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:
    non sort: A
    title: History of the Central Limit Theorem
    sub title: From Classical to Modern Probability Theory
  name:
    name part: Fischer, Hans.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 402 p. online resource.
  abstract: This study aims to embed the history of the central limit theorem within the history of the development of probability theory from its classical to its modern shape, and, more generally, within the corresponding development of mathematics. The history of the central limit theorem is not only expressed in light of "technical" achievement, but is also tied to the intellectual scope of its advancement. The history starts with Laplace's 1810 approximation to distributions of linear combinations of large numbers of independent random variables and its modifications by Poisson, Dirichlet, and Cauchy, and it proceeds up to the discussion of limit theorems in metric spaces by Donsker and Mourier around 1950. This self-contained exposition additionally describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The importance of historical connections between the history of analysis and the history of probability theory is demonstrated in great detail. With a thorough discussion of mathematical concepts and ideas of proofs, the reader will be able to understand the mathematical details in light of contemporary development. Special terminology and notations of probability and statistics are used in a modest way and explained in historical context.
  table of contents: Preface -- Introduction -- The central limit theorem from laplace to cauchy: changes in stochastic objectives and in analytical methods -- The hypothesis of elementary errors -- Chebyshev's and markov's contributions -- The way towards modern probability -- General limit problems -- Conclusion: the central limit theorem as a link between classical and modern probability -- Index -- Bibliography.
  note: by Hans Fischer.
  subject:
    topic: Mathematics
  subject:
    topic: History
  subject:
    topic: Probabilities
  subject:
    topic: Statistics
  subject:
    topic: Mathematics
  subject:
    topic: History of Mathematical Sciences
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Statistics, general
  classification: QA21-27
  classification: 510.9
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Sources and Studies in the History of Mathematics and Physical Sciences
  identifier: 9780387878577
  identifier: http://dx.doi.org/10.1007/978-0-387-87857-7
  record info:
    record creation date: 101013
    record change date: 20151204180957.0
    record identifier: 978-0-387-87857-7