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Making Transcendence Transparent


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Table of Contents

* A prequel to transcendence * Incredible numbers incredibly close to modest rational numbers * The powerful power series for e * Conjugation and symmetry as a means towards transcendence * The analytic adventures of exp(z) * Debunking conspiracy theories for independent functions * Class distinctions among complex numbers * Extending our reach through periodic functions * Transcending numbers and discovering a more formal e * Selected highlights from complex analysis

About the Author

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 acknowledging an outstanding expository article. To read more about Ed Burger go to


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!" (Alvaro 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.)

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