Making transcendence transparent : an intuitive approach to classical transcendental number theory 经典超越数论的直观探讨
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作者： Edward B. Burger 著
出 版 社：
出版时间： 2004-7-1字数：版次： 1页数： 263印刷时间： 2004/07/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387214443包装： 精装编辑推荐
作者介绍：Edward Burger
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 http://www.williams.edu/Mathematics/eburger/.
内容简介
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.
目录
Preface: The Journey Aheadix
Number 0.1.4142135623730950488016887242
Number 1.0.1100010000000000000000010000
Number 2.2.7182818284590452353602874713
Number 3.4.1132503787829275171735818151
Number 4.23.140692632779269005729086367
Number 5.2.6651441426902251886502972498
Number 6.2.718281828459 …… + 0.11000100000
Number 7.74162987092054876737354013887
Number 8.1 + 1/T2-T + 1/(T4-T)(T2-T)2 + 1/(T8-T)(T4-T)2(T2-T)4 +
Appendix: Selected highlights from complex analysis
A.1 Analytic and entire functions
A.2 Contour integrals
A.3 Cauchy's integral formula
A.4 The Maximum Modulus Principle
Acknowledgments
Index
