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Real Infinite Series (Classroom Resource Material) (Mathematical Association of America Textbooks)
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Daniel D. Bonar, Michael J. Khoury Jr.
List Price: $59.95
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Product Details
- Author: Daniel D. Bonar, Michael J. Khoury Jr.
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- Binding: Hardcover
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- Dewey Decimal Number: 515.243
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- EAN: 9780883857458
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- Format: Illustrated
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- ISBN: 0883857456
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- Label: The Mathematical Association of America
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- Language: English
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- Manufacturer: The Mathematical Association of America
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- Number of Items: 1
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- Number of Pages: 274
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- Product Group: Book
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- Publication Date: 2006-01-20
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- Publisher: The Mathematical Association of America
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- Studio: The Mathematical Association of America
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- Title: Real Infinite Series (Classroom Resource Material) (Mathematical Association of America Textbooks)
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Avg Customer Rating: 
Product Description: This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. "Real Infinite Series" presents the theory of real infinite series, including elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Recognizing the interest in problem solving that abounds with students of mathematics, the authors devote a chapter to problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals (what Martin Gardner calls "look-see" diagrams), and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works devoted entirely or partially to infinite series.
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Customer Reviews
Real Infinite Series For Beginners.
This is an excellent book. The prose is very readable and there are numerous illustrative examples to clarify the main points. Chapter 1 defines infinite series, discusses intuition and infinity, and covers the basic convergence tests. Chapter 2 covers the work of Cauchy and discusses more involved tests of convergence such as Kummer's results, the tests of Raabe and Gauss, and the tests of Abel. Chapter 3 examines the harmonic series. Chapter 4 covers a number of interesting results involving infinite series. Chapter 5 presents 101 problems involving infinite series from the Putnam Mathematical Competition. Answers to all problems are provided. Chapter 6 presents a plethora of puzzles, proofs without words, fallacious proofs, and fallacies, flaws, and flimflam. Answers to the puzzles are given. Two appendices present 101 True or False questions on infinite series with answers and a brief article on harmonic series. References, both books and journals, are also given. A brief but thorough index concludes the book. This book would serve very well as a resource for high school and college calculus teachers. Undergraduate mathematics majors with an interest in infinite series would find it appealing. Finally, readers like myself who majored in mathematics but pursued other careers would enjoy using it to refresh their knowledge of infinite series.(they may need to review a little calculus). The authors have produced a gem of a book and anyone who has a passion for mathematics will enjoy reading this volume. Chapters 1 and 6 are especially readable, informative, and enjoyable. Chapter 6 is just plain fun! Get your hands on a copy of this book as it will provide hours of fascinating reading and problem solving.
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Like Father, Like Son
I am pleased to say that I was one of the first to have this wonderful book. In all honesty - I don't understand anything in this book. I tried to just read chapter 1 - the definitions, and I fell asleep. I tried to read chapter 2 and I got a headache.
However, I'm the father of one of the author's and I'm awfully proud of him!
Please buy many copies.
Mike Sr.
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