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Making Transcendence Transparent : An intuitive approach to classical transcendental number theory - Edward B. Burger

Making Transcendence Transparent

An intuitive approach to classical transcendental number theory

Hardcover Published: 28th July 2004
ISBN: 9780387214443
Number Of Pages: 263

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While the theory of transcendental numbers is a fundamental and important branch of number theory, most mathematicians know only its most elementary results. The aim of "Making Transcendence Transparent" is to provide the reader with an understanding of the basic principles and tools of transcendence theory and an intuitive framework within which the major results can be appreciated and their proofs can be understood. The book includes big picture overviews of the over-arching ideas, and general points of attack in particular arguments, so the reader will enjoy and appreciate the panoramic view of transcendence. It is designed to appeal to interested mathematicians, graduate students, and advanced undergraduates.

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.)

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
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387214443
ISBN-10: 0387214445
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 263
Published: 28th July 2004
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.59

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