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)

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
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
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
http://library.link/vocab/creatorName
Dawson, Jr., John W
Image bit depth
0
LC call number
QA21-27
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
http://library.link/vocab/subjectName
  • Mathematics
  • Algebra
  • Global analysis (Mathematics)
  • Geometry
  • Topology
  • Mathematics
  • History of Mathematical Sciences
  • Geometry
  • Algebra
  • Analysis
  • Topology
Label
Why Prove it Again? : Alternative Proofs in Mathematical Practice, by John W. Dawson, Jr, (electronic resource)
Instantiates
Publication
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 First-Order Languages -- Other Case Studies
Dimensions
unknown
Extent
XI, 204 p. 54 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319173689
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-17368-9
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-17368-9
Label
Why Prove it Again? : Alternative Proofs in Mathematical Practice, by John W. Dawson, Jr, (electronic resource)
Publication
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 First-Order Languages -- Other Case Studies
Dimensions
unknown
Extent
XI, 204 p. 54 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319173689
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-17368-9
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-17368-9

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