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【2015新书】Why Prove it Again?: Alternative Proofs in Mathematical Practice
Book 图书名称：Why Prove it Again?: Alternative Proofs in Mathematical Practice
Author 作者： John W. Dawson Jr.
Publisher 出版社： Birkhäuser
Page 页数： 204
Publishing Date 出版时间： Sep 14, 2015
Language 语言： English
Size 大小： 5 MB
Format 格式： pdf 文字版
ISBN: 3319173677, 9783319173672
Edition: 第1版 搜索过论坛，没有该文档
This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different. While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems.
The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice. He then outlines various purposes that alternative proofs may serve. Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues’ Theorem, the Prime Number Theorem, and the proof of the irreducibility of cyclotomic polynomials.
Why Prove It Again? will appeal to a broad range of readers, including historians and philosophers of mathematics, students, and practicing mathematicians. Additionally, teachers will find it to be a useful source of alternative methods of presenting material to their students.
== Table of contents ==
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