Jr. Dawson: Why Prove it Again? | Buch

Cover: 9783319173672 | Why Prove it Again? | Alternative Proofs in Mathematical Practice | xi

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

John W. Dawson, Jr., is Professor Emeritus at Penn State York.

Zusammenfassung

Contains comparative studies of alternative proofs of various well-known theorems

Stresses the informal notion of what constitutes a proof, as opposed to the formal notion of proof in mathematical logic

Will appeal to a broad range of readers, including historians and philosophers of mathematics, students, and practicing mathematicians

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2015
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Buch
Inhalt:	xi 204 S. 54 s/w Illustr. 204 p. 54 illus.
ISBN-13:	9783319173672
ISBN-10:	3319173677
Sprache:	Englisch
Herstellernummer:	978-3-319-17367-2
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Dawson, Jr.
Auflage:	1st ed. 2015
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG
Maße:	241 x 160 x 18 mm
Von/Mit:	Jr. Dawson
Erscheinungsdatum:	24.07.2015
Gewicht:	0,5 kg

Artikel-ID: 104834535