Real Infinite Series (Mathematical Association of America Textbooks) 1st Edition by Daniel D. Bonar (PDF)

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. Included are 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. Another gives 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, 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 on infinite series.

User’s Reviews

Editorial Reviews: Review ‘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 of infinite series, and solutions …’ L’enseignement mathematique Book Description An introductory treatment of infinite series of real numbers, from basic definitions and tests to advanced results. Book 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. About the Author Daniel Donald Bonar did his Ph.D. work in complex analysis at Ohio State University where he graduated in 1968. In 1965 he joined the faculty of Denison University in Granville, OH where he has been teaching mathematics, statistics, and computer science. In 1995 he was appointed to the newly created George R. Stibitz Distinguished Professorship in Mathematics and Computer Science. He is the author of a book entitled “On Annular Functions”, and is co-author on several research papers. He has published joint work with the internationally acclaimed Hungarian mathematician Paul Erdos. Michael Khouryis currently pursuing a Ph.D. in number theory at the Ohio State University with the support of the NSF. Michael Khoury was a prizewinner in the Putnam Mathematical Competition, and participated twice in the Math Olympiad Summer Program in Lincoln, NE, a four-week program open to the top performers on the USA Math Olympiad. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐Lots of good information, and you can jump around in it as well. You don’t have to start from the beginning, which is what I like I jumped right into Harmonic series in chapter 3. Then I moved onto chapter 4 randomly skipping through the gems. There’s also an entire section of Putnam problems, which was nice when I was training for the Putnam. If I had worked through this section more thoroughly, I would have gotten one or two more problems on the 2010 exam lol. Anyways.Have fun with this book!

⭐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.

⭐Good quality and speedy delivery.

⭐

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