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: Markov's Theorem and 100 Years of the Uniqueness Conjecture
    sub title: A Mathematical Journey from Irrational Numbers to Perfect Matchings
  name:
    name part: Aigner, Martin.
    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: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 257 p. online resource.
  abstract: This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov’s theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov’s theorem. What makes the Markov theme so attractive is that it appears in an astounding variety of different fields, from number theory to combinatorics, from classical groups and geometry to the world of graphs and words. On the way, there are also introductory forays into some fascinating topics that do not belong to the standard curriculum, such as Farey fractions, modular and free groups, hyperbolic planes, and algebraic words. The book closes with a discussion of the current state of knowledge about the uniqueness conjecture, which remains an open challenge to this day. All the material should be accessible to upper-level undergraduates with some background in number theory, and anything beyond this level is fully explained in the text. This is not a monograph in the usual sense concentrating on a specific topic. Instead, it narrates in five parts – Numbers, Trees, Groups, Words, Finale – the story of a discovery in one field and its many manifestations in others, as a tribute to a great mathematical achievement and as an intellectual pleasure, contemplating the marvellous unity of all mathematics.
  table of contents: Approximation of Irrational Numbers -- Markov's Theorem and the Uniqueness Conjecture -- The Markov Tree -- The Cohn Tree -- The Modular Group SL(2,Z) -- The Free Group F2 -- Christoffel Words -- Sturmian Words -- Proof of Markov's Theorem -- The Uniqueness Conjecture. .
  note: by Martin Aigner.
  subject:
    topic: Mathematics
  subject:
    topic: Group theory
  subject:
    topic: Number theory
  subject:
    topic: Combinatorics
  subject:
    topic: Mathematics
  subject:
    topic: Number Theory
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Combinatorics
  classification: QA241-247.5
  classification: 512.7
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319008882
  identifier: http://dx.doi.org/10.1007/978-3-319-00888-2
  record info:
    record creation date: 130718
    record change date: 20151218121243.0
    record identifier: 978-3-319-00888-2