國立高雄大學圖資館 |

Language: English

Back

Why prove it again?alternative proof...

Dawson, John W.

Why prove it again?alternative proofs in mathematical practice /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Why prove it again?by John W. Dawson, Jr.
Reminder of title:	alternative proofs in mathematical practice /
Author:	Dawson, John W.
Published:	Cham :Springer International Publishing :2015.
Description:	xi, 204 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Proof theory.
Online resource:	http://dx.doi.org/10.1007/978-3-319-17368-9
ISBN:	9783319173689 (electronic bk.)

Why prove it again?alternative proofs in mathematical practice /
Dawson, John W.

Why prove it again?alternative proofs in mathematical practice /[electronic resource] :by John W. Dawson, Jr. - Cham :Springer International Publishing :2015. - xi, 204 p. :ill., digital ;24 cm.

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 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.

ISBN: 9783319173689 (electronic bk.)

Standard No.: 10.1007/978-3-319-17368-9doiSubjects--Topical Terms:

190840
Proof theory.

LC Class. No.: QA9.54

Dewey Class. No.: 511.3

Why prove it again?alternative proofs in mathematical practice /
LDR:02735nmm a2200313 a 4500 001 472784
003 DE-He213
005 20160222172721.0
006 m d
007 cr nn 008maaau
008 160316s2015 gw s 0 eng d
020 $a 9783319173689 (electronic bk.)
020 $a 9783319173672 (paper)
024 7 $a 10.1007/978-3-319-17368-9 $2 doi
035 $a 978-3-319-17368-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA9.54
072 7 $a PBX $2 bicssc
072 7 $a MAT015000 $2 bisacsh
082 0 4 $a 511.3 $2 23
090 $a QA9.54 $b .D272 2015
100 1 $a Dawson, John W. $3 728077
245 1 0 $a Why prove it again? $h [electronic resource] : $b alternative proofs in mathematical practice / $c by John W. Dawson, Jr.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2015.
300 $a xi, 204 p. : $b ill., digital ; $c 24 cm.
505 0 $a 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.
520 $a 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.
650 0 $a Proof theory. $3 190840
650 1 4 $a Mathematics. $3 184409
650 2 4 $a History of Mathematical Sciences. $3 511733
650 2 4 $a Geometry. $3 183883
650 2 4 $a Algebra. $3 188312
650 2 4 $a Analysis. $3 273775
650 2 4 $a Topology. $3 185965
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-17368-9
950 $a Mathematics and Statistics (Springer-11649)