The Resource Why Prove it Again? : Alternative Proofs in Mathematical Practice, by John W. Dawson, Jr, (electronic resource)
Why Prove it Again? : Alternative Proofs in Mathematical Practice, by John W. Dawson, Jr, (electronic resource)
Resource Information
The item Why Prove it Again? : Alternative Proofs in Mathematical Practice, by John W. Dawson, Jr, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Why Prove it Again? : Alternative Proofs in Mathematical Practice, by John W. Dawson, Jr, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This monograph considers several wellknown mathematical theorems and asks the question, zWhy prove it again?y 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
 Language
 eng
 Extent
 XI, 204 p. 54 illus.
 Contents

 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 FirstOrder Languages
 Other Case Studies
 Isbn
 9783319173689
 Label
 Why Prove it Again? : Alternative Proofs in Mathematical Practice
 Title
 Why Prove it Again?
 Title remainder
 Alternative Proofs in Mathematical Practice
 Statement of responsibility
 by John W. Dawson, Jr
 Language
 eng
 Summary
 This monograph considers several wellknown mathematical theorems and asks the question, zWhy prove it again?y 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
 http://library.link/vocab/creatorName
 Dawson, Jr., John W
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink (Online service)
 http://library.link/vocab/subjectName

 Mathematics
 Algebra
 Mathematical analysis
 Analysis (Mathematics)
 Geometry
 History
 Topology
 Label
 Why Prove it Again? : Alternative Proofs in Mathematical Practice, by John W. Dawson, Jr, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 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 FirstOrder Languages  Other Case Studies
 Control code
 9783319173689
 Dimensions
 unknown
 Extent
 XI, 204 p. 54 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319173689
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319173689
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)921673822
 Label
 Why Prove it Again? : Alternative Proofs in Mathematical Practice, by John W. Dawson, Jr, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 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 FirstOrder Languages  Other Case Studies
 Control code
 9783319173689
 Dimensions
 unknown
 Extent
 XI, 204 p. 54 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319173689
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319173689
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)921673822
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/WhyProveitAgainAlternativeProofsin/C2S5_qlVgQE/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/WhyProveitAgainAlternativeProofsin/C2S5_qlVgQE/">Why Prove it Again? : Alternative Proofs in Mathematical Practice, by John W. Dawson, Jr, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>