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Sett i gang I consists of 15 chapters organized around five main themes. The textbook is 229 pages and suitable for the first semester of a university course or during the first year of a community... More > education class.< Less Sett i gang II consists of 15 chapters organized around five main themes. The textbook is 229 pages and suitable for the second semester of a university course or during the second year of a... More > community education class.< Less Beginning and Intermediate Algebra was designed to reduce textbook costs to students while not reducing the quality of materials. This text includes many detailed examples for each section along with... More > several problems for students to practice and master concepts. Complete answers are included for students to check work and receive immediate feedback on their progress. Topics covered include: pre-algebra review, solving linear equations, graphing linear equations, inequalities, systems of linear equations, polynomials, factoring, rational expressions and equations, radicals, quadratics, and functions including exponential, logarithmic and trigonometric. Each lesson also includes a World View Note which describes how the lesson fits into math history and into the world, including China, Russia, Central America, Persia, Ancient Babylon (present day Iraq) and more!< Less This is a prealgebra textbook, used by the Department of Mathematics at College of the Redwoods, Eureka, California, in their Math 376 course. Errata and Individual chapter and solutions are... More > available at: Mixcraft 6 is a fun and easy-to-use program that instantly turns your computer into a fully-stocked music recording studio. Mixcraft 6 Teacher's Guide is the ideal compliment for educational... More > programs that use Mixcraft in the classroom. The book examines Mixcraft's many capabilities including composing music, recording, mixing, adding effects, and working with video. The Teacher's Guide provides numerous examples of how to incorporate Mixcraft into both music and non-music assignments, including marketing and advertising, podcast creation, and spoken word performances. Included within this book are 13 inventive lessons designed for grade school through high school classes. Together, these lessons address all of the National Standards for Music Education (NSME). Along with the book, there is a free "Additional Materials Download" which includes helpful teaching aids, such as printable lesson plans, fun example projects, video clips, and other useful resources.< Less The first of a two-volume textbook for college General Chemistry students, this book takes a "novel" approach on two fronts. It's written and formatted in a way that encourages it... More > be read just like any other book, while also eschewing many of the traditional tropes of traditional chemistry textbooks. Figures, graphs and tables are embedded within the text itself, usually without labels or captions, in an attempt to keep the "narrative flow" going. Similarly, sample calculations are presented in a step-by-step fashion to mimic how an instructor would guide a student through a problem if he or she were doing it in person.< Less This is a textbook for differential calculus with explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the... More > author. Topics are typically introduced by way of applications, and the text contains the usual theorems and techniques of a first course in calculus. Besides technique practice and applications of the techniques, the examples and problem sets are also designed to help students develop a visual and conceptual understanding of the main ideas of differential calculus. The exposition and problem sets have been highly rated by reviewers.< Less The Upper Level Independent School Entrance Exam® (ISEE) is often required for admission to American private high schools. This book is one of the only, if not the only, offering of its kind that... More > focuses solely on the ISEE and specifically the test for students applying to grades 9 through 12. Focusing purely on the Upper Level ISEE allows us to offer an extraordinarily comprehensive guide that includes 6, full-length practice Upper Level ISEEs, 850+ vocabulary words with definitions, and nearly 2000 practice problems. General Academic is an academic consulting firm with offices in Houston and Dallas. We created this book initially for use in our own test preparation courses and with our private clients; however, now we hope that you too will benefit from our research and experience even if you cannot make it into one of our offices. Please note that ISEE® is a registered trademark of the Educational Records Bureau, which does not endorse this product.< including Charm Bracelet Project: Culture and Community on Pittsburgh's North Side tells the story of cultural, educational and recreational organizations transforming traditional understandings of how... More > The ensuing partnerships and collaborations launched an intentional practice of sharing agendas and joining agendas by and between the 'charms' of the North Side, creating a 'bracelet' on the North Side to strengthen family experiences, guide future development and invigorate the everyday spaces of a city. < Less
Overview of Lower Division Courses General Information for Freshmen and Sophomores: Most freshmen and sophomores interested in science, engineering or finance take courses from the standard calculus and linear algebra sequence 103-104-201-202 which emphasizes concrete computations over more theoretical considerations. Note that 201 and 202 can be taken in either order. More mathematically inclined students, especially prospective physics majors, may opt to replace 201-202 with 203-204 for greater emphasis on theory and more challenging computational problems. Students who are not prepared to begin with 103 may take 100, a rigorous precalculus/prestatistics refresher. 100 may be followed by 102 or 103; 102 is a one-semester survey of selected topics from 103 and 104, for students who do not intend to take further calculus courses. Students who will later need 104 should not take 102. Prospective economics majors can minimally fulfill their mathematical prerequisites with (100)-102-175, but 103-175 is strongly preferred. 175 covers selected topics from 104, 201 and 202 with biology and economics applications in mind. Some future economics majors will need the standard sequence 103-104-201-202 instead, especially recommended for those who plan to continue with 300-level mathematics courses and/or go on to graduate school in economics or finance. Prospective mathematics majors must take at least one course introducing formal mathematical argument and rigorous proofs. For many this will be 215, but 214 or 217 are more algebraic alternatives. One recommended sequence for prospective majors is 215-217-218, especially suitable for those who already have some experience with constructing proofs. Other possible sequences for prospective majors include 214-217-203 and 203-204-215, although the latter is relatively rare. Note that 215 and 217 may be taken in either order, as can 203 and 204. Placement Overview: Students with little or no background in calculus are placed in 103, or in 100 if their SAT mathematics scores indicate insufficient background in precalculus topics. To qualify for placement in 104 or 175, a student should score 5 on the AB Advanced Placement Examination or a 4 on the BC Advanced Placement Examination. To qualify for placement into 201 or 202, a student should have a score of 5 on the BC Examination. Students who possess in addition a particularly strong interest in mathematics as well as a SAT mathematics score of at least 750 may opt for 203 or 214 or 215 instead. Initial placement into 217 or higher for incoming freshmen requires consultation with the placement officer.
Math for Nurses A Pocket Guide to Dosage Calculation and Drug Preparact and easy-to-use, Math for Nurses is a pocket-sized guide/reference to dosage calculation and drug administration. It includes a review of basic math skills, measurement systems, and drug calculations/preparations. Math for Nurses helps students to calculate dosages accurately and improve the accuracy of drug delivery. The author uses a step-by-step approach with frequent examples to illustrate problem-solving and practical applications. Readers will find it great for use in the clinical setting or as a study aid. Practice problems throu... MOREghout the text and end-of-chapter and end-of-unit review questions will aid students' application and recall of material. A handy pull-out card contains basic equivalents, conversion factors, and math formulas.
The fifth edition of Essential MATLAB for Engineers and Scientists provides a concise, balanced overview of MATLAB's functionality that facilitates independent learning, with coverage of both the fundamentals and applications. The essentials of MATLAB are illustrated throughout, featuring complete coverage of the software's windows and menus. Program design and algorithm development are presented clearly and intuitively, along with many examples from a wide range of familiar scientific and engineering areas. This is an ideal book for a first course on MATLAB or for an engineering problem-solving course using MATLAB, as well as a self-learning tutorial for professionals and students expected to learn and apply MATLAB. Updated with the features of MATLAB R2012b Expanded discussion of writing functions and scripts Revised and expanded Part II: Applications Expanded section on GUIs More exercises and examples throughout Companion website for students providing M-files used within the book and selected solutions to end-of-chapter problems
この書籍内から Great overview of how to introduce and teach math concepts. It doesn't contain specific lesson plans, but would be useful to read before beginning a new math unit - it will give you an overall view on ...レビュー全文を読む
Mathematics All Around Plus MyMathLab Student Access KitMathematics u... MOREnderstand the math, not just get the correct answers on the test. Useful features throughout the book enable students to become comfortable with thinking about numbers and interpreting the numerical world around them. Problem For all readers interested in mathematics. Mathematics understand the math, not just get the correct answers on the test. Useful features throughout the book enable students to become comfortable with thinking about numbers and interpreting the numerical world around them. Problem For all readers interested in mathematics. 6. Number Theory and the Real Number System: Understanding the Numbers All Around Us 6.1 Number Theory 6.2 The Integers 6.3 The Rational Numbers 6.4 The Real Number System 6.5 Exponents and Scientific Notation 6.6 Looking Deeper: Sequences 7. Algebraic Models: How Do We Approximate Reality? 7.1 Linear Equations 7.2 Modeling with Linear Equations 7.3 Modeling with Quadratic Equations 7.4 Exponential Equations and Growth 7.5 Proportions and Variation 7.6 Functions 7.7 Looking Deeper: Dynamical Systems 8. Modeling with Systems of Linear Equations and Inequalities: What's the Best Way to Do It? 8.1 Systems of Linear Equations 8.2 Systems of Linear Inequalities 8.3 Looking Deeper: Linear Programming 9. Consumer Mathematics: The Mathematics of Everyday Life 9.1 Percent 9.2 Interest 9.3 Consumer Loans 9.4 Annuities 9.5 Amortization 9.6 Personal Finance 9.7 Looking Deeper: The Annual Percentage Rate 10. Geometry: Ancient and Modern Mathematics Embrace 10.1 Lines, Angles, and Circles 10.2 Polygons 10.3 Perimeter and Area 10.4 Volume and Surface Area 10.5 The Metric System and Dimensional Analysis 10.6 Geometric Symmetry and Tessellations 10.7 Looking Deeper: Fractals 11. Apportionment: How Do We Measure Fairness? 11.1 Understanding Apportionment 11.2 The Huntington-Hill Apportionment Principle 11.3 Applications of the Apportionment Principle 11.4 Other Paradoxes and Apportionment Methods 11.5 Looking Deeper: Fair Division 12. Voting: Using Mathematics to Make Choices 12.1 Voting Methods 12.2 Defects in Voting Methods 12.3 Weighted Voting Systems 12.4 Looking Deeper: The Shapley-Shubik Index 13. Counting: Just How Many Are There? 13.1 Introduction to Counting Methods 13.2 The Fundamental Counting Principle 13.3 Permutations and Combinations 13.4 Looking Deeper: Counting and Gambling 14. Probability: What Are the Chances? 14.1 The Basics of Probability Theory 14.2 Complements and Unions of Events 14.3 Conditional Probability and Intersections of Events 14.4 Expected Value 14.5 Looking Deeper: Binomial Experiments 15. Descriptive Statistics: What a Data Set Tells Us 15.1 Organizing and Visualizing Data 15.2 Measures of Central Tendency 15.3 Measures of Dispersion 15.4 The Normal Distribution 15.5 Looking Deeper: Linear Correlation Appendix A Basic Mathematics Review Tom Pirnot received his bachelor's degree in music from Wilkes College and his PhD in mathematics from The Pennsylvania State University. He taught both mathematics and computer science at Kutztown University for thirty eight years. He has long been an innovator in liberal arts mathematics, writing his first text Mathematics: Tools and Models with Dalton Hunkins in 1977 which introduced topics such as apportionment, graph theory, and modeling to liberal arts students. His current text, Mathematics All Around, is now in its fourth edition. Tom continues to enjoy the loving support and encouragement of his wife Ann, their four children, and three grandchildren.
Product Details: The TI-Nspire™ CAS with Touchpad handheld device lets you map out your lessons, steer learners on their journey and help them to reach their goals with state-of-the-art TI-Nspire technology. With CAS (Computer Algebra Systems) you can perform numeric, exact and symbolic calculations, factor and expand expressions and solve equations and prepare and teach mathematically-rich lessons in less time. Description: The latest TI math and science learning technology features the TI Nspire family of products and services. This technology goes beyond graphing to help students see math and science in new and different ways. TI Nspire technology was developed
Calculus: Early Transcendentals - 9th edition Summary: The ninth edition continues to provide engineers with an accessible resource for learning calculus. The book includes carefully worked examples and special problem types that help improve comprehension. New applied exercises demonstrate the usefulness of the mathematics. Additional summary tables with step-by-step details are also incorporated into the chapters to make the concepts easier to understand. The Quick Check and Focus on Concepts exercises have been updated as well. Engine...show moreers become engaged in the material because of the easy-to-read style and real-world examples. ...show less Chapter 5 Integration 5.1 An Overview of the Area Problem 5.2 The Indefinite Integral 5.3 Integration by Substitution 5.4 The Definition of Area as a Limit; Sigma Notation 5.5 The Definite Integral 5.6 The Fundamental Theorem of Calculus 5.7 Rectilinear Motion Revisited Using Integration 5.8 Average Value of a Function and its Applications 5.9 Evaluating Definite Integrals by Substitution 5.10 Logarithmic and Other Functions Defined by Integrals Chapter 6 Applications of the Definite Integral in Geometry, Science, and Engineering 6.1 Area Between Two Curves 6.2 Volumes by Slicing; Disks and Washers 6.3 Volumes by Cylindrical Shells 6.4 Length of a Plane Curve 6.5 Area of a Surface of Revolution 6.6 Work 6.7 Moments, Centers of Gravity, and Centroids 6.8 Fluid Pressure and Force 6.9 Hyperbolic Functions and Hanging Cables0183454047018345413.68 +$3.99 s/h Good eCampus.com Lexington, KY May contain some highlighting. Supplemental materials may not be included. We select best copy available. - 9th Edition - Hardcover - ISBN 9780470183458 $26.03 +$3.99 s/h Good One Stop Text Books Store Sherman Oaks, CA 2008-11-24 Hardcover Good $26.03 +$3.99 s/h Good One Stop Text Books Store Sherman Oaks, CA 2008-11-24 Hardcover Good Good. $31.49 +$3.99 s/h VeryGood DGABooks AL Helena, AL 2008-11-24 Hardcover Very Good Text has no markings noted. Cover is clean, binding tight. Expedited available with tracking number. $34
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The Kumon Math Curriculum Curriculum Objectives The main aim of the program is to prepare students for Advanced High School and College level Math through a mastery of the core skils and an ability for self-learning. The lower level Kumon worksheets are designed to build mastery of the four operations, which are the basics of Mathematics. Students with a mastery of addition, subtraction, multiplication and division can easily learn more complex operations such as long division, fractions, equation solving and factorization. Next, positive and negative numbers are introduced, followed by algebra, factoring, functions, and finally, calculus. Curriculum Structure The Math Program consists of 23 levels, numbered levels 7A through to level Q. Each Level consists of 200 pages (with the exception of Level P) and is broken down by topic into sections. Additionally, each section is broken down into sets of 10 pages each. Therefore, each level consists of 20 sets. The worksheets are designed in minute steps to facilitate self-learning. The worksheets contain mostly computational problems. As students study higher levels of Mathematics, the percentage of calculations, both in school curriculum and textbooks, increases. The worksheets focus on developing the students´ computational skills. The ability to calculate develops the ability to think and lead the way to creativity. Whenever there are new lessons presented, examples are provided to help students comprehend the concepts behind the exercises. The Program begins with very basic number recognition, counting and writing, and progresses through addition, subtraction, multiplication, division and fractions. From there it goes to negative numbers, followed by algebra, factoring, functions, calculus and other CEGEP and university level topics. The Kumon Math Program takes a linear approach to math education. Each concept that is introduced builds on knowledge and skills learned from the previous concept. For this reason, it is important that students completely master and understand their current concept before advancing to the next
Master Your Basics: The number one reason that people struggle in math class is because their basics and their fundamentals are not fully developed. Algebra and Geometry are the building blocks for the more advanced math later on (Calculus, Differential Equations, etc...). 2 Get Ahead: Most schools give you a textbook for math and it's a pretty big book. What you can do is, study ahead. Whenever you have time, you can look a section ahead, and be prepared for tomorrow's material. 3 Self-Study: This is the most efficient way of studying math. I would recommend you to buy math textbooks from a local bookstore. You can also search on the internet for great math books.Don't get a book that is very short (100 pages) for a topic like Geometry. Get a textbook or a few workbooks on the topic. It's good to buy more than one book, since some books leave out certain things. 4 Studying: When you self-study, it's good to have the book and a notebook with you, college ruled preferably. Write down all the vocabulary and terms and the example problems. You don't have to do each and every single practice problem if you find it repetitive, just have an intuitive answer. (As long as you know the process of solving it) It's also good to get into a habit of working on more Word Problems, which can help you apply the concept into real-life situations. 5 Competition: If you do enough self-studying, and you look through your studying notes when you have free time, you should already have a very good basis in math. If you're a fast learner, then it would be even better since you can learn the higher level concepts quicker. If your school has a math club or team that you can join, go for it! Chances are, you'll meet individuals who are very talented in math and can help you expand your knowledge by attending competitions. 6 Loving Math: Once you do this part, math would be no challenge whatsoever. Once you get good in math, help others, it's okay to show off you knowledge, in a good way. Once you start to take interest in math and start studying it and attend math competitions and expand your knowledge on math, you will love it. Once you have a passion for math, you will want to learn more, achieve more, and become the mathematician you've never imagined
MATH 420 : Combinatorics An introduction to fundamental combinatorial objects, their uses in other fields of mathematics and its applications, and their analysis. Does an object with certain prescribed properties exist? How many of them are there? What structure do they have? Paired with MATH 720. Students who have completed MATH 720 may not take MATH 420 for credit.
» Science and Nature » Biology. (3.00 from 2 reviews)Science4U: Practical Math for Practical Science by Richard Ignace Price: $2.49 USD. Approx. 11,140 words. Language: English. Published on August 18, 2010. Category: Nonfiction » Science and Nature » Mathematics. (1.00 from 1 review) Helpful for college, high school, and homeschooled students, this book is for those who struggle with math in science. Scientific notation, algebra, geometry, trigonometry, and vector concepts are addressed as used in the sciences, with examples and exercises. Readers will gain proficiency with using math as the language of science.
...Prealgebra instruction includes a review of the basics of mathematics and a thorough introduction to integers, basic equations and word problems. This course is designed to develop the skills and understanding to perform the fundamental operations on whole numbers, fractions and decimals. Topic... be great. I grew up in Texas, so naturally I've been around Spanish my whole life
Book DescriptionEditorial Reviews From the Back Covermore than104,000 copies were bought of the prior edition!includes problems and examples using graphing calculators. Master calculus with Schaum's If you don't have a lot of time but want to excel in class, this book helps you: brush up before tests; find answers fast; study quickly and more effectivley; get the big picture without spending hours poring over lengthy textbooks. Schaum's Outlines give you the information your teachers expect you to know in a handy and succinct formatwithout overwhelming you with unnecessary details. You get a complete overview of the subject. Plus, you get plenty of practice exercises to test your skill. Compatible with any classroom text, Schaum's let you study at your own pace and remind you of all the important facts you need to rememberfast! And Schaum's are so complete. Inside, you will find: 1103 problems, with step-by-step solutions New graphing calculator help, with practical problems Math review sections to help the under prepared Complete explanations of calculus concepts If you want top grades and thorough understanding of calculus, this powerful study tool is the best tutor you can have! About the Author Frank Ayers, Ph.D., (deceased) was a professor and head of the department of mathematics at Dickinson College. Elliott Mendelson, Ph.D., (Roslyn, NY) is a professor of mathematics at Queens College. I found this book to be a very good supplement to anyone taking a calculus course. The main highlights (and some, but few) lowlights are as follows: The Good: 1. LOTS and LOTS of topics covered ranging from limit concepts to l'Hopital's rule to integral tests to multiple integrals, this book covers A LOT (and even a brief intro to differential equations.) 2. Enough practice problems to ensure that the reader will comprehend the material (as is the case with most Schaum Outline books). 3. Lots of graphs for visual learners. 4. A fraction of the price of most calculus books. The Bad: 1. The only bad thing I could possibly think of in this book is that it explains vector concepts and differentiation and integration of vector functions and gradient, divergence, and curl, but leaves out Green's and Stokes' theorems (must be covered in the vector analysis Schaum book). For more detail, check out the list of chapter topics on the back cover of the book (it's a pretty thick paragraph) I've worked with several versions of the Schaum's Calculus over the years. This work has excellent coverage of derivatives, integrals, curvilinear motion, polar coordinates, indeterminate forms, indefinite integrals, centroids, arc length, tests for divergence/convergence, partial derivatives, volumes, triple integrals and a host of exotic areas. There are many multi- dimensional diagrams to aid in your understanding of this fairly complex subject. I did well in Intermediate Calculus garnering an "A". In addition, the Fundamentals of Engineering Licensure Exam covered quite a bit of basic and intermediate calculus. This is an excellent supplementary work to complement the course textbook and class notes. This outline will work best for those looking for a concise supplement to their course text. The strength of this outline is in the solved problems. The weakness is in the explanation of concepts. As advertised, the book contains over 1100 fully worked problems. These problems are indeed fully worked and looking over them can be of tremendous value if you are struggling with solving particular problems in your class. If you are having a tough time with the concepts rather than the problems of calculus I would not recommend this book. The explanations are kept to a bare minimum and tough topics like delta-epsilon proofs and Reimann Integrals are not explained in detail. For instance, this book will not try to justify why you can set delta equal to epsilon to complete your limit proof, it just tells you to do it (which is exactly what you need to do to solve the problem). In other words, this book will help you solve the problems you need to solve in order to pass your exams, but it will not necessarily help you understand why those solutions work. So please do not buy this thinking it will have fuller conceptual explanations. Its strength is in its fully solved problems. My instructor had a nervous breakdown about 1 month into an integral calculus class. He spent the rest of the semester discussing his personal problems during class, instead of teaching. He stopped giving tests and cancelled his office hours. We had a midterm, which I failed (with a 28/100), along with the rest of the class. My entire grade hinged on the final exam. I bought this book and spent the last half of the year using this book to teach me integral calculus. Two weeks before the final, the instructuor told the class that he was throwing out the midterm, and that our grade for the class would be based solely on our performance on the final exam. I got a 96/100 on the final, and an "A" for the course. This book saved me. (This sounds ridiculous, I know...but it is absolutely true.) A good overview of calculus, though--admittedly--I am using it to review the subject rather than learn it for the first time. Very practical, and offers enough examples to get the hang of it in most cases. However, the egregious number of serious errors in the book (in a 4th edition?!) can often be frustrating if not misleading. Some errors are misstatements of theorems or errors in the worked problems! Others include mislabeled graphs, incorrect PROBLEMS (yes!), incorrect answers etc. Believe, me, I've spent hours checking my work, assuming I had made the mistake (but have verified using mathematica, graphing calculators etc.) For someone working nearly every problem, this leads to a lot of confusion and a huge waste of time. I estimate that I have found 20-30 major errors already, and I've only finished the chapters covering calculus of a single variable. :( If they had errata published, it might be a little better, but haven't been able to find any. Unfortunately, haven't tried other review texts...probably better just to get a real calculus book. I've forgotten the one I used in high school and subsequently sold. :( A good, fast review of your first two college semesters of calculus. A lot of material covered, 59 chapters, 575 pages but take note, it isn't called an outline for nothing. The worst problem is the problem that mars many technical efforts such as this - errors. Errors are abundant, especially in the figures containing graphics right where you don't need them most. If you are looking for a review like I was, it will work, but don't take this route your first time through.
Your teachers and parents will have information about ... contemporary works. R.F1: Use phonetic skills to decode ... STANDARD 4: Geometry General concepts you should know: Geometry Concepts and Skills from Holt McDougal meets the ... Across Time, The Early Ages - Ohio Version Glencoe/ McGraw ... It supports instruction with comprehensive teachers ... This activity works best when done in groups. ... The National Council of Teachers of Mathematics ... Mind Approach to Geometry (pp. 9-11). Glencoe/McGraw-Hill. ... students and preparing future teachers for this task. We view Hilberts geometry as ... This streamlining only works if the ... Geometry. Glencoe Mathematics.Glencoe, Chicago IL ... Hall Algebra 1, Geometry, and Algebra 2 2011the new Prentice Hall High School ... and leveled resources enables teachers to adapt to the changing needs of their ...
Formats Book Description Publication Date: Feb. 15 2007Last year in our homeschool, we switched to "Mastering Essential Math Skills: Middle Grade/High School, and it was the best switch we could have made. Both girls were to the point of dreading math, and after changing to this program, they now looked forward to math class and could make sense of it because of the step-by-step instructions. Great for 7th-8th grades. Our 2nd daughter actually moved from 5th grade to 7th grade because this program was available. 64 of 71 people found the following review helpful 1.0 out of 5 starsNot as advertisedFeb. 17 2007 By Parent - Published on Amazon.com Format:Paperback\|Amazon Verified Purchase I loved the grade 6-8 edition of this book for reviewing math with my daughter. It is an excellent step by step approach to middle school math. This edition is the same book with very little added. It is not "high school" math. I wouldn't call it "Book Two". I was expecting something very different based on the title. Highly recommended for 6-7 grade math practice and review. 16 of 16 people found the following review helpful 4.0 out of 5 starsGood math book, but has typo's.July 17 2007 By The Way - Published on Amazon.com Format:Paperback This book is helping me getting freshed up in math but it contains a few typo's. For example, on page 7 it says there are two #5 problems. There should be obviously one problem #5 and the other is problem #6. Nevertheless, it is a good math book. I just wished it gave more examples on how to actually DO some of the work.
More About This Textbook Overview There are a number of books on financial mathematics, which either discuss the methods or use HP financial calculators. Using HP calculators is slow and prone to error and the variables cannot be seen once entered. Since most financial managers have Excel on their desk, it is more efficient to solve the problems on spreadsheets and gain the benefits of layout and more comprehensive information. Mastering Financial Mathematics in Microsoft Excel is a practical guide with exercises and solutions throughout. It provides a comprehensive set of tools and methods that will help you apply Excel to solve mathematical problems. Alistair Day clearly explains the basic calculations for mathematical finance backed up with simple templates for further use and development, together with examples. The new edition includes the addition of end of chapter exercises to help you develop your knowledge. The accompanying CD allows you to use and adapt templates and models. Product Details Meet the Author Alastair Day has worked in the finance industry for 20 years in treasury and marketing functions. In 1990 he established Systematic Finance as a consultancy and financial lessor concentrating on the computer and communications industries. Alastair has a degree in Economics and German from London University, an MBA from the Open University Business School, and is an associate lecturer in corporate finance with the OUBS. He is the successful author of several books including Mastering financial Modelling, Mastering Risk Modelling and The Financial Director's Guide to Purchasing Leasing published by the Financial Times Prentice Hall and a range of software products. In addition, he develops and presents public and in-house courses on a range of topics including financial modelling, leasing, credit and cash flow analysis, and other corporate finance
This downloadable text features over 200 math problems that very closely follow the standard curriculum for high school Algebra 2 courses, but with a strong emphasis on space science and astronomy. Fourteen chapters featuring on-grade-level Algebra 2 concepts and skill areas including statistics, probability, conics, trigonometry, complex numbers and matrix algebra. Science topics are drawn from all areas of planetary, solar and astrophysics, in addition to space exploration and rocketry.
03958185 entry text is designed to follow either the combined algebra or individual elementary and intermediate algebra texts. College Algebra follows a logical "see first, then do" progression. To reinforce the concept that graphical approaches are used most effectively along with algebraic approaches, the authors present an example first under the heading Visualizing the Solution. This shows students how to depict the problem using a graphing calculator and then estimate its solution. The text then presents an algebraic solution, called Determining the Solution
To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Math Calculus Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists) You know how to use definite integrals to find areas under curves. We now take that idea for "spin" by thinking about the volumes of things created when you rotate functions around various lines. This tutorial focuses on the "disc method" and the "washer method" for these types of problems. You want to rotate a function around a vertical line, but do all your integrating in terms of x and f(x), then the shell method is your new friend. It is similarly fantastic when you want to rotate around a horizontal line but integrate in terms of y. Using definite integration, we know how to find the area under a curve. But what about the volume of the 3-D shape generated by rotating a section of the curve about one of the axes (or any horizontal or vertical line for that matter). This in an older tutorial that is now covered in other tutorials. This tutorial will give you a powerful tool and stretch your powers of 3-D visualization!
Helping students through their GCSE maths course, this title provides short units to facilitate quick learning. Thoroughly covering the range of Intermediate topics, the explanations are designed to work from the basics up to examination standard. Synopsis: Edexcel GCSE Mathematics 16+ helps students through their maths course in a year, whether they are new to GCSE or preparing to retake the exam. It provides coverage of all the key intermediate tier topics. Edexcel GCSE Mathematics 16+ helps students through their maths course in a year, whether they are new to GCSE or preparing to retake the exam. It provides coverage of all the key intermediate tier topics
Matematika (Universitas Negeri Malang). Name and logo belong to their respective owner.
Calculations in research-backed learning system for preparatory chemistry that systematically reinforces both the fundamental concepts and math skills that are prerequisites for success in general chemistry. Recent research has documented that in K-12 programs over the past decade, instruction in math computation has been de-emphasized. Calculations in Chemistry addresses these gaps in student background, applying the findings of recent scientific research on cognition, fluency in applied mathematics, and reading comprehension, ... MOREto prepare students for the rigor and pace of general chemistry.
The Mathematics Curriculum: from Graphs to Calculus the curriculum at the time and the textbooks available. The first five chapters set the scene by discussing graphical work and functions. Two separate themes develop from this: area leading to integration, and gradient leading to differentiation. These themes are developed throughout the book in parallel with developments based on students' experiences of distance, time and speed. The chapters on area and integration always precede the corresponding chapters on gradient and differentiation, because the authors believed that area is conceptually simpler than gradient. Chapters 9 and 10 on numbers and limits take their place because they provide essential background and Chapter 6 covers Some Special Graphs. A detailed contents page is
How to Think Like a Mathematician: A Companion to Undergraduate Mathematics 1 rating: 5.0 A book by Kevin Houston "In this book, Houston has created a primer on the fundamental abstract ideas of mathematics; the primary emphasis is on demonstrating the many principles and tactics used in proofs. The material is explained in ways that are comprehensible, which … see full wiki A systematic and gentle approach to explaining the main ideas of mathematics To be successful in mathematics, your mind must perform operations that are unlike the operations needed to do most other things. You must be able to hold abstract ideas, sometimes several at a time, as well as see the relationships between multiple concepts. Furthermore, those abstract ideas are built on other abstract ideas; for example, most of mathematics is built on the fundamental abstract idea of the use of a variable. However, being different and at times being hard does not mean that the ideas of mathematics are incomprehensible. Humans excel at understanding abstract ideas, a strong argument can be made that such a skill is the very definition of human intelligence. In. Many students are capable of leaping the comprehension hurdle; yet hit a wall when it comes time to apply the concepts in order to generate a proof. In this book, Houston takes a systematic and gentle approach to explaining the ideas of mathematics and how tactics of reasoning can be combined with those ideas to generate what would be considered a convincing proof. Published in Journal of Recreational Mathematics, reprinted with permission
INTRODUCTION Economics is, of course, a field that involves a lot of mathematics. After all, the amount of money you have is a number, and you want that number to be as big as it can get, right? There are whole fields of mathematics designed to help you do just that. One field of mathematics with a lot of business application is finite math. Finite mathematics includes things like matrix algebra, probability & statistics, and even game theory. What is game theory? It's the mathematical description of the best strategies for games or decision-making in general. TABLE OF CONTENTS
More About This Book In Introduction to Connections, Cynthia W. Langrall, Sherry L. Meier, Edward S. Mooney, and Honi J. Bamberger familiarize you with ways to help students see the relationships between and among mathematical skills and content. They offer an array of entry points for understanding, planning, and teaching, including strategies that help students build upon and link mathematical thinking across units by recognizing connections among math concepts, real-world applications, and other content areas. The book and accompanying CD-ROM are filled with activities that are modifiable for immediate use with students of all levels customizable to match your specific lessons. In addition, a correlation guide helps you match the math content you teach with the mathematical processes it utilizes. If your students aren't making mathematical connections, or if you're simply looking for ways to work the connections standard into your curriculum, read, dog-ear, and teach with Introduction to Connections. And if you'd like to learn about any of NCTM's process standards, or you're looking for classroom-tested ways to address them, look no further than Heinemann's Math Process Standards Series. You'll find them explained in the most understandable and practical way: from one teacher to another.Cynthia W. Langrall is coauthor of Introduction to Connections, Grades 6 - 8, part of Heinemann's Math Process Standards Series. She is a professor in the Mathematics Department at Illinois State University. A former classroom teacher, she now teaches undergraduate and graduate students and works with teachers in professional development settings. She conducts research in mathematics education and has been published widely in journals and books. Sherry L. Meier is coauthor of Introduction to Connections, Grades 6 - 8, part of Heinemann's Math Process Standards Series. She is an associate professor of mathematics education at Illinois State University. She worked for sixteen years in K - 12 public schools, supervising teachers in math. Her research interests include interdisciplinary instruction, assessment, and mathematical problem solving at the middle school level. Edward S. Mooney is coauthor of Introduction to Connections, Grades 6 - 8, part of Heinemann's Math Process Standards Series. He is an associate professor of mathematics education at Illinois State University. His research focuses on middle school students' understanding of statistics and probability. Prior to entering postsecondary education, he was a middle school mathematics teacher in Milwaukee, Wisconsin. Honi J. Bamberger is coauthor of Math Misconceptions and Activities to Undo Math Misconceptions, as well as Introduction to Connections (PreK - 2, 3 - 5, and 6 - 8), part of Heinemann's Math Process Standards Series. She is a professor in the department of mathematics at Towson University. A former classroom teacher, she is a mathematics education researcher, the author of numerous other books and articles, and a nationally recognized speaker on math
Precalculus - 9th edition Summary: Larson's market-leading text, PRECALCULUS is known for delivering sound, consistently structured explanations and exercises of mathematical concepts to expertly prepare students for the study of calculus featur...show morees, Checkpoint problems, and a Companion Website reinforce understanding of the skill sets to help students better prepare218.25269
'Taking statistics? Then you need the Wolfram Statistics Course Assistant. This definitive app for statistics--from the world... see more 'Taking statistics? Then you need the Wolfram Statistics Course Assistant. This definitive app for statistics--from the world leader in math software--will help you work through your homework problems, ace your tests, and learn statistics concepts. Forget canned examples! The Wolfram Statistics Course Assistant solves your specific problems on the fly, covering descriptive statistics, distributions, and much more.This app covers the following topics applicable to Statistics and Introduction to Statistics:- Create a bar chart, histogram, or scatter plot of any set of data- Find the mean, median, mode, standard deviation, quartiles, and interquartile range of a dataset- Calculate normal probabilities and find information about the normal distribution- Calculate binomial probabilities and find information about the binomial distribution- Compute probabilities based on dice rolls and coin flips- Find the best-fit line of a set of data points- Select random integers or random real numbersThe Wolfram Statistics algebra? Then you need the Wolfram Algebra Course Assistant. This definitive app for algebra--from the world leader... see more 'Taking algebra? Then you need the Wolfram Algebra Course Assistant. This definitive app for algebra--from the world leader in math software--will help you quickly solve your homework problems, ace your tests, and learn algebra concepts so you're prepared for your next courses. Forget canned examples! The Wolfram Algebra Course Assistant solves your specific algebra problems on the fly, often showing you how to work through the problem step by step.This app covers the following topics applicable to Algebra I, Algebra II, and College Algebra:- Evaluate any numeric expression or substitute a value for a variable.- Simplify fractions, square roots, or any other expression.- Solve a simple equation or a system of equations for specific variables.- Plot basic, parametric, or polar plots of the function(s) of your choice.- Expand any polynomial.- Factor numeric expressions, polynomials, and symbolic expressions.- Divide any two expressions. - Find the partial fraction decomposition of rational expressions.The Wolfram Al calculus? Then you need the Wolfram Calculus Course Assistant. This definitive app for calculus--from the world... see more 'Taking calculus? Then you need the Wolfram Calculus Course Assistant. This definitive app for calculus--from the world leader in math software--will help you work through your homework problems, ace your tests, and learn calculus concepts. Forget canned examples! The Wolfram Calculus Course Assistant solves your specific Calculus problems on the fly including step-by-step guidance for derivatives, integrals, and much more.This app covers the following topics applicable to Calculus, AP Calculus AB, AP Calculus BC, Calculus I, and Calculus II:- Evaluate any numeric expression or substitute a value for a variable.- Plot basic, parametric, or polar plots of the function(s) of your choice.- Determine the limit of a function as it approaches a specific value.- Differentiate any function or implicit function.- Find the critical points and inflection points of a function.- Identify the local and absolute extrema of a function.- Integrate a function, with or without limits.- Sum a function given a lower and upper bound.- Find the closed form of a sequence or generate terms for a specific sequence.'This app costs $3.99 'Taking precalculus? Then you need the Wolfram Precalculus Course Assistant. This definitive app for precalculus--from the... see more 'Taking precalculus? Then you need the Wolfram Precalculus Course Assistant. This definitive app for precalculus--from the world leader in math software--will help you work through your homework problems, ace your tests, and learn calculus concepts. Forget canned examples! The Wolfram Precalculus Course Assistant solves your specific precalculus problems on the fly, including solving equations, vector arithmetic, statistics, and much more.This app covers the following topics applicable to precalculus and trigonometry:- Evaluate any numeric expression or substitute a value for a variable- Solve a single equation or a system of equations- Plot functions on the x-y plane or draw a parametric or polar plot- Determine the sine, cosine, and tangent of a specific angle in a right triangle- Simplify, expand, or factor trigonometric functions- Find the partial fraction decomposition of an expression- Calculate the dot product, cross product, and magnitude of two vectors- Identify the mean, median, mode, and standard deviation of a set of data- Calculate permutations and combinationsThe Wolfram Precalculus pre-algebra? Then you need the Wolfram Pre-Algebra Course Assistant. This definitive app for pre-algebra--from the... see more 'Taking pre-algebra? Then you need the Wolfram Pre-Algebra Course Assistant. This definitive app for pre-algebra--from the world leader in math software--will help you work through your homework problems, ace your tests, and learn pre-algebra concepts. Forget canned examples! The Wolfram Pre-Algebra Course Assistant solves your specific pre-algebra problems on the fly.This app covers the following pre-algebra topics:- Find the divisors and prime factorization of a number- Calculate the GCD and LCM of two numbers- Determine the percent change- Reduce and round numbers- Evaluate expressions- Solve equations and simplify expressions- Convert units of length, area, volume, and weight- Compute the mean, median, and mode of a dataset- Plot equations on the coordinate plane- Graph inequalities on a number line- Calculate the area, surface area, or volume of a geometric figure- Find the midpoint, slope, and distance between two pointsThe Wolfram Pre-AlMath Ref Free is a free version of the great math reference application, Math Ref. This app gives you just a sample (over... see more 'Math Ref Free is a free version of the great math reference application, Math Ref. This app gives you just a sample (over 700.Features: ✓ New Tools - Ranging from Algebra to Physics✓ Search - Easily find what you're looking for✓ Print Support - Print equations or groups✓ Editable Notes - Write what will help you best✓ Zoomable Equations✓ App Orientation Locking✓ Greek Alphabet- Prime NumbersThis is a free app.
Pre MBA Math Boot Camp This workshop is designed to refresh and strengthen your business math skills. Topics include percentages, decimals, fractions, ratios and basic algebra. You will work on problem solving skills, test taking skills, and building math confidence. This course will refresh and strengthen business math skills. Spring 14 Dates: TBA
Precalculus - Text - 4 and helpful features. The result is an easy-to-use, comprehensive text that is the best edition yet.821528841 $8.60
The TI-84 Plus graphing calculator offers three times the memory, more than twice the speed and a higher contrast screen than the TI-83 Plus model. It's keystroke-for-keystroke compatible, too. Count on TI calculators at exam time.
The study of ecology is the study of complex systems that are intrinsically dynamic and quantitative. Ecologists formulate mathematical models to describe this complexity; the equations that result are interesting both for their biological predictions and their mathematical form. Full analytical solution of model equations is typically impossible, yet to the mathematically prepared mind, they can yield up their secrets. This course is intended to provide students with the tools needed to formulate and analyze ecological models. It is an overview of the major categories of models and the mathematical techniques available for their analysis. Although the focus is on ecological dynamics, students in other disciplines will find the methods readily applicable to their own fields. Course Requirements: The course presumes mathematical maturity at the level of advanced calculus with prior exposure to ordinary differential equations, linear algebra, and probability
License information Related content No related items provided in this feed Introduction To Algebra This 11:25 video uses many "notes" to help students. This video should be stopped several times so students can discuss the contents. A good video for an introduction to Algebra, but it does cover too much for one session. Author(s): No creator set License information Related content No related items provided in this feed Trigonometry Introduction - Yay Math Definition of trigonometric ratios, degrees, radians, sin, cos, tan. Finding sign of ratios. White board in a class setting, some interaction, engaging, several examples of increasing complexity. The discussion is clear and understandable. Preview - full version at Produced by Robert Ahdoot, yaymath.org Author(s): No creator set License information Related content No related items provided in this feed An Anthropological introduction to YouTube This video is a presentation by Dr. Michael Wesch at the Library of Congress, June 23rd 2008. It discusses YouTube and most of the Web 2.0 tools. This video is a lecture with english captions.(55:33) Author(s): No creator set License information Related content No related items provided in this feed Introduction to Rocks and Minerals Examine the characteristics of common rocks and minerals and learn identification procedures. Find out all about the physical properties of minerals including hardness, luster and color as well as the chemical compositions of important rock-forming minerals. Information in the video is accurate, but narration is somewhat monotone. Run time 03:34. Author(s): No creator set License information Related content No related items provided in this feed Introduction to Multiplication Part 1 This video indicates it is for pre-algebra, however this video would be good for anyone who is reviewing or learning multiplication. This video starts with the different ways people write multiplication equations, using a dot, the times symbol, or parenthesis. They talk about what mulitiplication means, it is repeated addtion. Then they discuss the commutative property for multiplication. They show this using the number line. They show this using many different problems. The video concludes with Author(s): No creator set License information Related content No related items provided in this feed Introduction to Multiplication Part 2 This video starts where part 1 left off. They start with using subtraction to find the product of two numbers. For example, 7 x 8 = ?, I know 7 x 10 = 70, then I subtract 14 to get 56, need to look at the pattern that is occuring. Review what multiplication means, repeated addition. Then they move on to two digit numbers mulitplied by a two digit number, using a number line. They do this with a number of different problems. Video is good quality and good for all students as review or initial lea Author(s): No creator set Introduction to Division Learn the basics of division, including vocabulary and how to solve simple division problems. A teacher is using a whiteboard to explain the process as well as the vocabulary. He demonstrates two ways to write these division problems. Sound quality is poor. (7:23) Author(s): No creator set License information Related content No related items provided in this feed Introduction to Division Part 1 Part 1 of a series by Professor Lawrence Perez at Saddleback College. Live action movie has an interesting perspective. The people are very small and the interactive white board is very large. Professor Perez teaches a single student, Charlie. While designed for college, the explanations are simple and clear. It shows the different ways division is indicated, then uses the number line to show division, and long division. This video shows many different examples using the various metho Author(s): No creator set Part 2 of a series by Professor Lawrence Perez at Saddleback College. Live action movie has an interesting perspective. The people are very small and the interactive white board is very large. Author(s): No creator set License information Related content No related items provided in this feed Introduction to Decimals, Part I This is part one of a two-part video. This video starts with a review of place value, then proceeds to a decimal into a word statement, then writes the decimal as a fraction. Many examples are done. Then it moves on to whole numbers and decimals, writing them out, and showing the fraction equivalent. A few more examples are done. Video is good quality and good for all students as a review or initial learning of the topic. Author(s): No creator set License information Related content No related items provided in this feed Introduction to Interest Explains that interest is rent for money. Simple versus compound interest described. Production is basic using computer software and calculator. However the explanation is clear and concise. Author(s): No creator set License information Related content No related items provided in this feed Introduction to Present Value - Khan Academy Looks at present value - as being a choice between - money now and its value later. This production is demonstrated with computer software and a calculator. The explanation is clear and understandable. Author: Salman KhanIntroduction to Compound Interest This is an introduction to compound interest. The instructor uses computer software for instruction. The explanation is clear and understandable. This is a Khan Academy video. Author(s): No creator set License information Related content No related items provided in this feed Introduction to Newton's Three Laws - Lesson 1 This NASA video segment explores how Newton's Laws of Motion apply to the development and operation of airplanes. Viewers watch an instructor at NASA's National Test Pilot School as he describes and then demonstrates why seatbelts are an important force on pilots; what it means to pull 2, 4 and even 6 g in a jet; and how the thrust of a jet engine causes an aircraft to move forward. Formulas are presented onscreen along with the calculations discussed in the segment. For example, the instructor Author(s): No creator set License information Related content No related items provided in this feed An Introduction to Primates This video covers 41 species of primates ranging from the 300-gram sized pygmy slow loris to the 200-kilogram-sized gorilla. The animals are organized by taxonomic categories. Run time 03:53. Author(s): No creator set License information Related content No related items provided in this feed An Introduction to Humanism This video is from a lecture in Canada in 2008. It is a brief introduction to Humanism (a non believer, man centered person) and its varied aspects, including Athiesm, Freethought, Agnosticism, Transhumanism, and Skepticism. Humanists believe that they can be good without God. Recorded in left audio channel only. (7:57) Author(s): No creator set
On this site, students can practice classifying statistics problems. They first click to check the statistical methods that... see more On this site, students can practice classifying statistics problems. They first click to check the statistical methods that they want to practice classifying. Then they click the "Submit" button to get a description of a research project that involves a statistical technique. Students then click on the technique that will most likely be used in the project. If they choose the incorrect answer, they must read the hint and try again. When they get something correct, they click on the "Next" button to try another problem. Mathway is a mathematics problem solving tool where students can select their math course - Basic Math, Pre-Algebra, Algebra,... see more Mathway is a mathematics problem solving tool where students can select their math course - Basic Math, Pre-Algebra, Algebra, Trigonometry, PreCalculus, Calculus or Statistics and enter a problem. The computer solves the problem and shows the steps for the solution. It also has a worksheet generator. math911 contains step by step tutorials in Introductory Algebra, Intermediate Algebra, PreCalculus and Introductory... see more Introdu 'Soulver is the essential app for doing quick calculations and figuring stuff out on the iPad. Write out calculations line by... see more 'Soulver is the essential app for doing quick calculations and figuring stuff out on the iPad. Write out calculations line by line on the notepad on the left, and the answers are displayed instantly on the right. All your work is visible all the time, and you can go back and change any line. It's like doing math on paper, except the calculator is part of the page. Soulver is unique in that it allows you to use words alongside your numbers, so your calculations actually make sense. It's great for shopping (discounts, totals), or just about any day-to-day calculations. It's so easy to play around with different scenarios, figure out profit margins, and compare different options lines by line.Soulver displays a total of all your lines, and your work is automatically saved, which is perfect for keeping track of daily expenses, budgeting and travelling. You can easily work out percentages too, as Soulver supports over 14 different percentage operations which is great for quick markups (tax tips, etc). You can also do currency conversions.Once you try Soulver, you'll never want to use a traditional calculator again.FEATURES:- Refined, clean interface for doing quick calculations.- Do calculations naturally over multiple lines; edit any part of them.- Use words alongside your numbers so they make sense.- Do calculations and conversions with different currencies.- A custom keyboard designed for doing quick math with big pressable buttons. - Keyboard displays more advanced features in landscape mode.- Multiline calculations where you can refer to the results of previous lines.- Automatically saves your work for later reference, and includes multi-document support.- Send beautifully formatted emails of your calculations from within Soulver.- Sync your documents to the iPhone version of Soulver, and your Mac, using Dropbox.'This app costs $2.99
This poster illustrates many of the attributes of the Cartesian coordinate system with the complete unit circle, and is an ideal teaching aid for secondary mathematics and geometry teachers. Included is a set of transparent Sine and Hypotenuse arms to t.. Hypatia, Sophie Germain, Sonya Kovalensky, Emmy Noether, and Grace Hopper are among the greatest female mathematicians of all time. Portraits and text highlight the events and accomplishments of their lives. Measures 22" x 29". Explore the development of mathematical ideas by people all over the world. Students will discover more than 50 accomplishments from counting to computers, to ancient ideas and modern. Richly illustrated with cultural and mathematical artifacts, the pos.. More than 50 colorful figures represent a variety of jobs and indicate high school mathematics courses typically required in the career paths to each occupation. Illustrated lines of work include an accountant, architect, bricklayer, plumber, physician,.. Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the United States may be charged additional distributor, customs, and shipping charges.
books.google.com - Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. The text also helps stude... Mathematics and Computing
Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses
... Show More blocks initially standing in the way ofcalculus students. Calculus without Limits presents its subject in nine chapters: 1) 'Introduction', 2) 'Barrow'sDiagram', 3) 'The Two Fundamental Problems of Calculus', 4) 'Foundations', 5)'Solving the First Problem', 6) 'Antiprocesses', 7) 'Solving the SecondProblem', 8) 'Sampling the Power of Differential Equations', and 9)'Conclusion: Magnificent Shoulders'. Approximately 85 diagrams and a plethoraof worked examples help facilitate student understanding in an exposition thatmeasures a mere 330 pages from cover to cover. Real-life applications examineproblems from a variety of disciplines ranging from physics to finance. Additionally,Calculus without Limits provides plenty of practice for the beginning calculusstudent via 200 exercises from routine to quite challenging-all answered in an'Answer to Problems' section in the back of the book. Five appendices summarizekey formulas from various mathematical disciplines, and a brief one-page bibliographycompletes the book. Calculus without Limits is suitable as a self-study text or as supplementarytext augmenting a regular multi-term college calculus sequence. It can alsoserve as the primary text for a one-term Business Calculus or Calculus forAppreciation Course. Advanced High School Students will find it ideal forquickly mastering calculus basics before engaging a more rigorous collegeoffering. Lastly, Calculus without Limits is meant for all those peoplewho really never learned the why behind calculus, and now, many yearslater-perhaps as a practicing professional-may want to reacquaint themselveswith an old academic friend for th
Learn geometry at your own pace What are congruent circles? How do you find the hypotenuse of a triangle? What is the sum of the angles in a decagon? How can you apply geometric equations to your daily life? With the unbeatable study companion Geometry: A Self-Teaching Guide, you'll discover the answers to these questions and many more. This thorough primer presents an easy-to-follow, proven method for grasping the key concepts of geometry. You'll progress step by step through plane, solid, and analytic geometry and then move on to geometric applications for calculus. You'll build your problem-solving skills along the way through detailed examples, reviews, exercises, and answer explanations. The clearly structured format of Geometry makes it fully accessible, providing an easily understood, comprehensive overview for everyone from high school students to adult learners to math mavens. Like all Self-Teaching Guides, Geometry allows you to build gradually on what you have learned-at improve his or her understanding of basic geometry. We do not deliver the extra material sometimes included in printed books (CDs or DVDs).
The present book is a marvelous introduction in the modern theory of manifolds and differential forms. The undergraduate student can closely examine tangent spaces, basic concepts of differential forms, integration on manifolds, Stokes theorem, de Rham- cohomology theorem, differential forms on Riema-nnian manifolds, elements of the theory of differential equations on manifolds (Laplace-Beltrami operators). Every chapter contains useful exercises for the students. ZENTRALBLATT MATH Differentiable manifolds Tangent vector space Differential forms Orientability Integration on manifolds Open manifolds The intuitive meaning of Stoke's theorem The hat product and the definition of Cartan's derivative Stoke's theorem Classical vector analysis De Rham cohomology Differential forms on Riemannian manifolds Calculating in coordinates Answers
CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. CliffsQuickReview Trigonometry provides you with all you need to know to understand the basic concepts of trigonometry ? whether you need a supplement to your textbook... more... more... Most math and science study guides are a reflection of the college professors who write them-dry, difficult, and pretentious. The Humongous Book of Trigonometry Problems is the exception. Author Mike Kelley has taken what appears to be a typical t more... From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines... more... 500 Ways to Achieve Your Best Grades. We want you to succeed on your college algebra and trigonometry midterm and final exams. That's why we've selected these 500 questions to help you study more effectively, use your preparation time wisely, and getyour best grades. These questions and answers are similar to the ones you'll find on a typical... more... Presents the results on positive trigonometric polynomials within a unitary framework; the theoretical results obtained partly from the general theory of real polynomials, partly from self-sustained developments. This book provides information on the theory of sum-of-squares trigonometric polynomials in two parts: theory and applications. more... This book on symmetric geometric patterns of Islamic art has educational, aesthetic, cultural and practical purposes. Its central purpose is to bring to the attention of the world in general, and the people of Islamic culture in particular, the potential of the art for providing a unified experience of science and art in the context of mathematical... more...
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Other Courses I Teach Algebra I Course Overview Algebra I is the branch of mathematics that uses mathematical statements that describe relationships that vary over time. Course Objectives Algebra I students will: 1. Understand that a function represents a dependence of one quantity on another and can be described in a variety of ways. 2. Use the properties and attributes of functions. 3. Understand how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. 4. Understand the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. 5. Understand that linear functions can be represented in different ways and translates among their various representations. 6. Understand the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and will interpret and desrcibe the effects of changes in parameters of linear functions in real-world and mathematical situations. 7. Formulate equations and inequalities based on linear functions, use a variety of methods to solve them, and analyze the solutions in terms of the situation. 8. Formulate systems of linear equations from problem situations, use a variety of methods to solve them, and analyze the solutions in terms of the situation. 9. Understand that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in parameters of quadratic functions. 10. Understand that there is more than one way to solve a quadratic equation and solves them using appropriate methods. 11. Understand there are situations modeled by functions that are neither linear nor quadratic and models the situations. Grading Policy Performance is measured in two categories: Daily Grades and Assessment Grades. Daily grades include blogs, classwork, quizzes and exit tickets. Assessment grades include formal and informal tests and projects. Daily Grades 40% Assessments 60% Class Schedule Our Kids in Action! Planning For College Fri, 12 Nov 2010 06:46:42 +0000 Living and eating at college obviously gets expensive, but as with all things, there are ways around the large sticker cost of your school???s recommended meal plan or your housing choices.If you go to a college that grades its… More » Fri, 12 Nov 2010 06:44:41 +0000 Many college students love shopping, but more often than not, it results in unnecessary expenses. Shopping can be fantastic, to be sure, but it???s a great way to throw away money, and we???re trying to save.If you break down… More » Fri, 12 Nov 2010 06:42:55 +0000 Assembling your academic resume is an important challenge to rise up to, as a good resume is crucial for a college application. Writing up your resume isn???t as easy as you may think, however; a good resume is essentially a… More » Fri, 12 Nov 2010 06:40:46 +0000 This is an important question. It seems pretty simple, but your answer is going to have a huge impact on four years of your life. When you???re looking at colleges and beginning to put a list together, there are a… More » Fri, 12 Nov 2010 06:39:03 +0000 The whole college admissions process is pretty confusing???I don???t think anyone would disagree with that statement. Sometimes it???s confusing as a result of having to juggle five, eight, ten, even fourteen applications at once; if you don???t know what???s going… More » Wed, 03 Nov 2010 16:45:03 +0000 College is expensive, and a cocktail of financial aid, scholarships, grants, work-study jobs, as well as both federal and private loans is often prescribed to help alleviate the immediate financial burden of paying for college. That said, there are some… More » Wed, 03 Nov 2010 16:38:40 +0000 As a college student, the easiest mistake to make is letting your newfound independence hijack your finances. It???s incredibly easy to spend money left and right when you go off to school, so here are a few tips to live… More » Wed, 03 Nov 2010 16:33:28 +0000 ???Sticker prices??? of colleges these days are so high that the numbers can make one???s heart skip a beat or two in financial fear. Well, we???re here to tell you that the intimidating cost of college shouldn???t stop you from… More » Wed, 03 Nov 2010 16:30:58 +0000 Concerned about paying for college? Read up on these common myths and mistakes made throughout the paying-for-college process, and be sure not to make them yourself.Mistake #1. We will have plenty of time to deal with the cost issue… More » Wed, 13 Oct 2010 03:11:59 +0000 There are many costs of college apart from tuition, and the high cost of college textbooks is perhaps the most notorious. Just speak to a student or their parents around the beginning of a semester and you???re bound to hear… More »
More About This Textbook Overview Graph theory is one of the fastest growing branches of mathematics. Until recently, it was regarded as a branch of combinatorics and was best known by the famous four-color theorem stating that any map can be colored using only four colors such that no two bordering countries have the same color. Now graph theory is an area of its own with many deep results and beautiful open problems. Graph theory has numerous applications in almost every field of science and has attracted new interest because of its relevance to such technological problems as computer and telephone networking and, of course, the internet. In this new book in the Johns Hopkins Studies in the Mathematical Science series, Bojan Mohar and Carsten Thomassen look at a relatively new area of graph theory: that associated with curved surfaces. Graphs on surfaces form a natural link between discrete and continuous mathematics. The book provides a rigorous and concise introduction to graphs on surfaces and surveys some of the recent developments in this area. Among the basic results discussed are Kuratowski's theorem and other planarity criteria, the Jordan Curve Theorem and some of its extensions, the classification of surfaces, and the Heffter-Edmonds-Ringel rotation principle, which makes it possible to treat graphs on surfaces in a purely combinatorial way. The genus of a graph, contractability of cycles, edge-width, and face-width are treated purely combinatorially, and several results related to these concepts are included. The extension by Robertson and Seymour of Kuratowski's theorem to higher surfaces is discussed in detail, and a shorter proof is presented. The book concludes with a survey of recent developments on coloring graphs on surfaces. Editorial ReviewsThomas Tucker This is a long-awaited book by two of the most powerful practitioners in the field. There is nothing else like it, and it will remain the definitive book on the subject for many, many years to come. Related Subjects Meet the Author Bojan Mohar is a professor in the Department of Mathematics at the University of Ljubljana in Slovenia and a member of the Engineering Academy of Slovenia. Carsten Thomassen is a professor at the Mathematical Institute of the Technical University of Denmark, the editor-in-chief of the Journal of Graph Theory, and a member of the Royal Danish Academy of Sciences
Algebra in Motion™ Description An Algebra course designed to help students supplement, replace, or preview. Focused on concepts so that students leave with fundamental mathematical ideas. Mathematics is best learned in context. To this end Algebra in Motion uses the Laws of Motion and simple geometry to naturally describe the fundamental concepts of Algebra that many high school and college students lack: formulas - how to derive a formula, how to algebraically manipulate formulas functions - theory of functions, application of functions graphing - graphical interpretation, slope-intercept form, parabolas This course was designed to exceed all of the normal algebra standards at the state and national levels. Algebraic thinking is a conceptualization of arithmetic properties and as such requires students to be proficient in fractions, decimals, and percents to be successful. Sequence Algebraic Relationships Students will explore the mathematics of motion and other various physical phenomena in order to attain mastery over variables and the methods of solving equations of single variables. In this quarter students will study a wide range of linear systems from 1-D motion, to composite motion, and other co-linear physical systems. Students will be working to master linear functions and linear graphs. In this final quarter students will be working to understand the mathematics of acceleration, projectile motion and gravity. Students will be working to master quadratic functions and quadratic graphs. Each Algebra in Motion course is a 30-hour laboratory workshop lecture, and practice problems. Academic year students are required to complete a minimal amount of practice problems. Prerequisites Students should have mastery over fractions, decimals, and percents. The document at the bottom of this page is a 38 question Algebra Readiness Assessment that will help determine whether your student is ready for Algebra (Algebra in Motion) or Pre-Algebra (Applied Mathematics).
Contemporary Mathematics: For Business And ConsumersCONTEMPORARY MATHEMATICS FOR BUSINESS AND CONSUMERS, BRIEF is a 14-chapter educational adventure into today?s business world and its associated mathematical procedures. The book is designed to provide solid mathematical preparation and foundation for students going on to business courses and careers. It begins with a business-oriented review of the basic operations, including whole numbers, fractions, and decimals. Once students have mastered these operations, they are introduced to the concept of basic equations and how they are used to solve ... MOREbusiness problems. From that point, each chapter presents a business math topic that utilizes the student?s knowledge of these basic operations and equations. In keeping with the philosophy of ?practice makes perfect,? the text contains over 2,000 realistic business math exercises--many with multiple steps and answers designed to prepare students to use math to make business decisions and develop critical-thinking and problem-solving skills. Many of the exercises in each chapter are written in a ?you are the manager? format, to enhance student involvement. The exercises cover a full range of difficulty levels, from those designed for beginners to those requiring moderate to challenge-level skills.
ieigenvalue Analysis Karl Gustafson is the creator of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, ...Show synopsisKarl Gustafson is the creator of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance. Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every result in operator theory and matrix theory, together with their applications. This book will open up its methods to
Select a content and you will automatically be redirected to the list of performance expectations. A1.1. Core Content: Solving Problems (Algebra) Students learn to solve many new types of problems in Algebra 1, and this first core content area highlights the types of problems students will be able to solve after they master the concepts and skills in this course. Students are introduced to several types of functions, including exponential and functions defined piecewise, and they spend considerable time with linear and quadratic functions. Each type of function included in Algebra 1 provides students a tool to solve yet another class of problems. They learn that specific functions model situations described in word problems, and so functions are used to solve various types of problems. The ability to determine functions and write equations that represent problems is an important mathematical skill in itself. Many problems that initially appear to be very different from each other can actually be represented by identical equations. Students encounter this important and unifying principle of algebra—that the same algebraic techniques can be applied to a wide variety of different situations. A1.2. Core Content: Numbers, expressions, and operations (Numbers, Operations, Algebra) Students see the number system extended to the real numbers represented by the number line. They work with integer exponents, scientific notation, and radicals, and use variables and expressions to solve problems from purely mathematical as well as applied contexts. They build on their understanding of computation using arithmetic operations and properties and expand this understanding to include the symbolic language of algebra. Students demonstrate this ability to write and manipulate a wide variety of algebraic expressions throughout high school mathematics as they apply algebraic procedures to solve problems. A1.3. Core Content: Characteristics and behaviors of functions (Algebra) Students formalize and deepen their understanding of functions, the defining characteristics and uses of functions, and the mathematical language used to describe functions. They learn that functions are often specified by an equation of the form y = f(x), where any allowable x-value yields a unique y-value. While Algebra 1 has a particular focus on linear and quadratic equations and systems of equations, students also learn about exponential functions and those that can be defined piecewise, particularly step functions and functions that contain the absolute value of an expression. Students learn about the representations and basic transformations of these functions and the practical and mathematical limitations that must be considered when working with functions and when using functions to model situations. A1.4. Core Content: Linear functions, equations, and inequalities (Algebra) Students understand that linear functions can be used to model situations involving a constant rate of change. They build on the work done in middle school to solve sets of linear equations and inequalities in two variables, learning to interpret the intersection of the lines as the solution. While the focus is on solving equations, students also learn graphical and numerical methods for approximating solutions to equations. They use linear functions to analyze relationships, represent and model problems, and answer questions. These algebraic skills are applied in other Core Content areas across high school courses. A1.5. Core Content: Quadratic functions and equations (Algebra) Students study quadratic functions and their graphs, and solve quadratic equations with real roots in Algebra 1. They use quadratic functions to represent and model problems and answer questions in situations that are modeled by these functions. Students solve quadratic equations by factoring and computing with polynomials. The important mathematical technique of completing the square is developed enough so that the quadratic formula can be derived. A1.6. Core Content: Data and distributions (Data/Statistics/Probability) Students select mathematical models for data sets and use those models to represent, describe, and compare data sets. They analyze data to determine the relationship between two variables and make and defend appropriate predictions, conjectures, and generalizations. Students understand limitations of conclusions based on results of a study or experiment and recognize common misconceptions and misrepresentations in interpreting conclusions. A1.7. Additional Key Content: (Algebra) Students develop a basic understanding of arithmetic and geometric sequences and of exponential functions, including their graphs and other representations. They use exponential functions to analyze relationships, represent and model problems, and answer questions in situations that are modeled by these nonlinear functions. Students learn graphical and numerical methods for approximating solutions to exponential equations. Students interpret the meaning of problem solutions and explain limitations related to solutions. A1.8. Core Processes: Reasoning, problem solving, and communication Students formalize the development of reasoning in Algebra 1 as they use algebra and the properties of number systems to develop valid mathematical arguments, make and prove conjectures, and find counterexamples to refute false statements,
PUZZLE MATH: Trigonometry and Logarithms PDF (Acrobat) Document File Be sure that you have an application to open this file type before downloading and/or purchasing. 0.22 MB \| 23 pages PRODUCT DESCRIPTION This is a collection of 20 math worksheets on trigonometry and logarithms. They provide instant feedback and fun to students because the answers correspond to letters or images that decode secret messages and pictures. They are self-grading, which makes them ideal for customized treatment of learners. They are tested by multiple teachers, including the author and her colleagues. In "PUZZLE MATH: Trigonometry and Logarithms" students find trig functions' values, missing angles, create and use wave graphs and the unit circle, draw and use special triangles, use one trig equation to find others, use and convert between degrees and radians, learn and evaluate trig identities, find scales for similarity, learn log definitions, identify and use log properties, utilize the change of base formula for logs, find missing values in log equations, and more. Thank you very much for your feedback. I have to confess that it has taken me a while to figure out the interface to email you back regarding your comment "Wish there was an answer key" to "PUZZLE MATH: Trigonometry and Logarithms". I do not include the answer key with the decoders for sale because the price at which I sell the books and worksheets is low cost enough that I have found students will purchase them too, sometimes undermining the sale made by the teacher! I'm sorry for the inconvenience. Please email me at my regular email account, email_rox@email.com and I can offer a better solution for you that way rather than adding the answers to the product where your students can get them too. :) Have an excellent day, and, again, I'm sorry for the delay in answering this need for you. Product Questions & Answers Be the first to ask Roxanne Kloper
Algebra for College Students - 9th edition Summary: Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; practice the skill to help solve equations; and then apply what you have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundamental problem solving skills necessary for future mathematics c...show moreourses. Algebraic ideas are developed in a logical sequence, and in an easy-to-read manner, without excessive vocabulary and formalism. The open and uncluttered design helps keep students focused on the concepts while minimizing distractions. Problems and examples reference a broad range of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life. ...show less8.258.45 +$3.99 s/h VeryGood SellBackYourBook Aurora, IL10.49 +$3.99 s/h VeryGood DGABooks AL Helena, AL 2010-01-01 Hardcover Very Good Looks practically new. Text has no markings or bent pages. Cover is clean, shiny & bright. $50.00 +$3.99 s/h VeryGood Roy Haws Bargain Books TX Jacksonville, TX Belmont, CA 2011 Hard cover 29579 Very good. No dust jacket. Glued binding. Paper over boards. 803 p. Contains: Illustrations. Audience: General/trade. I have for sale a VERY GOOD CONDITION hardboun...show mored textbook29579) This textbook has very minor cover, corner and edge wear. There is a small area of dulling to the front cover finish. Glimpsing through the pages, I did not see any markings and/or highlighting. ...show less $50.00 +$3.99 s/h VeryGood Roy Haws Bargain Books TX Jacksonville, TX 29872 2011 Hard cover 9th ed. Very good. No dust jacket. Glued binding. Paper over boards. 803 p. Contains: Illustrations. Audience: General/trade. I have for sale a VERY GOOD CONDITION hardbound te...show morextbook29872) This textbook has very minor cover, corner and edge wear. Glimpsing through the pages, I did not see any markings and/or highlighting. ...show less $131139
Introduction; Overture: Newton's published work on the calculus of fluxions; Part I. The Early Period: 1. The diffusion of the calculus (1700–1730); 2. Developments in the calculus of fluxions (1714–1733); 3. The controversy on the foundations of the calculus (1734–1742); Part II. The Middle Period: 4. The textbooks on fluxions (1736–1758); 5. Some applications of the calculus (1740–1743); 6. The analytic art (1755–1785); Part III. The Reform: 7. Scotland (1785–1809); 8. The Military Schools (1773–1819); 9. Cambridge and Dublin (1790–1820); 10. Tables; Endnotes; Bibliography; Index.
RealCalc Plus Description RealCalc Plus is the enhanced version of Android's #1 Scientific Calculator, RealCalc - a fully featured scientific calculator which looks and operates like the real thing. RealCalc Plus includes the following features: * Traditional algebraic or RPN operation * Fraction calculations and conversion to/from decimal * Degrees/minutes/seconds calculations and conversion * Result history * User-cus...
GeoGebra Publisher Review: GeoGebra is a very useful mathematics tool for education in secondary schools, which brings together geometry, algebra and calculus. GeoGebra is also a dynamic geometry system, meaning you can do constructions with points, segments, vectors, lines, conic sections as well as functions and change them dynamically afterwards. On the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum. These two views are characteristic of GeoGebra: an expression in the algebra window corresponds to an object in the geometry window and vice versa.GeoGebra' 4.4.0.0 Stable is GPL Science software design by GeoGebra Inc.. It runs on following operating system: Windows 8, Windows 7, Windows Vista, Windows XP, Windows 2000, Windows 98 GeoGebra key features: Captions enabled for all objects New option "Force Reflex Angle" forces angles to be between 180 and 360 degrees Pressing toggles the focus between the Input Bar and the Graphics View Comparing objects of different types doesn\'t return an error, can now compare Text and Image objects If the Points Export_1 and Export_2 exist, they will be used to define the export rectangle (Export_1 and Export_2 must be within the visible area) Checkbox now consistent across all platforms Options -> Checkbox Size -> Regular/Large Perpendicular check added to "Relation between two objects" Tool Messages from "Relation between two objects" Tool rewritten Angular Bisector Command and Tool renamed to Angle Bisector Line Bisector Command and Tool renamed to Perpendicular Bisector BMP import Unicode fonts used in LaTeX equations LaTeX equations exported at full resolution in SVG and PDF export, option to export text as editable text or shapes. Stores the text either as text (lets you edit the text in eg InkScape) or as bezier curves (ie guaranteed to look the same even if the correct font is not installed).
Using many step-by-step demonstration examples, helpful diagrams, informative "Math Fact" summaries, and graphing calculator approaches, this book presents:A clearly organized chapter-by-chapter review of all New York State Regents Integrated Algebra topicsExercise sections within each chapter with a large sampling of Regents-type multiple-choice and extended-response questionsRecent New York State Regents Integrated Algebra ExamAnswers are provided for all questions in the exercise sections and all questions on the Regents exam. Preface Sets, Operations, and Algebraic Language Numbers, Variables, and Symbols Classifying Real Numbers Learning More About Sets Operations with Signed Numbers Properties of Real Numbers Exponents and Scientific Notation Order of Operations Translating Between English and Algebra Linear Equations and Inequalities Solving One-Step Equations Solving Multistep Equations Solving Equations with Like Terms Algebraic Modeling Literal Equations and Formulas One-Variable Linear Inequalities Problem Solving and Technology Problem Solving Strategies Using a Graphing Calculator Comparing Mathematical Models Ratios, Rates, and Proportions Ratios and Rates Proportions Solving Motion Problems Solving Percent Problems Probability Ratios Polynomial Arithmetic and Factoring Combining Polynomials Multipying and Dividing Polynomials Factoring Polynomials Multiplying and Factoring Special Binomial Pairs Factoring Quadratic Trinomials Solving Quadratic Equations by Factoring Solving Word Problems with Quadratic Equations Rational Expressions and Equations Simplifying Rational Expressions Multiplying and Dividing Rational Expressions Combining Rational Expressions Rational Equations and Inequalities Radicals and Right Triangles Square and Cube Roots Operations with Radicals Combining Radicals The Pythagorean Theorem General Methods for Solving Quadratic Equations Similar Triangles and Trigonometry Trigonometric Ratios Solving Problems Using Trigonometry Area and Volume Areas of Parallelograms and Triangles Area of a Trapezoid Circumference and Area of a Circle Areas of Overlapping Figures Surface Area and Volume Graphing and Writing Equations of Lines Slope of a Line Slope-Intercept Form of a Linear Equation Slopes of Parallel Lines Graphing Linear Equations Direct Variation Point-Slope Form of a Linear Equation Functions, Graphs, and Models Function Concepts Function Graphs as Models The Absolute Value Function Creating a Scatter Plot Finding a Line of Best Fit Systems of Linear Equations and Inequalities Solving Linear Systems Graphically Solving Linear Systems By Substitution Solving Linear Systems By Combining Equations Graphing Systems of Linear Inequalities Quadratic and Exponential Functions Graphing a Quadratic Function Solving Quadratic Equations Graphically Solving a Linear-Quadratic System Exponential Growth and Decay Statistics and Visual Representations of Data Measures of Central Tendency Box-and-Whisker Plots Histograms Cumulative Frequency Histograms Counting and Probability of Compound Events Counting Using Permutations Probability of Compound Events Probability Formulas for Compound Events Answers and Solution Hints to Practice Exercises Glossary of Integrated Algebra Terms The Integrated Algebra Regents Examination June 2011 Regents Examination Answers June 2012 Regents Examination Answers
MATH ENRICHMENT:Students who will be in Algebra I will have the opportunity to practice math concepts in the Math Enrichment Course. In addition to strengthening the student's mathematical foundation and building confidence in math, this course allows freshmen to meet future classmates and become familiar with SPX. General math concepts such integers, fractions and decimals, simplifying and evaluating expressions, and solving equations will be presented and practiced using a variety of activities in a relaxed atmosphere. GEOMETRY JUMP START:Students who will be in Geometry will have the opportunity to learn geometry study techniques in the Geometry Jump Start course. The course will teach students how to learn and apply the many definitions, theorems and postulates in order to be successful. Additionally, we will review the algebra topics that will be covered in the initial chapters of geometry. ALGEBRA REFRESHER: The Algebra Refresher class is for students who just completed Geometry and will be in Algebra II in the fall designed to review important concepts learned in Algebra One to help students transition into Algebra Two. Even though there is Algebra in Geometry, many students have a hard time remembering the concepts and the procedures of Algebra One at the pace of the Algebra Two course. This summer review course is extremely beneficial because it will allow students to not stress over relearning old material but concentrate solely on new information.
This book by an expert presents a clear, concise introduction to the special techniques for creating complex polyhedra models. Based on the classic Platonic solids, these 17 projects are appropriate for folders at all levels. Step-by-step diagrams offer detailed views of the models' assembly, and photos depict completed models. Description: This book is a great resource for people who enjoy polyhedra, symmetry, geometry, mathematics and origami. The types of models presented are similar in nature to the models in Mukerji''s "Marvelous Modular Origami," but some of the chapters are ...
A large volume of material useful for notetaking in math class. Covers Algebra and Geometry, Trig, basic math (Math A and Math B) and some sciences. Prepared by the Oswego City School District and meant to help students pass the New York State Regents exams. " The goal of this nonprofit site is to help high school students meet the New York State Regents requirements in English, Mathematics, Science, and Social Studies. This project is supported by a federally-funded Title III Technology Literacy Challenge Grant and the Learning Technology Grant. Please let us know if you have any suggestions for improving the site. For more information, contact:" Grades 9-12 Offers lessons and practice for help in getting ready for the regents exams for Integated Algebra, Geometry, Algebra 2/Trig, Global History, US History, Earth Science, Living Environment, Chemestry, and Physics. Classroom Connection: Website would be given to students as a resource for specific topics throughout the year as well as for NYS Regents Review. I use this site often for teaching suggestions on a topic. It has different ways to explain things and examples for students to work through. Works for a variety of subject areas for those who don't teach mathTest Prep Exam Center-The goal of this nonprofit site is to help high school students meet the New York State Regents requirements in English, Mathematics, Science, and Social Studies. Many of these questions can be used to help Middle and High School Stu
Intermediate Algebra A Graphing college-level courses in intermediate algebra with a graphing approach or a graphing emphasis. Martin-Gay/Greene presents the topics in intermediate algebra using a graphing approach. The text requires the use of a graphing calculator. Where possible, topics are presented using side by side algebraic, numeric, and graphical approaches. Elayn Martin-Gay's success as a developmental math author and teacher starts with a strong focus on mastering the basics through well-written explanations, innovative pedagogy and a meaningful, integrated pro... MOREgram Explain key concepts clearly with an excellent, accessible writing style. Build problem-solving skills with thoroughly integrated problem solving techniques and explanations. Relate to students through real-life applications that are interesting, relevant, and practical. Martin-Gay believes that every student can: Test better: The new Chapter Test Prep Video shows Martin-Gay working step-by-step video solutions to every problem in each Chapter Test to enhance mastery of key chapter content. Study better: New, integrated Study Skills Reminders reinforce the skills introduced in section 1.1, "Tips for Success in Mathematics" to promote an increased focus on the development of all-important study skills. Learn Elayn Martin-Gay's success as a developmental math author starts with a strong focus on mastering the basics through well-written explanations, innovative pedagogy and a meaningful, integrated program of learning resources. The revisions to this edition provide new pedagogy and resources to build reader confidence and help readers develop basic skills and understand concepts. Features incorporation of AMATYC and NCTM standards-reflected in an increased emphasis on visualization graphing, and data analysis. In addition, Martin-Gay's 4-step problem solving process-Understand, Translate, Solve and Interpret-is integrated throughout. Also includes new features such as Study Skills Reminders, "Integrated Reviews", and "Concept Checks." For those in need of a graphing utility resource in intermediate algebra, and for readers who need to prepare for advanced algebra or finite math.
Introduction to Numerical Analysis This first semester introduction to the field of numerical analysis will investigate numerical techniques in: solving equations in one variable (a.k.a. root finding) interpolation and polynomial approximation numerical differentiation and integration solving ordinary differential equations and the errors associated with each of these techniques. There will be a significant component of the class the comes from implementing or using these methods to complete homework projects. Objectives To develop students' understanding of computing in a finite precision environment, to familiarize students with types of problems where numerical methods are used to approximate solutions, to cover the basic algorithms of numerical analysis in these areas, and to provide an understanding of the mathematical analysis behind the numerical methods discussed.
Mathematics (18) - Archived Browse by An undergraduate degree in mathematics provides an excellent basis for graduate work in mathematics or computer science, or for employment in such mathematics-related fields as systems analysis, operations research, or actuarial science. Because the career objectives of undergraduate mathematics majors are so diverse, each undergraduate's program is individually arranged through collaboration between the student and his or her faculty advisor. In general, students are encouraged to explore the various branches of mathematics, both pure and applied. Undergraduates seriously interested in mathematics are encouraged to elect an upper-level mathematics seminar. This is normally done during the junior year or the first semester of the senior year. The experience gained from active participation in a seminar conducted by a research mathematician is particularly valuable for a student planning to pursue graduate work. There are three undergraduate programs that lead to the degree Bachelor's of Science in Mathematics: a General Mathematics Option, an Applied Mathematics Option for those who wish to specialize in that aspect of mathematics, and a Theoretical Mathematics Option for those who expect to pursue graduate work in pure mathematics. A fourth undergraduate program leads to the degree Bachelor's of Science in Mathematics with Computer Science; it is intended for students seriously interested in theoretical computer science. Recent Submissions This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized. We will cover basic notions in real analysis: point-set topology, metric spaces, sequences and ... This seminar focuses on the knowledge and skills necessary for teaching science and engineering in higher education. Topics include: using current research in student learning to improve teaching; developing courses; ... Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence ...
A perfect resource for high school mathematics teachers, this book helps them develop or refine their own teaching philosophy. They''ll learn how to create a supportive classroom environment in which their students think together, take intellectual risks, and debate ideas. They''ll gain a better understanding about the importance of cooperative learning strategies through immersion. And they''ll engage in logic and reasoning. Puzzles and activities are presented to bring the material to life as well. All of this will help high school mathematics bring the excitement of the subject into the classroom. From the Publisher: A bring the excitement of the subject into the classroom. Description: This practical book helps middle and high school mathematics teachers effectively reach English learners in their classrooms. Designed for teachers who have had limited preparation for teaching mathematics to English learners, the guide offers an integrated approach to teaching ... Description: This book provides student activities grouped in algebra, geometry, and algebra 2 sections that parallel the traditional sequencing in major texts. Through activity design, students are lead through an inductive inquiry in which they conjecture, formulate, and test ideas ...
This course aims to provide a basis for Maths for the Artist that says "If I'd known Maths would have been central to effects and animation I would have paid attention in school!" Mike Seymour works through the major areas of maths that are useful to understand for visual effects and animation. This really is a maths course, teaching you both actual maths and the principles of areas of maths in more advanced areas. The aim is to equip you with the tools you need and to demystify the jargon – so you can understand the principles and approaches we use maths for everyday in production and post. Learn the basic and advanced features of SolidWorks step by step with the SolidWorks Tutorial DVD by Magnitude Engineering Solutions. The DVD plays instantly on your computer and comes with its own menu and media player so there is no instillation required. Just insert the DVD and choose what lesson you want from the menu. You're able to play, pause, rewind or fast forward at anytime giving you the flexibility to learn at your own individual pace. Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in electrical engineering, applied mathematics, statistics and computer science. This book provides the first detailed introduction to the subject, highlighting recent theoretical advances and a range of applications, as well as outlining numerous remaining research challenges. After a thorough review of the basic theory, many cutting-edge techniques are presented, including advanced signal modeling, sub-Nyquist sampling of analog signals, non-asymptotic analysis of random matrices, adaptive sensing, greedy algorithms and use of graphical models. All chapters are written by leading researchers in the field, and consistent style and notation are utilized throughout. Dr. Jenny Switkes will help you master the intricacies of Calculus from Limits to Derivatives to Integrals. In Educator``sShow your plan, sketches, technical draw with style! Create a realistic Engineering and Architectural Design Mock-up in few seconds. These PSD files uses the Smart-Object feature, so you can replace the mockup content easily and quickly.
Use the graphics and animations in Computer Tutor 1.0 to practice and assess your math skills. Customized to correspond chapter-by-chapter with your Houghton Mifflin math text, this tutorial will help you reinforce skills you haven't yet mastered, make up classes you may have missed, or review for exams. As you advance through your current and future courses, feel free to access any of the tutorials that may have relevant material. Chapter modules are divided into two sections: Study this Lesson and Problem Solving. Problems are algorithmically generated to ensure an appropriate variety and range of exercises. Each exercise includes specific page references to the text. Animated solution steps help you catch and understand mistakes before they are made. You'll have access to complete solutions for each exercise attempted, and may request progress reports to assess your understanding.
Textbooks from Eleven Learning Interested in adopting one of our titles in your classroom? Please contact us with any questions. Titles Available Now David Lippman's Math in Society is a survey of contemporary mathematical topics for liberal arts majors. Most chapters are independent of each other, allowing instructors to choose which subjects to cover. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. Professor Lippman teaches at Pierce College. Charles Severance's Python For Informatics is an informatics-oriented introduction to programming. Instead of a traditional computer science approach to the subject, this book uses Python to solve data analysis problems common in the world of informatics, the science of information systems design. Professor Severance teaches at the University of Michigan. Professor Severance has prepared supplementary materials for this text; they are available at his website. Steve Krause's The Process of Research Writing is suitable for research-oriented composition and rhetoric classes. As the title implies, it focuses on the process of research writing, not merely the final product. Instead of having students compose one major paper, the book presents an innovative series of assignments through which students hone their skills. As a result, students are not only prepared to write a traditional research paper; they better understand what it means to conduct academic research. Additionally, educators will find that this text has much more of a focus on internet research than do competitive offerings. Professor Krause teaches at Eastern Michigan University. Not yet ready to register? Click here to view the book in straight HTML. Coming Attractions Jim Hefferon's Linear Algebra covers the material in an introductory undergraduate-level linear algebra course. Unlike competing titles that focus on rote computation or assume that students are already able to perform abstract work, this textbook has a developmental approach to help students build their understanding of the underlying mathematics. It proceeds with a great deal of motivation with many illustrative examples, and the exercises range from routine verifications to medium-difficult questions designed to challenge but not overwhelm. Professor Hefferon teaches at Saint Michael's College. Textbook availability: This title is currently being peersourced. Its expected publication date is April 2011, and it will be available both online and in print.
2007 Hardcover New Book New and in stock. 8Co-authored by four leading scientists from academia and industry, Numerical Recipes Third Edition starts with basic mathematics and computer science and proceeds to complete, working routines. Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Please visit or for more details. More information concerning licenses is available at: New key features: And much, much more! This book/CD bundle of the greatly expanded third edition of Numerical Recipes now has wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. Visit the authors' web site for information about electronic subscriptions Editorial Reviews From the Publisher "This monumental and classic work is beautifully produced and of literary as well as mathematical quality. It is an essential component of any serious scientific or engineering library." Computing Reviews "… an instant 'classic,' a book that should be purchased and read by anyone who uses numerical methods …" American Journal of Physics "… replete with the standard spectrum of mathematically pretreated and coded/numerical routines for linear equations, matrices and arrays, curves, splines, polynomials, functions, roots, series, integrals, eigenvectors, FFT and other transforms, distributions, statistics, and on to ODE's and PDE's … delightful." Physics in Canada "… if you were to have only a single book on numerical methods, this is the one I would recommend." IEEE Computational Science & Engineering "This encyclopedic book should be read (or at least owned) not only by those who must roll their own numerical methods, but by all who must use prepackaged programs." New Scientist "These books are a must for anyone doing scientific computing." Journal of the American Chemical Society "The authors are to be congratulated for providing the scientific community with a valuable resource." The Scientist "I think this is an incredibly valuable book for both learning and reference and I recommend it for any scientists or student in a numerate discipline who need to understand and/or program numerical algorithms." International Association for Pattern Recognition "The attractive style of the text and the availability of the codes ensured the popularity of the previous editions and also recommended this recent volume to different categories of readers, more or less experienced in numerical computation." Octavian Pastravanu, Zentralblatt MATH
Product Description These activity-based books extend the concept of our best-selling Mathworks! Series by exploring how science is put to use in exciting, real-world situations that will fascinate readers. They use charts, tables, and diagrams to solve the same type of science problems that experts face every day. The colorful, high-interest approach motivates students to think about science in new and exciting ways
from '03 student enrolled in Laboratories in Mathematical Experimentation. Math 350 (new in 2003) Explorations in Analysis - Fractals This course is an exciting mathematical study of convergence and limits. Students actively investigate concepts using numerical techniques followed by precise and careful analysis. Topics include fractals, linear and nonlinear function iteration, basins of attraction, chaos, complex numbers and Newton's method. Math 246 (new in 2003) Laboratories in Mathematical Experimentation This is a course in mathematical discovery. Students "do" mathematics by designing mathematical experiments, obtaining mathematical results, analyzing data and making mathematical conjectures. Students are exposed to several very different fields of mathematics including fractals, game strategy, coding theory, graphs and networks, function iteration and chaos. "Hollins does an excellent job in teaching students how to analyze, think, and write intelligently." from '97 Hollins mathematics major. Math 241 Calculus I This coursestarts with a very simple question:How do we define the slope of a graph that is not a straight line?This leads to the study of limits, derivatives, rules of differentiation, and applications of the derivative.Students actively investigate all concepts from graphic, numeric, and algebraic points of view.Weekly computer lab sessions are an integral part of the course.Students also apply these concepts to real world problems:Can you mathematically argue the McDonalds hot coffee lawsuit?Can you find the most economical path through marsh land and dry land for an oil pipeline?Can you design a window that allows a maximum amount of light? Math 242 Calculus II This course also starts with a very simple question:How do we find areas of"weird" regions?This leads to the study of area under curves, antiderivatives, integrals, techniques (exact and approximate) of integration, and applications of the integral.Students are actively engaged in the material through group projects, computer lab sessions, and class presentations.Students apply these concepts to real world problems:Can you design an attractive floor tile pattern and then determine the amount of paint required?Can you determine exactly the volume of a pear or banana?After integration, students are introduced to infinite sequences and series. In this course, students learn how to discover mathematics.Many students incorrectly believe that much of mathematics is the result of "divine inspiration" but nothing could be further from the truth.Students learn that the first step in discovering mathematics is experimentation.Using trial and error and intuition, students "experiment" until they recognize a pattern.Then students learn to formulate a conjecture (of the pattern) and to formally prove the conjecture using direct proofs, proofs by induction, proofs by contradiction and/orproofs by contraposition.Mathematical topics covered include set theory, number theory, functions, function iteration and CHAOS! Math 372 Introduction to Real Analysis In this course, students take a more detailed look at the ideas from single variable calculus.Emphasis of this course is on comprehension, construction and communication, both written and oral (see above), offormal mathematical proofs.Students are active learners. They present proofs on the board, they critique other students' proofs, and they lead class discussions.Topics in the course includesequences, limits, continuity, differentiation, and integration.
Summary: With its combination of concepts and skill-building, as well as the focus on functions, the new third edition better prepares readers for calculus. In order to make this complex subject more engaging, the authors incorporate the rule of four, superior exercises, a concise presentation, rich real-world data and an appropriate integration of technology. They also introduce linear, exponential, power, and periodic functions before polynomial and rational functions to take ...show moreadvantage of their use to model physical phenomena
Multiple representations of concepts; Concepts and skills are introduced algebraically, graphically, numerically, and verbally-often in the same lesson to help students make the connection and to address diverse learning styles. More Views Details Prentice Hall Algebra 1. Prentice Hall offers a legacy of strong mathematics publishing, helping students develop a deep understanding of mathematics through thinking, reasoning and problem solving. Algebra success for all. Multiple representations of concepts; Concepts and skills are introduced algebraically, graphically, numerically, and verbally-often in the same lesson to help students make the connection and to address diverse learning styles. Focused on developing algebra concepts and skills. Key algebraic concepts are introduced early and opportunities to develop conceptual understanding appear throughout the text, including in Activity Labs. Frequent and varied skill practice ensures student proficiency and success. Bundles include: Student Edition Student Workbook Instructor Edition Workbook Instructor's Guide
Fractions and Multiplication and Division of Fractions: Proficiency Exam Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is a proficiency exam to the chapter "Introduction to Fractions and Multiplication and Division of Fractions." Each problem is accompanied with a reference link pointing back to the module that discusses the type of problem demonstrated in the question. The problems in this exam are accompanied by solutions
KS4 GCSE MATHEMATICS General objectives The Mathematics courses for Key Stage Four build on the foundations already laid in Ysgol Gyfun Bro Morgannwg. The aim of presenting mathematics as both a vibrant and relevant subject persists and it is regarded as an essential element in the personal development of our pupils. In studying the subject each pupil shall be given every opportunity not only to increase his mathematical skills but also to increase his logical understanding in tandem with a greater numerical appreciation. Course Details Each pupil will follow a course which best reflects his level of ability. In line with the requirements of the National Curriculum, each course consists of four assessment objectives (A.O), namely: A.O 1) Recall and use knowledge of the prescribed content. A.O 2) Select and apply mathematical methods in a range of contexts. A.O 3) Interpret and analyse problems and generate strategies to solve them. Information Technology and Communication will be an integral part of the course, both in its explication and execution. This is especially so with regard to statistical investigations. Each pupil will either follow the G.C.S.E course which best reflects his ability, or, in the case of those working at a more rudimentary level, the Entry Level Mathematics course. Two tiers of entry are available for G.C.S.E pupils – Higher and Foundation. Each tier offers two written papers. Assessment All G.C.S.E courses are comprised of the following assessment elements: Two written papers (100 marks each) There is no coursework There are two tiers of entry for G.C.S.E. The possible grades are as shown: Tier Possible Grades Higher A*,A,B,C,D Foundation C,D,E,F,G The results for candidates achieving less than the minimum mark for Grade D on the Higher Tier or Grade G on the Foundation Tier will be recorded as U. The duration of each paper is as follows: Tier Duration (Papers 1 and 2) Higher 2 hours Foundation 2 hours Entry Level Mathematics The Entry Level Mathematics course is appropriate for those pupils who have failed to reach level 3 or 4 of the National Curriculum at the end of Key Stage 3. The course is well structured and provides opportunities to learn mathematics in a relevant and engaging context. The course assessment is comprised of a number of elements over a two-year period. This is summarised below:
Product Description By June Oliver. Grade 9 and up. Worksheets contain a number of mathematical problems to be solved and matched to the answers provided. Ample drill, practice, and review with a sense of humor. Blackline masters include a review of functions, continuity and limits, differentiation and its applications, and integration and its applications. The jokes reinforce the concepts. Matching worksheets give instant feedback and students will be eager to solve the problems to determine the entertaining answers. Includes a teacher resource CD-ROM with electronic versions of activity sheets. 67 pages. Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the United States may be charged additional distributor, customs, and shipping charges.
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... The book provides the first full length exploration of fuzzy computability. It describes the notion of fuzziness and present the foundation of computability theory. It then presents the various approaches to fuzzy computability. This text provides a glimpse into the different approaches in this area, which is important for researchers in order to...This book contains advanced-level research material in the area of lubrication theory and related aspects, presented by eminent researchers during the International Conference on Advances in Tribology and Engineering Systems (ICATES 2013) held at Gujarat Technological University, Ahmedabad, India during October 15â??17, 2013. The material in this book... more... A large part of the research currently being conducted in the fields of materials science and engineering mechanics is devoted to carbon nanotubes and their applications. In this process, modeling is a very attractive investigation tool due to the difficulties in manufacturing and testing of nanomaterials. Continuum modeling offers significant advantages... more... This book provides an example of a thorough statistical treatment of ocean wave data in space and time. It demonstrates how the flexible framework of Bayesian hierarchical space-time models can be applied to oceanographic processes such as significant wave height in order to describe dependence structures and uncertainties in the data. This monograph... more... Evolution strategies have more than 50 years of history in the field of evolutionary computation. Since the early 1990s, many algorithmic variations of evolution strategies have been developed, characterized by the fact that they use the so-called derandomization concept for strategy parameter adaptation. Most importantly, the covariance matrix adaptation... more... This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw Lesniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school. The authorâ??s nuanced survey eschews secondary commentary, analyzing Lesniewski's core philosophical views and evaluating... more...
You are here Mathematical Time Capsules Dick Jardine and Amy Shell-Gellasch, Editors Mathematical Time Capsules offers teachers historical modules for immediate use in the mathematics classroom. Readers will find articles and activities from mathematics history that enhance the learning of topics covered in the undergraduate or secondary mathematics curricula. Each capsule presents at least one topic or a historical thread that can be used throughout a course. The capsules were written by experienced practitioners to provide teachers with historical background and classroom activities designed for immediate use in the classroom, along with further references and resources on the chapter subject. Print-on-Demand (POD) books are not returnable because they are printed at your request. Damaged books will, of course, be replaced (customer support information is on your receipt). Please note that all Print-on-Demand books are paperbound.
TutorVideo: Algebra Want an on-the-go algebra study guide? Algebra is the branch of mathematics concerning the study of the rules of operations and the things which can be constructed from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. With TutorVideo, you'll have access to basic tutorials on algebra - all on your iPhone or iPod Touch! TutorVideo: Algebra also allows you to chat right within the application - you can immediately share your thoughts and comments on a moderated discussion panel. Share your favorite study tips with other students. == Satisfaction Guaranteed! == If you are not 100% satisfied with TutorVideo: Algebra then we will happily return your money. Please contact Interave Media directly with your feedback.
Overview Editorial Reviews From the Publisher "Thinking Mathematically provides a rich portrait of arithmetic set in a broader perspective on mathematics, and on what it means to do and learn it. . . . The book overflows with supports for the mathematical work of the teacher in pressing students, provoking, supporting, pointing, and attending with care."–Hyman Bass and Deborah Loewenberg Ball Related Subjects Meet the Author Thomas Carpenter is Professor of Curriculum and Instruction at the University of Wisconsin-Madison, where he has taught for twenty-five years. He is the former editor of the National Council of Teachers of Mathematics (NCTM) Journal for Research in Mathematics Education, and has received the NCTM Lifetime Achievement award for Distinguished Service to Mathematics Education among other awards. Megan Loef Franke is an Associate Professor in the Department of Education at the University of California-Los Angeles and Director of Center X: Where Research and Practice Intersect for Urban School Professionals. Her work focuses on understanding and supporting teacher learning through professional development
More About This Textbook Overview Perfect for the one-term course, Essentials of Precalculus with Calculus Previews, Fifth Edition provides a complete, yet concise, introduction to precalculus concepts, focusing on important topics that will be of direct and immediate use in most calculus courses. Consistent with Professor Zill's eloquent writing style , this full-color text offers numerous exercise sets and examples to aid in student comprehension, while graphs and figures throughout serve to illuminate key concepts. The exercise sets include engaging problems that focus on algebra, graphing, and function theory, the sub-text of many calculus problems. The authors are careful to use calculus terminology in an informal and accessible way to facilitate the students successful transition into future calculus courses. With an outstanding collection of student and instructor resources, Essentials of Precalculus with Calculus Previews offers a complete teaching and learning
The fun and easy way to learn pre-calculus Getting....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 four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects... more... Do you want to better understand the statistics you hear everyday - and recognise if you're being misled? Here is a straightforward introduction to the principles of this vital field of mathematics. Assuming minimal knowledge and using examples from a wide variety of everyday contexts, this book makes even complex concepts and techniques easy to grasp. NOT... more...
Algebra, Trigonometry, and StatisticsPeople who bought this also bought...One, Two, Three: Absolutely Elementary Mathematics UNABRIDGED (6 hrs and 38 mins) By David Berlinski Narrated By Byron Wagner Whispersync for Voice-ready Overall (16) Performance (13) Story (12) In his latest foray into mathematics, David Berlinski takes on the simplest questions that can be asked: What is a number? How do addition, subtraction, multiplication, and division actually work? What are geometry and logic? As he delves into these subjects, he discovers and lucidly describes the beauty and complexity behind their seemingly simple exteriors, making clear how and why these mercurial, often slippery concepts are essential to who we are. J. Doe says:"A combination of banal, confusing, and dull" AP Psychology Test AudioLearn Study Guide: AudioLearn AP Series UNABRIDGED (3 hrs and 53 mins) By AudioLearn Editors Narrated By AudioLearn Voice Over Team Overall (1) Performance (1) Story (1) From cognition and perception to personality and motivation, AudioLearn is your complete audio study guide to advanced placement psychology. And AudioLearn comes complete with a question and answer session following each section and a free complete test. Publisher's SummaryFor the price, it is great. It might should be longer or more in depth but then it would cost more. How would you have changed the story to make it more enjoyable? It is a little dry but there are not many math books on here as of now. What three words best describe James Powers's voice? Straight-forward, easy, fast. Do you think Algebra, Trigonometry, and Statistics needs a follow-up book? Why or why not? Sure, hopefully as cheap again. Any additional comments? It seems to be the perfect book to throw on when I cannot decide which book to do next. I do not really care if I absorb it through each time; repeated usage will do the trick. Quick and painless but overall
For this capacitance worksheet, students solve 19 problems about capacitance, voltage, electric charge and Ohm's Law. They use calculus to solve some of the problems and they are given equations used to solve different capacitance problems. Students calculate the maxima and minima of quadratic equations. In this calculus lesson, students apply the derivatives by finding the maxima and minima using real life application. They solve optimization using the derivative. Students derive functions given a limit. In this calculus lesson, student define the derivative of f at x=a, knowing the derivative is a point or just a number. This assignment requires students to work independently as much as possible. Students discuss the following topics of Calculus: The Tangent Line Problem, The Area Problem, and Exercises. They find limits graphically and numerically. Students write a mathematical autobiography, they write their earliest memories of mathematics or numbers. In this solar flare reconstruction worksheet, students read about the 'saturation' point of satellite detectors when solar flares are at their most intense phase of brightness. Students are given x-ray flare data and they re-plot the data to estimate the peak of intensity. They create 2 exponential functions to fit the data and estimate the peak intensity and time. Students use calculus to integrate one of the functions and calculate the total energy radiated by the flare. In this calculus worksheet, students observe graphs and identify the limits of the functions listed in the graph. They determine the definite integrals and derivatives. Students use the trapezoid rule to estimate distance. This five-page worksheet contains 14 problems. Students investigate the fundamental theorem of calculus. In this calculus instructional activity, students derive the fundamental theorem of calculus. They differentiate between the first and second theorem. Looking for an interractive presentation for your high schoolers dealing with calculus? Then this PowerPoint is for you! Problems that cover area, volume, and other calculus-related topics are presented. Students are led through the steps necessary to solve the problems, and are given instant feedback. Young scholars calculate area under a curve using Riemann Sums. For this calculus lesson, students investigate the integral through estimation and calculation. They compare their approximate answer to their true answer. Calculus students find the limit of piecewise functions at a value. They find the limit of piecewise functions as x approaches a given value. They find the limit of linear, quadratic, exponential, and trigonometric piecewise functions. Students use the derivative and integral to solve problems involving areas. In this calculus lesson, students calculate the area under a curve as they follow a robot off road making different curves along the drive. They use Riemann Sums and Trapezoidal rules to solve the problem. Learners explore the concept of minimization. In this minimization worksheet, students determine the least expensive box given specific requirements. Learners solve a question from the AP Calculus exam in 1982; the same question from the movie Stand and Deliver. Students read about AP calculus online. In this calculus lesson, students learn real life usage for calculus. They read about instructors and their experience teaching and incorporating calculus into the real world. Students review and analyze topics needed to be successful in calculus. In this precalculus instructional activity, students review the unit circle and its properties. The trigonometric ratios and its identities. In this A.P. Calculus worksheet, students complete a sixteen question test covering trigonometric integration, area under a curve, differential equations, and slope fields. Some of the problems are multiple choice, while others are free-response.
9The Student Solutions Manual and Study Guide contains worked-out solutions to selected exercises from the text. The solved exercises cover all of the techniques discussed in the text, and include step-by-step instruction on working through the algorithms.
Incorporating the ratio and proportion, formula, and dimensional analysis methods, this online course presents a step-by-step approach to the calculation and administration of drug dosages. This Drug Calculations Online course is designed to be used with the 5th edition of Gray: Calculate with Confidence. Once you have read topics in the text, the online course provides you with an opportunity for application and practice. Animations, voice-overs, and interactive self-assessment activities are used to provide an engaging and interactive course platform. This course includes practice problems to promote active learning and quizzes that can be used to evaluate your understanding of content presented in the course
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History of Mathematics An Introduction 9780072885231 ISBN: 0072885238 Publisher: McGraw-Hill Higher Education Summary: This text is designed for the junior/senior mathematics major who intends to teach mathematics in high school or college. It concentrates on the history of those topics typically covered in an undergraduate curriculum or in elementary schools or high schools. At least one year of calculus is a prerequisite for this course. This book contains enough material for a 2 semester course but it is flexible enough to be used... in the more common 1 semester course. Burton, David M. is the author of History of Mathematics An Introduction, published under ISBN 9780072885231 and 0072885238. Twenty History of Mathematics An Introduction textbooks are available for sale on ValoreBooks.com, fourteen used from the cheapest price of $3.52, or buy new starting at $54.73
MATHEMATICS DEPARTMENT Algebra I Prerequisite: Pre-Algebra 1 Credit Open to Grade: 9 A preparatory course that places an emphasis on the Systematic development of the language through which most of mathematics is communicated. Provides the Mathematical understanding top operate with concepts at an abstract level, and then apply them in a process that fosters generalizations and insights beyond the original content. Topics covered are: properties of the number system, linear functions, inequalities, operations and real numbers and polynomials, exponents, radicals, and quadratics. Honors Algebra 1 1 credit Open to Grade: 9 Prerequisite: 8th Grade Algebra 1 This course is designed to enhance the honors math curriculum by providing an extended rigorous study of Algebra concepts including exponential relations: absolute value functions, right triangle trigonometry and topics in probability and statistics. Experiments involving graphing calculator technology will support the study of concepts. Data and Measurement Prerequisite: Algebra 1 1 Credit Open to Grade: 10 Measurement within a problem-solving context will include calculating rates using appropriate units and converting within measurement systems. Data analysis including measure of central tendency and visual representations of data will be studied. An understanding of correlation and causation will be developed and reasonable lines of best fit will be used to make predictions. Students will solve problem situations requiring right triangle trigonometry. Elementary probability theory will be used to determine the probability of events including independence, dependence and mutually exclusive events. Additional topics will include quadratics and radicals. Geometry 1 Credit Enrolled in Honors Algebra 1), 10-11-12 Within this course, students will have the opportunity to study points, lines, planes, triangle congruence and similarity; properties of quadrilaterals; right triangles; circles; basics constructions; perimeters, areas, volumes; and basic trigonometry. Introduction to Algebra II Prerequisite: Algebra 1 and Teacher Recommendation 1 Credit Open to Grades: 10-11-12 This course is designed for students who may not be academically ready for Algebra II. Placement of students is by recommendation of the Algebra 1 teacher and not student request. Topics in this course will include algebraic functions, number systems, systems of equations, polynomials, matrices, inequalities, factoring, quadratic formula, and graphing. Algebra II Prerequisite: Algebra 1 1 Credit Open to Grade: 10-11-12 The study of functions and an extension of the concepts of Algebra I and many of the concepts of geometry are provided. Topics covered are: linear and quadratic equations and functions; systems equations and inequalities; polynomials and rational polynomial expressions; polynomial functions. Honors Algebra II Prerequisite: Students from Honors Algebra I or Algebra I with Teacher recommendation. 1 credit Open to Grades: 10-11 This course provides a rigorous preparation for Pre-Calculus, with an emphasis on algebraic proof and provides an enriched version of Algebra II through the study of additional objectives and topics including conic sections, statistics, and sequences and series. Successful completion of this course prepares students for entry into Pre- Calculus. Honors Algebra II is a weighted course. Statistics Prerequisite: Algebra II and Geometry 1 Credit Open to Grades: 11-12 This course analyzes data by various means including Classification of data; the representation of data by graphs; the computation on sample means: and the computation of sample variables. Mathematics for Business & Industry Prerequisite: Algebra II and Geometry 1 Credit Open to grade: 12 This course enables the student to explore mathematical content for personal, business, and industrial use. Math concepts and skills are applied through study and problem- solving activities in real-world situations in the following areas: banking, measurement, borrowing, and investing, consumer purchases, and financial management. Leadership development will be provided through FBLA. Introduction to College Algebra Prerequisite: Geometry and Algebra II 1 Credit Open to Grades: 10-11-12 This course is designed for students who may need some additional skills prior to entering Pre-Calculus or college mathematics. Topics from Algebra II are reviewed and the following additional topics are studied in depth: functions, trigonometry, and sequences and series. Pre-Calculus Prerequisite: Teacher recommendation, and grade of "B" In Algebra II and Geometry 1 Credit Open to Grades: 11-12 Topics for this course include quadratic equations and their graphs; linear and quadratic inequalities; functions and their graphs, trigonometry functions, analytical trigonometry, logarithms and sequences and series. Pre-calculus is a weighed course. Advanced Placement Calculus AB Prerequisite: Honors/ AP Policy with grade of a least a "B" in Pre-Calculus, teacher recommendation required. 1 Credit Open to grade: 12 AP Calculus AB begins the sequence of the Advanced Placement preparatory program. This course follows the AP College Board curriculum. Topics included in this course are; elementary functions and the study of differential and integral calculus. Graphing calculators are required and used when appropriate. Students selecting this course are undertaking a college level program both require considerable study time outside the classroom in addition to assigned class work and homework. Students taking AB Calculus will be expected to take BC and will be required to take the AP exam. Successful completion of the AP exam may result in college credit. Calculus is a weighted course. Advanced Placement Calculus BC Prerequisite: Advanced Placement Calculus AB 1 Credit Open to Grades: 12 AP Calculus BC is a continuation of the topics covered in Calculus AB. Major topics include: differential equations, Polar functions, parametric functions, sequences, and series. Upon completion of Calculus BC the students will be required to take either the Calculus AB Exam or the Calculus BC Exam. Math 150- College Algebra Prerequisite: Admission to ACTC Dual Credit Program 1 Credit + 3 Hours College Credit Open to Grade: 12 Selected topics in algebra and analytic geometry. Develops Manipulative algebraic skills required for successful Calculus study. Includes brief review of basic algebra quadratic formulas, systems of linear equations, introduction to Analytic geometry, including conic sections and graphing. Students selecting this course are undertaking a college level program both in content and teacher expectation. Payment of college tuition
Creative Geometry is a set of web pages designed by a geometry teacher and written for both geometry teachers and geometry... see more Creative Geometry is a set of web pages designed by a geometry teacher and written for both geometry teachers and geometry students. In these web pages, teachers and students will find creative and interesting "hands-on" projects for most topics in the geometry curriculum. Each project is designed to help students understand, remember, and find value in the concepts of geometryA collection of mathlets for Precalculus, Single Variable Calculus, Multivariable Calculus and Vector Analysis, Parametric... see more A collection of mathlets for Precalculus, Single Variable Calculus, Multivariable Calculus and Vector Analysis, Parametric Curves and Surfaces, Derivatives, Integrals and Integration Theorems, and Topology and Geometry. Quoted from the site: [This site contains...] "Free mathematics tutorials to help you explore and gain deep understanding of... see more Quoted from the site: [This site contains...] "Free mathematics tutorials to help you explore and gain deep understanding of math topics." The math topics covered include 1) Precalculus Tutorials 2) Calculus Tutorials and Problems 3) Geometry Tutorials and Problems 3) Trigonometry Tutorials and Problems for Self Tests 4) Elementary statistics and probability tutorials 5) Applications of mathematics in physics and engineering. And much more, including many applets.
Math 197S: Seminar in Geometry Visit my home page for contact information. The information from Duke's On-Line Course Synopsis is reproduced below. For more detailed information, visit the home page for the course. Information from the On-Line Course Synopsis A proper course title could be "Symmetry, Geometry, and Optimization". We will look at some classical problems involving soap bubbles and films, curves of shortest descent (Brachistochrone problems), shortest paths on curved surfaces, and the motion and shape of elastic rods and strings. All of these will be used as motivation for introducing the ideas of the calculus of variations and studying how they interact with geometric notions, such as symmetry, both in problems and solutions. If time permits, we may study some higher dimensional problems, such as Poincare's famous analysis of the three-body problem in celestial mechanics. Textbooks There will not be a textbook. Instead, I will hand out lecture notes. Assignments Weekly homework assignments will be made and each student will be expected to present a number of these homework assignments in class. Exams There will be no inclass examinations (or final exam). Term Papers Each student will be required to write one term paper of approximately 15-20 pages that explains a problem of the type we will be developing and discussing in the course, together with its solution. The problem is to be selected in consultation with the the instructor. Grade to be based on A student's grade in the course will be based on the in-class presentations of homework assignments and the term paper, including a presentation of the term paper at the end of the semester.
The CliffsStudySolver workbooks combine 20 percent review material with 80 percent practice problems (and the answers!) to help make your lessons stick. CliffsStudySolver Algebra I is for students who want to reinforce their knowledge with a learn-by-doing approach. Inside, you'll get the practice you need to tackle numbers and operations withData Mining Applications with R is a great resource for researchers and professionals to understand the wide use of R, a free software environment for statistical computing and graphics, in solving different problems in industry. R is widely used in leveraging data mining techniques across many different industries, including government, finance,... more... Includes 40 papers presented at the 4th ESERA conference held in The Netherlands, in August 2003. The papers presented at the conference deal with actual issues in the field, such as the learning of scientific concepts and skills, scientific literacy, informal science learning, science teacher education, modeling in science education. more...
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Computer graphics is important in many areas including engineering design, architecture, education, and computer art and animation. This book examines a wide array of current methods used in creating real-looking objects in the computer, one of the main aims of computer graphics. Key features: - Good foundational mathematical introduction to curves and surfaces; no advanced math required - Topics organized by different interpolation/approximation techniques, each technique providing useful information about curves and surfaces - Exposition motivated by numerous examples and exercises sprinkled throughout, aiding the reader - Includes a gallery of color images, Mathematica code listings, and sections on curves and surfaces by refinement and on sweep surfaces - Web site maintained and updated by the author, providing readers with errata and auxiliary material This engaging text is geared to a broad and general readership of computer science/architecture engineers using computer graphics to design objects, programmers for computer gamemakers, applied mathematicians, and students majoring in computer graphics and its applications. It may be used in a classroom setting or as a general reference. Table of Contents Table of Contents Preface. Basic Theory. Linear Interpolation. Polynomial Interpolation. Hermite Interpolation. Spline Interpolation. Bezier Approximation. B Spline Approximation. Subdivision Methods. Sweep Surfaces. A. Conic Sections. B. Approximate Circles. C. Graphics Gallery. D. Mathematica Notes. Answers to Exercises. Bibliography
The ultimate aim of the field of numerical analysis is to provide convenient methods for obtaining useful solutions to mathematical problems and for extracting useful information from available solutions which are not expressed in tractable forms. This well-known, highly respected volume provides an introduction to the fundamental processes of numerical analysis, including substantial grounding in the basic operations of computation, approximation, interpolation, numerical differentiation and integration, and the numerical solution of equations, as well as in applications to such processes as the smoothing of data, the numerical summation of series, and the numerical solution of ordinary differential equations. Chapter headings include: l. Introduction 2. Interpolation with Divided Differences 3. Lagrangian Methods 4. Finite-Difference Interpolation 5. Operations with Finite Differences 6. Numerical Solution of Differential Equations 7. Least-Squares Polynomial Approximation In this revised and updated second edition, Professor Hildebrand (Emeritus, Mathematics, MIT) made a special effort to include more recent significant developments in the field, increasing the focus on concepts and procedures associated with computers. This new material includes discussions of machine errors and recursive calculation, increased emphasis on the midpoint rule and the consideration of Romberg integration and the classical Filon integration; a modified treatment of prediction-correction methods and the addition of Hamming's method, and numerous other important topics. In addition, reference lists have been expanded and updated, and more than 150 new problems have been added. Widely considered the classic book in the field, Hildebrand's Introduction to Numerical Analysis is aimed at advanced undergraduate and graduate students, or the general reader in search of a strong, clear introduction to the theory and analysis of numbers. Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to ... This Second Edition of a standard numerical analysis text retains organization of the original edition, but all sections have been revised, some extensively, and bibliographies have been updated. New ... This highly technical introduction to formal languages in computer science covers all areas of mainstream formal language theory, including such topics as operations on languages, context-sensitive ... Hundreds of solved examples, exercises, and applications help students gain a firm understanding of the most important topics in the theory and applications of complex variables. Topics include the ... Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such ...
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Numerical Linear Algebra Chris Rambicure Guojin Chen Christopher Cprek WHY USE LINEAR ALGEBRA? 1) Because it is applicable in many problems…. 2)…And it's usually easier than calculus TRUE "Linear algebra has become as basic and as applicable as calculus,and fortunately it is easier." -Gilbert Strang Calculus HERE COME THE BASICS… SCALARS What you're used to dealing with Have magnitude, but no direction VECTORS Represent both a magnitude and a direction Can add or subtract, multiply by scalars, or do dot or cross products THE MATRIX It's an mxn array Holds a set of numerical values Especially useful in solving certain types of equations Operations: Transpose, Scalar Multiply, Matrix Add, Matrix Multiply EIGENVALUES You can choose a matrix A, a vector x, and a scalar x so that Ax = sx, meaning the matrix just scales the vector X in this case is called an eigenvector, and s is its eigenvalue CHARACTERISTIC EQUATION det(M-tI) = 0 M: the matrix I: the identity t: eigenvalues CAYLEY-HAMILTON THEOREM IF AND THEN p(A) = 0, meaning A satisfies its characteristic equation A Couple Names, A Couple Algorithms IN THE BEGINNING… (Grassmann's Linear Algebra) Grassmann is considered to be the "father" of linear algebra Developed the idea of a linear algebra in which the symbols representing geometric objects can be manipulated Several of his operations: the interior product, the exterior product, and the multiproduct What's a Multiproduct Equation Look Like? d1d2 + d1d2 = 0 The multiproduct has many uses, including scientific, mathematic, and industrial Got updated by William Clifford CLIFFORD'S MODIFICATION TO GRASSMAN'S EQUATION d1d2 + d1d2 = 2kij The 2kij is what's referred to as Kronecker's Symbol Both of these equations are used for Quantum Theory Math VECTOR SPACE Another idea which is kind of tied with Grassman Vector Space refers to some set of vectors that contains the origin It is usually infinite Subspace is a subset of vector space. It, of course, is also vector space Cholesky Decomposition Algorithm developed by Arthur Cayley Takes a matrix and factors it into a triangular matrix times its transpose A=R'R Useful for matrix applications Becomes even more worthwhile in parallel HOW TO USE LINEAR ALGEBRA FOR PDE'S You can use matrices and vectors to solve partial differential equations For equations with lots of variables, you'll wind up with really sparse matrices Hence, the project we've been working on all year BIBLIOGRAPHY "Hermann Grassmann." Online. .htm "Abstract Linear Spaces. Online. groups.dcs.stand.ac.uk/~history/HistTopics/Abstract_ linear_spaces.html Liberman, M. "Linear Algebra Review." Online. gebra_review.html "Cholesky Factorization." Online. Numerical Linear Algebra Guojin Chen Christopher Cprek Chris Rambicure Johann Carl Friedrich Gauss Born: April 30, 1777 (Germany) Died: Feb 23, 1855 (Germany) Gaussian Elimination LU Factorization Operation Count Instability of Gaussian Elimination without Pivoting Gaussian Elimination with Partial Pivoting Linear systems A linear system of equations (n equations with n unknowns) can be written: a11 x1 + a12 x2 + ... + a1n xn = b1 a21 x1 + a22 x2 + ... + a2n xn = b2 ... an1 x1 + an2 x2 + ... + ann xn = bn Using matrices, the above system of linear equations can be written: Gauss Elimination and Back Substitution Convert this to triangular form: Then solve the system by Back Substitution. LU Factorization Gaussian elimination transforms a full linear system into an upper-triangular one by applying simple linear transformations on the left. Let A be a square matrix. The idea is to transform A into upper-triangular matrix U by introducing zeros below the diagonal. LU Factorization This "elimination" process is equivalent to multiplying by a sequence of lower- triangular matrices Lk on the left: Lm-1 … L2L1A = U LU Factorization Setting L = (Lm-1 )-1… (L2)-1(L1)-1 We obtain an LU factorization of A A = LU In order to find a general solution of a system of equations, it is helpful to simplify the system as much as possible. Gauss elimination is a standard method (which has the advantage of being easy to implement on a computer) for doing this. Gauss elimination uses elementary operations. We can: interchange any two equations multiply an equation by a (nonzero) constant add a multiple of one equation to any other one and aim to reduce the system to triangular form. The system obtained after each operation is equivalent to the original one, meaning that they have the same solutions. Algorithm of Gaussian Elimination without Pivoting U = A, L = I For k = 1 to m-1 for j = k +1 to m ljk = ujk/ukk uj,k:m = uj,k:m – ljkuk,k:m Operation Count There are 3 loops in the previous algorithm There are 2 flops per entry For each value of k, the inner loop is repeated for rows k+1, …, m. Work for Gaussian elimination is ~ 2 m3 flops 3 Instability of Gaussian Elimination without Pivoting Consider the following matrices: A1 = 0 1 1 1   1020 A2 =  1   1 1 Pivoting Pivots Partial Pivoting Example Complete Pivoting Pivot Partial Pivoting Example 2 1 1 0 4 3 3 1 A =8  7 9  5   6 7 9 8  1  2 1 1 0 8 7 9 5 4 1 4   1    3 3  =  3 3 1  1  8 7 9 5 2 1 1 0        1 6 7 9 8 6 7 9 8 P1 L1  1  8 7 9 5  1/ 2 1  4 3 3 1      1/ 4 1  2 1 1 0      3 / 4 1 6 7 9 8 8 7 9 5  0 1/ 2 3/ 2  3 / 2 =   0 3/ 4 5/ 4  5 / 4   0 7/4 9/4 17 / 4  Reference: Numerical Linear Algebra by Lloyd Trefethen and David Bau, III Numerical Linear Algebra: The Computer Age Christopher Cprek Chris Rambicure Guojin Chen What I'll Be Covering How Computers made Numerical Linear Algebra relevant. LAPACK Solving Dense Matrices on Parallel Computers. Why All the Sudden Interest? Gregory Moore regards the axiomatization of abstract vector spaces to have been completed in the 1920s. Linear Algebra wasn't offered as a separate mathematics course at major universities until the 1950's and 60's. Interest in linear algebra skyrocketed. Computers Made it Practical Before computers, solving a system of 100 equations with 100 unknowns was unheard of. The brute mathematical force of computers made linear algebra systems incredibly useful for all kinds of applications involving linear algebra. Computers and Linear Algebra The computer software Matlab provides a good example: it is among the most popular in engineering applications and at its core it treats every problem as a linear algebra problem. A need for more advanced large matrix operations resulted in LAPACK. What is LAPACK? Linear Algebra PACKage Software package designed specifically for linear algebra applications. The original goal of the LAPACK project was to make the widely used EISPACK and LINPACK libraries run efficiently on shared-memory vector and parallel processors. LAPACK continued… LAPACK is written in Fortran77 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision. Parallel Dense Matrix Partitioning Parallel computers are well suited for processing large matrices. In order to process a matrix in parallel, it is necessary to partition the matrix so that the different partitions can be mapped to different processors. Partitioning Dense Matrices Striped Partitioning  Block-Striped  Cyclic-Striped  Block-Cyclic-Striped Checkerboard Partitioning  Block-Checkerboard  Cyclic-Checkerboard  Block-Cyclic-Checkerboard Striped Partitioning Matrix is divided into groups of complete rows or columns, and each processor is assigned one such group. Striped Partitioning cont… Block-striped Partitioning is when contiguous rows or columns are assigned to each processor together. Cyclic-striped Partitioning is when rows or columns are sequentially assigned to processors in a wraparound manner. Block-Cyclic-Striped is a combination of the two. Striped Partitioning cont… In a column-wise block striping of an nn matrix on p processors (labeled P(0), P(1), …, P(P-1):  P(I) contains columns with indices (n/p)I, (n/p)I + 1, … , (n/p)(I+1) – 1. In row-wise striping:  P(I) contains rows with indices I, I+p, I+2p, … , I+n-p. Checkerboard Partitioning The matrix is divided into smaller square or rectangular blocks or submatrices that are distributed among processors. Checkerboard Partitioning cont… Much like striped-partitioning, checkerboard partitioning may use block, cyclic, or a combination. A checkerboard-partitioned square matrix maps naturally onto a two-dimensional square mesh of processors. An nn matrix onto a p processor mesh divides the blocks into size (n/p)(n/p). Matrix Transposition on a Mesh Assume that an nn matrix is stored in an nn mesh of processors, so each processor holds a single element. A diagonal runs down the mesh. An element above the diagonal moves down to the diagonal and then to the left to its destination processor. An element below the diagonal moves up to the diagonal and then to the right to its destination processor. Matrix Transposition cont… Matrix Tranposition cont… An element at initial p8 moves to p4, p0, p1, and finally to p2. If p<nn, then the tranpose can be computed in two phases.  Square matrix blocks are treated as indivisible units, and whole blocks are communicated instead of individual elements.  Then do a local rearrangement within the blocks. Matrix Transposition cont… Communication and the Local Rearrangement Matrix Transposition cont… The total parallel run-time of the procedure for transposition of matrix on a parallel computer: Parallelization of Linear Algebra Transposition is just an example of how numerical linear algebra can be easily and effectively parallelized. The same techniques and principles can be applied to operations like multiplication, addition, solving, etc. This explains their current popularity. Conclusion Linear algebra is flourishing in an age of computers, where there are limitless applications. LAPACK exists as an efficient code library for processing large systems of equations on parallel processing computers. Parallel Computers are very well suited to these kinds of problems. Useful Links… pdf a.htm matrix
Linear Algebra Introduction With Concurrent Examples 9780521325172 ISBN: 052132517X Publisher: Cambridge University Press Summary: This readable introduction to linear algebra, begins at an elementary level. It will be useful both for students of pure mathematics who may wish to pursue a more advanced study of the subject and for those who need to use linear algebra and its applications in other fields. Hamilton, A. G. is the author of Linear Algebra Introduction With Concurrent Examples, published under ISBN 9780521325172 and 052132517...X. One Linear Algebra Introduction With Concurrent Examples textbook is available for sale on ValoreBooks.com, and one used from the cheapest price of $172.69.[read more]
Unbounded Linear Operations Theory and Applications ISBN 0486648303 / 9780486648309 / 0-486-64830-3 Book summary This classic of mathematics offers advanced undergraduates, graduate students, and professionals a comprehensive exposition of unbounded linear operator theory. Its self-contained, systematic treatment covers both theory and applications to differential equations. Expressed in simple notation and a readable style, it includes examples and motivations for certain definitions and proofs.
Abstract Over the past several years math education has moved from a period where all math calculations were done by hand to an era where most calculations are done using a calculator or computer. There are certainly benefits to this approach, but when one concomitantly recognizes the declining scores on national standardized mathematics exams, it raises the question, "Could the lack of technology-assisted arithmetic manipulation skills have a carryover to understanding higher-level mathematical concepts or is it just a spurious correlation?" Eighty-seven students were tested for their ability to do simple arithmetic and algebra by hand. These scores were then regressed on three important areas of quantitative analysis: recognizing the appropriate tool to use in an analysis, creating a model to carry out the analysis, and interpreting the results of the analysis. The study revealed a significant relationship between the ability to accurately do arithmetic calculations and the ability to recognize the appropriate tool and creating a model. It found no significant relationship between results interpretation and arithmetic skills. 1. Introduction For more than 30 years, the United States has been concerned about the performance of their students in mathematics [1]. But things seem to remain the same with respect to mathematical training. Witness the following headlines: "In a Global Test of Math Skills, U.S. Students Behind the Curve [2]; U.S. Teens Trail Peers Around World on Math-Science Test [3]; and U.S. Math Scores Hit a Wall National Test Shows No Gains for Fourth-Graders, Slight Rise for Eighth-Graders [4]." Various explanations have been offered for American students' poor relative math skills including not enough time in the classroom [1], cultural differences and expectations [5], and too much emphasis being placed on making the subject "accessible and fun," and not enough on repetitive drills [6]. This later study specifically stated, "Two key reasons … that students in other countries tend to follow math curricula that involve significantly more drilling of basic math operations, and also tend to use calculators much less in the classroom than do students in the U.S." [6]. One may be tempted to ask, "In an era of computers, why should students be required to approach arithmetic through repetitive drills?" Indeed, this issue has been examined by several authors. Henningsen and Stein [7] suggest classroom time should be devoted to developing students' "21st century skills." They suggest mathematical reasoning and communication rather than doing arithmetic will improve mathematical understanding and skill. In Sweden, Brolin and Björk [8] did a long-term study on the use of calculators and concluded they did not negatively impact mathematical understanding. Similar results were reported in Australia [9] and England [10]. More recent studies have reached different conclusions. Loveless [11], in a report for the National Research Council, concluded that mastery of basic mathematical operations, including computational skills, was obligatory for solving more complicated mathematical problems. It may be that those arguing for and against using calculators may be missing an important point. Although there is not a lot of research at the brain level, Dr. Moocow's research ( has concluded that one reason students donot do well in math is because of deficiencies in the parietal cortex in the top back part of the head. She found that students with "math dyslexia" do not stimulate parietal cortex as much as students who are good at math. Although she was able to demonstrate the lack of development in the parietal cortex contributed to poor math scores, she also states that little is known about what, if anything, could be done to increase stimulation in that area. What if performing math calculations by hand had the same effect on physical development of the parietal cortex area of the brain that the physical act of reading has been shown to have on other areas of the brain? In short, there is a battle going on at the secondary level about how to teach mathematics from grade school through the middle school levels. Those in higher education are not a direct part of this battle but are certainly "collateral damage" from its impact. The authors of this research are not secondary school educators and therefore lack the credentials to enter the fray about HOW to teach fundamental mathematics, but we are positioned to question the impact of what is being done, whatever it is, on students' abilities to master the skills required for business quantitative analysis. The impetus for this research was motivated, in part, by the divergent opinions outlined above. More specifically we are interested in the impact that fundamental mathematical skills have, if any, on specific areas of quantitative analysis: tool recognition, model formulation, and interpretation of solutions. The next section describes how the research was conducted. That section is followed by a report of the results and an explanation of why they occurred. 2. Research Methodology and Analysis Quantitative analysis (QA) is a class required of all business majors. On the second day of that class, 124 students enrolled in three QA sections were given a computational skills/algebra test and told they could not use a calculator. A study number was assigned to each student. These numbers were recorded and given to a graduate student to assure anonymity from the course instructor, who taught all three sections. The computational skills/algebra test was divided into the following sections: mathematical manipulation, which included adding, subtracting, multiplication, and division of two or more digit numbers; fractions, including adding, subtracting, multiplication, and division; decimals, including converting fractions to decimals, weighted averages, making change, and finding percentages of numbers; and algebra, including expansion of algebraic relations and gathering terms to force an equation to have all variables on one side of the equality and constants on the other. All sections had multiple items to assess each skill. An overall score was calculated as well as a score for each section. The final exam for the course was comprehensive. It has been used by the College of Business for six years as part of its AACSB Assurance of Learning measurement. The exam is structured such that, in addition to other items, three important areas of quantitative analysis are measured across all topics: tool recognition, the ability to examine a situation and select the most appropriate quantitative analysis tool; model development, the ability to represent a situation in the correct mathematical form for solution; and interpretation, the ability to address specific questions about the results from a quantitative analysis. Scores for each area were recorded as well as an overall score for the exam. A student's scores on the final exam were paired with his/her scores on the computational skills test. Eighty-eight students completed the course and had usable scores for analysis (NOTE: 9 students completed the course who did not have usable data because of missing study numbers or missing computational skills/algebra test scores). After all data were recorded on a spreadsheet for analysis, two of the computational skills test scores were salient by their consistency: the scores on the fractions and decimals sections. Only six students correctly answered more than three questions in the two sections combined. The lack of variability in these scores led the researchers to eliminate them from further consideration as individual predictors of the dependent variables under consideration. The weighting of these scores remained, however, in the overall computational skills/algebra test score. Several researchers have argued that arithmetic manipulation skills have an influence on students' algebra skills ([6, 12, 13]). To examine that claim and to check the strength of relationship among the dependent variables and independent variables, a correlation analysis was performed. Table 1 reports the results of that analysis. The data showed a strong correlation between arithmetic manipulation skills and algebra skills; therefore, it appeared the data had the important characteristic reported by other researchers—a link between arithmetic manipulation skills and algebra knowledge. Furthermore, the correlations between the QA skills and the computational/algebra test and test sections appear strong enough to warrant further study. Table 1: Correlation analysis. The first statistical tests performed were regression analyses using the areas of quantitative analysis as the dependent variables against the overall computational skills test score. Table 2 reports the regression of computational test against the skill of tool recognition. The P value for this equation is 0.006. Based on this analysis, there appears to be a highly significant relationship between a student's ability to do computational mathematics and his/her ability to determine which quantitative tool is appropriate for a situational analysis. Table 2: Tool recognition versus computational test. Table 3 reports the regression of computational test against the skill of model development. The P value for this equation is 0.0110. Based on this analysis, there appears to be a significant relationship between a student's ability to do computational mathematics and his/her ability to create a quantitative model for situational analysis. Table 3: Model development versus computational test. Table 4 reports the regression of computational test against the skill of results interpretation. The P value for this equation is 0.1134. Based on this analysis, there appears to be no significant relationship between a student's ability to do computational mathematics and his/her ability to interpret results from a model. Table 4: Results interpretation versus computational test. The above analysis shows overall computational skills have a significant relationship to a student's ability both to select an appropriate quantitative tool and to create a quantitative model. We found no significant relationship between a student's computational skills and his/her ability to interpret the results of a quantitative analysis—it appears this is a skill that can be taught to students regardless of their mathematical backgrounds. The next logical inquiry is to determine if arithmetic skills or algebra skills are at the root of students' problems with selecting and creating quantitative models. Since previous researchers found significant relationships between arithmetic skills and algebra, we also included a cross term composed of these two variables. In all analyses reported in Tables 5 and 6, inclusion of this variable yielded a higher adjusted R square. Table 5: Tool recognition versus items. Table 6: Model development versus items. Table 5 reports the regression of arithmetic manipulation, algebra, and the cross term on tool recognition. The significance F for the equation is 0.0006, highly significant. Interpretation of the individual P values must be done prudently, because of the correlation among the independent variables. A student's ability to recognize the appropriate analysis tool for problem solving appears to be related to his/her arithmetic skills and algebra skills. Table 6 reports the regression of manipulation, algebra, and the cross term on model development. The significance F for the equation is 0.001, highly significant. A student's ability to construct mathematical models appears to be related to his/her arithmetic and algebra skills. The data in this study does support, at least at the correlational level, the notion that the ability to solve math problems by hand does have a connection to how well students are able to perform more advanced work that doesnot directly require computation but requires the ability to use higher-order quantitative reasoning skills which are assumed to be associated with physical brain development. Given the result of this study, it would be fascinating to partner with someone doing brain research to see if doing math computations by hand would increase the stimulation in the parietal cortex. If so, we would be much closer to a casual explanation that could have a significant impact on how math deficiencies are viewed and potential strategies for addressing the math deficiency problem. On a more practical level, it does suggest one possible strategy for improving performance on quantitative task: requiring students to work through at least some calculations by hand. The correlations in our student would suggest that teaching students by requiring them to perform at least some math calculations and manipulations by hand could improve their ability to perform more complex quantitative reasoning. In an era of declining math performance it certainly seems like an option worthy of further study and research. H. Shuard, "CAN: calculator use in the primary grades in England and Wales," in Calculators in Mathematics Education, National Council of teachers of Mathematics, J. Fey and C. Hirsch, Eds., pp. 33–45, Reston, Va, USA, 1992.
new edition is intended for a one semester course in optics for juniors and seniors in science and engineering. It uses scripts from Maple, MathCad, Mathematica, and MATLAB to provide a simulated laboratory where students can learn by exploration and discovery instead of passive absorption. The text covers all the standard topics of a traditional optics course. It contains step by step derivations of all basic formulas in geometrical, wave and Fourier optics. The threefold arrangement of text, applications, and files makes the book suitable for "self-learning" by scientists or engineers who would like to refresh their knowledge of optics.

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