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: Number Theory
    sub title: An Introduction via the Density of Primes
  name:
    name part: Fine, Benjamin.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Rosenberger, Gerhard.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    edition: 2nd ed. 2016.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 413 p. 12 illus., 1 illus. in color. online resource.
  abstract: Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing. Key topics and features include: A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals Discussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers The user-friendly style, historical context, and wide range of exercises that range from simple to quite difficult (with solutions and hints provided for select exercises) make Number Theory: An Introduction via the Density of Primes ideal for both self-study and classroom use. Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced where needed.
  table of contents: Introduction and Historical Remarks -- Basic Number Theory -- The Infinitude of Primes -- The Density of Primes -- Primality Testing: An Overview -- Primes and Algebraic Number Theory -- The Fields Q_p of p-adic Numbers: Hensel's Lemma -- References -- Index.
  note: by Benjamin Fine, Gerhard Rosenberger.
  subject:
    topic: Mathematics
  subject:
    topic: Data structures (Computer science)
  subject:
    topic: Matrix theory
  subject:
    topic: Algebra
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Mathematical logic
  subject:
    topic: Number theory
  subject:
    topic: Mathematics
  subject:
    topic: Number Theory
  subject:
    topic: Mathematical Logic and Foundations
  subject:
    topic: Linear and Multilinear Algebras, Matrix Theory
  subject:
    topic: Analysis
  subject:
    topic: Applications of Mathematics
  subject:
    topic: Data Structures, Cryptology and Information Theory
  classification: QA241-247.5
  classification: 512.7
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319438757
  identifier: http://dx.doi.org/10.1007/978-3-319-43875-7
  record info:
    record creation date: 160919
    record change date: 20160919145705.0
    record identifier: 978-3-319-43875-7