Why prove it again? : alternative proofs in mathematical practice / John W. Dawson, Jr., with the assistance of Bruce S. Babcock and with a chapter by Steven H. Weintraub
- Proofs in mathematical practice -- Motives for finding alternative proofs -- Sums of integers -- Quadratic surds -- The Pythagorean theorem -- The fundamental theorem of arithmetic -- The infinitude of the primes -- The fundamental theorem of algebra -- Desargues's theorem -- The prime number theorem -- The irreducibility of the cyclotomic polynomials -- The compactness of first-order languages -- Other case studies.
- This monograph considers several well-known mathematical theorems and asks the question, "Why prove it again?" while examining alternative proofs. It explores of previously established results, as well as how they judge whether two proofs of a given result are different. While a numberof 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 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 Arithmatic, 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 matieral to their students. -- from back cover.
- 3319173677 hardback, 9783319173672 hardback, and 9783319173689 eBook
- PSU Archives copy signed by author.
- Bibliography Note:
- Includes bibliographical references and index.
- Source of Acquisition:
- PSU Archives copy: Gift of John W. Dawson, Jr.; 2017.
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