostly about her teaching middle school math. Posts, which date back to November, 2011, have included "Teaching 101 -- How I Got Like This," "Puzzles and Brainteasers, Set 11," "Pi Day Activities," "Always Sometimes Never," "Using Excel for ...more>> garysmathsblog One maths teacher's "personal musings" about his experiences, as well as maths resources and teaching tips to help teach maths. Blog posts, which date back to May, 2011, have included "Fraction word problem," "Dyscalculia," "Mean, median and mode rhyme," ...more>> gealgerobophysiculus - Evan Weinberg Thoughts on teaching, learning, and "the crazy process of having fun doing both with students." Posts, which date back to September, 2011, have included "How China Keeps Me Learning: Part I," "Lens Ray Tracing in Geogebra," "Take Time to Tech – Perspectives ...more>>
51 FREE About the Book Designed for students who are new to the graphing calculator, or for people who would like to brush up on their skills, this instructional graphing calculator videotape covers basic calculations, the custom menu, graphing, advanced graphing, matrix operations, trigonometry, parametric equations, polar coordinates, calculus, Statistics I and one variable data, and Statistics II with Linear Regression. This wonderful tool is 105 minutes in length and covers all the important functions of a graphing calculator.
"Your best class mate" Math Helper is a comprehensive higher mathematics calculator Actually, Math Helper is a mix of textbook and complex calculator. This means that besides calculation features, there's the theory and the calculation procedure of each math category that you can find on this app. Thus, you can look up any doubt in the theory, refresh how to calculate it and then fill up the parameters and let the app solve it. There are four categories: Linear Algebra (including matrices and systems of linear equations, Vector Algebra (vectors and figures), The mathematical analysis (Derivatives), and Other (including probability theory and number & sequences). We're used to review all kind of calculators. However, Math Helper goes a step further with higher mathematics, including operations like "calculate determinant of a matrix", "finding the number of permutations", "arithmetic and geometric progressions". The added-value feature of this app is precisely that it allows users to perform lots of complex calculations from a single mobile app while helping them remember main rules and theories. Only one catch: interface should be enhanced. Anyway, recommended app.
Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory. For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter. New to the Second Edition: Expanded chapter on stochastic integration that introduces modern mathematical finance Introduction of Girsanov transformation and the Feynman-Kac formula Expanded discussion of Itô's formula and the Black-Scholes formula for pricing options New topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motion Applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals

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