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Exploring the Number Jungle: A Journey into Diophantine Analysis (Student Mathematical Library, V. 8) First Edition

by Edward B. Burger (Author)

4.2 3 ratings

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Welcome to diophantine analysis--an area of number theory in which we attempt to discover hidden treasures and truths within the jungle of numbers by exploring rational numbers. Diophantine analysis comprises two different but interconnected domains--diophantine approximation and diophantine equations. This highly readable book brings to life the fundamental ideas and theorems from diophantine approximation, geometry of numbers, diophantine geometry and $p$-adic analysis. Through an engaging style, readers participate in a journey through these areas of number theory. Each mathematical theme is presented in a self-contained manner and is motivated by very basic notions. The reader becomes an active participant in the explorations, as each module includes a sequence of numbered questions to be answered and statements to be verified. Many hints and remarks are provided to be freely used and enjoyed. Each module then closes with a Big Picture Question that invites the reader to step back from all the technical details and take a panoramic view of how the ideas at hand fit into the larger mathematical landscape. This book enlists the reader to build intuition, develop ideas and prove results in a very user-friendly and enjoyable environment.

Editorial Reviews

Review

"A wealth of information ... designed as a textbook at the undergraduate level, with lots of exercises. The choice of material is very nice: Diophantine approximation is the unifying theme, but the tour has side trips to elliptic curves, Riemann surfaces, and $p$-adic analysis. The writing style is relaxed and pleasant ... For this trip, the guide has chosen an ascent to an accessible summit, but with the emphasis always on teaching and motivating important techniques so that the beginner can advance to a higher level." ---- MAA Monthly

"The author invites the reader right from the beginning, through his engaging and motivating style, to develop ideas actively and to find proofs for himself ... Remarks at the end of each of the 20 short sections, into which this readily readable introduction to diophantine analysis is divided, extend the material and stimulate the reader to deeper study and involvement with it." ---- Zentralblatt MATH

"This short book presents a nice enjoyable introduction to Diophantine analysis, which invites the motivated reader to rediscover by himself or herself many of the fundamental results of the subject, with hints given in an appendix for the more difficult results." ---- Mathematical Reviews

From the Inside Flap

Here ... is something truly different ... number theory is such a large subject, and so much of it is initially accessible without too many prerequisites, that one would expect to see a different take on the subject every once in a while. And that, happily, is what we have here both, in content and in style of presentation ... For professors with the requisite background, this may be just the right book to use in an upper-level undergraduate seminar. Students working through this book will learn some nice material and will probably also emerge from the course with a much greater confidence in their ability to do mathematics.

--MAA Online

Product details

Publisher ‏ : ‎ American Mathematical Society; First Edition (July 25, 2000)
Language ‏ : ‎ English
Paperback ‏ : ‎ 151 pages
ISBN-10 ‏ : ‎ 0821826409
ISBN-13 ‏ : ‎ 978-0821826409
Item Weight ‏ : ‎ 7 ounces
Dimensions ‏ : ‎ 5.75 x 0.25 x 8.75 inches

Best Sellers Rank: #3,734,265 in Books (See Top 100 in Books)
- #498 in Algebraic Geometry (Books)
- #907 in Geometry
- #988 in Number Theory (Books)

Customer Reviews:
4.2 3 ratings

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Edward B. Burger

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Edward Burger is the President of Southwestern University as well as an educational and business consultant. Most recently he was the Francis Christopher Oakley Third Century Professor of Mathematics at Williams College, and served as Vice Provost for Strategic Educational Initiatives at Baylor University. He is the author of over 60 research articles, books, and video series (starring in over 3,000 on-line videos). Burger was awarded the 2000 Northeastern Section of the Mathematical Association of America (MAA) Award for Distinguished Teaching and 2001 MAA Deborah and Franklin Tepper Haimo National Award for Distinguished Teaching of Mathematics. The MAA also named him their 2001-2003 Polya Lecturer. He was awarded the 2003 Residence Life Teaching Award from the University of Colorado at Boulder. In 2004 he was awarded Mathematical Association of America's Chauvenet Prize and in 2006 he was a recipient of the Lester R. Ford Prize. In 2007, 2008, and 2011 he received awards for his video work. In 2007 Williams College awarded him the Nelson Bushnell Prize for Scholarship and Teaching. Burger is an associate editor of the American Mathematical Monthly and Math Horizons Magazine and serves as a Trustee of the Kenan Institute for the Arts at the University of North Carolina School of the Arts. In 2006, Reader's Digest listed Burger in their annual "100 Best of America" as America's Best Math Teacher. In 2010 he was named the winner of the Robert Foster Cherry Award for Great Teaching---the largest and most prestigious prize in higher education teaching across all disciplines in the English speaking world. Also in 2010 he starred in a mathematics segment for NBC-TV on the Today Show and throughout the 2010 Winter Olympic coverage. That television appearance won him a 2010 Telly Award. The Huffington Post named him one of their 2010 Game Changers; "HuffPost's Game Changers salutes 100 innovators, visionaries, mavericks, and leaders who are reshaping their fields and changing the world." In 2012, Microsoft Worldwide Education selected him as one of their "Global Heroes in Education." In 2013 Burger was inducted as a Fellow of the American Mathematical Society.