rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Why Prove it Again?
    sub title: Alternative Proofs in Mathematical Practice
  name:
    name part: Dawson, Jr., John W.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2015
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XI, 204 p. 54 illus. online resource.
  abstract: 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.
  table of 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.
  note: by John W. Dawson, Jr.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Geometry
  subject:
    topic: History
  subject:
    topic: Topology
  subject:
    topic: Mathematics
  subject:
    topic: History of Mathematical Sciences
  subject:
    topic: Geometry
  subject:
    topic: Algebra
  subject:
    topic: Analysis
  subject:
    topic: Topology
  classification: QA21-27
  classification: 510.9
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319173689
  identifier: http://dx.doi.org/10.1007/978-3-319-17368-9
  record info:
    record creation date: 150715
    record change date: 20151104183037.0
    record identifier: 978-3-319-17368-9