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: Proof Patterns
  name:
    name part: Joshi, Mark.
    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: XIII, 190 p. 24 illus. online resource.
  abstract: This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics, and Euclidean geometry, enabling a broad familiarity. The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.
  table of contents: Induction and complete induction -- Double Counting -- The pigeonhole principle -- Divisions -- Contrapositive and contradiction -- Intersection-enclosure and Generation -- Difference of invariants -- Linear dependence, fields and transcendence -- Formal equivalence -- Equivalence extension -- Proof by classification -- Specific-generality -- Diagonal tricks and cardinality -- Connectedness and the Jordan curve theorem -- The Euler characteristic and the classification of regular polyhedra -- Discharging -- The matching problem -- Games -- Analytical patterns -- Counterexamples.
  note: by Mark Joshi.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Geometry
  subject:
    topic: Number theory
  subject:
    topic: Topology
  subject:
    topic: Combinatorics
  subject:
    topic: Mathematics
    topic: Study and teaching
  subject:
    topic: Mathematics
  subject:
    topic: Number Theory
  subject:
    topic: Geometry
  subject:
    topic: Combinatorics
  subject:
    topic: Analysis
  subject:
    topic: Topology
  subject:
    topic: Mathematics Education
  classification: QA241-247.5
  classification: 512.7
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319162508
  identifier: http://dx.doi.org/10.1007/978-3-319-16250-8
  record info:
    record creation date: 150317
    record change date: 20151204143514.0
    record identifier: 978-3-319-16250-8