Making Transcendence Transparent: An intuitive approach to classical transcendental number theory [Hardcover]

Edward B. Burger (Author), Robert Tubbs (Author)

Book Description

ISBN-10: 0387214445 | ISBN-13: 978-0387214443 | Publication Date: July 28, 2004 | Edition: 1

This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students.

Edward Burger is one of the authors of The Heart of Mathematics, winner of a 2001 Robert W. Hamilton Book Award. He will also be awarded the 2004 Chauvenet Prize, one of the most prestigious MAA prizes for outstanding exposition.

Editorial Reviews

Review

From the reviews:

"Making Transcendence Transparent is one of those books that stand out from the crowd because the authors have put a lot of good work into it, and plenty of imagination and creativity. It is witty, funny at times, highly entertaining, very readable and interesting to both the casual and advanced reader. ... The text helps us understand the concepts by building a very strong intuition and also motivates the concepts from a historical point of view. … Conclusion: read this one!" (Álvaro Lozano-Robledo, MathDL, January, 2006)

"One of the goals of the authors is to provide the reader with an intuitive framework in which the major classical results of transcendental number theory can be appreciated. … This book is an introduction to the subject which is supposed to enable the reader to pursue later his study with more modern results. … An appendix provides basic facts from complex analysis which are required for the proofs. This book is aimed at beginners who like to have examples and detailed proofs." (Zentralblatt MATH, August, 2005)

"The book under review covers much wonderful material, heads in several directions, and could be used in many ways." (MAA reviews, D'Angelo, John P.)

From the Back Cover

While the study of transcendental numbers is a fundamental pursuit within number theory, the general mathematics community is familiar only with its most elementary results. The aim of Making Transcendence Transparent is to introduce readers to the major "classical" results and themes of transcendental number theory and to provide an intuitive framework in which the basic principles and tools of transcendence can be understood. The text includes not just the myriad of technical details requisite for transcendence proofs, but also intuitive overviews of the central ideas of those arguments so that readers can appreciate and enjoy a panoramic view of transcendence. In addition, the text offers a number of excursions into the basic algebraic notions necessary for the journey. Thus the book is designed to appeal not only to interested mathematicians, but also to both graduate students and advanced undergraduates.

Edward Burger is Professor of Mathematics and Chair at Williams College. His research interests are in Diophantine analysis, and he is the author of over forty papers, books, and videos. The Mathematical Association of America has honored Burger on a number of occasions including, most recently, in awarding him the prestigious 2004 Chauvenet Prize.

Robert Tubbs is a Professor at the University of Colorado in Boulder. He has written numerous papers in transcendental number theory. Tubbs has held visiting positions at the Institute for Advanced Study, MSRI, and at Paris VI. He has recently completed a book on the cultural history of mathematical truth.

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Product Details

• Hardcover: 272 pages
• Publisher: Springer; 1 edition (July 28, 2004)
• Language: English
• ISBN-10: 0387214445
• ISBN-13: 978-0387214443
• Product Dimensions: 9.5 x 6.1 x 0.7 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #505,841 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

5 of 5 people found the following review helpful:

4.0 out of 5 stars Review of Making Transcendence Transparent, August 31, 2008

By 

Scott Tillinghast (Houston TX) - See all my reviews
(REAL NAME)   

This review is from: Making Transcendence Transparent: An intuitive approach to classical transcendental number theory (Hardcover)

This is a good introduction to the study of transcendental numbers, and it is pretty new (2004).
The authors provide motivation for complex proofs by working up from simpler proofs for special cases. For example, they prove various properties of the exponential function, and these culminate in proof of the full Lindemann theorem. Likewise a series of special cases leads up to proof of the Gelfond-Schneider theorem.
There is a nice description of Mahler's classification of transcendental numbers.
Chapter 7 concerns elliptic functions and does a good job of introducing the concepts surrounding elliptic curves.
One weakness in this book is that it does not have a good bibliography. It could better fill its niche in the market if the authors had made one. Moreover, there are many proofs I would like to see laid out better, and for this reason I have decided to give just 4 stars.