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: Integers, Polynomials, and Rings
    sub title: A Course in Algebra
  name:
    name part: Irving, Ronald S.
    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: 2004
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 288 p. online resource.
  abstract: Mathematics is often regarded as the study of calculation, but in fact, mathematics is much more. It combines creativity and logic in order to arrive at abstract truths. This book is intended to illustrate how calculation, creativity, and logic can be combined to solve a range of problems in algebra. Originally conceived as a text for a course for future secondary-school mathematics teachers, this book has developed into one that could serve well in an undergraduate course in abstract algebra or a course designed as an introduction to higher mathematics. Not all topics in a traditional algebra course are covered. Rather, the author focuses on integers, polynomials, their ring structure, and fields, with the aim that students master a small number of serious mathematical ideas. The topics studied should be of interest to all mathematics students and are especially appropriate for future teachers. One nonstandard feature of the book is the small number of theorems for which full proofs are given. Many proofs are left as exercises, and for almost every such exercise a detailed hint or outline of the proof is provided. These exercises form the heart of the text. Unwinding the meaning of the hint or outline can be a significant challenge, and the unwinding process serves as the catalyst for learning. Ron Irving is the Divisional Dean of Natural Sciences at the University of Washington. Prior to assuming this position, he served as Chair of the Department of Mathematics. He has published research articles in several areas of algebra, including ring theory and the representation theory of Lie groups and Lie algebras. In 2001, he received the University of Washington's Distinguished Teaching Award for the course on which this book is based.
  table of contents: Introduction: The McNugget Problem -- Introduction: The McNugget Problem -- Integers -- Induction and the Division Theorem -- The Euclidean Algorithm -- Congruences -- Prime Numbers -- Rings -- Euler’ Theorem -- Binomial Coefficients -- Polynomials -- Polynomials and Roots -- Polynomials with Real Coefficients -- Polynomials with Rational Coefficients -- Polynomial Rings -- Quadratic Polynomials -- Polynomial Congruence Rings -- All Together Now -- Euclidean Rings -- The Ring of Gaussian Integers -- Finite Fields.
  note: by Ronald S. Irving.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Associative rings
  subject:
    topic: Rings (Algebra)
  subject:
    topic: Field theory (Physics)
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Associative Rings and Algebras
  subject:
    topic: Field Theory and Polynomials
  classification: QA150-272
  classification: 512
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Undergraduate Texts in Mathematics
  identifier: 9780387218311
  identifier: http://dx.doi.org/10.1007/b97633
  record info:
    record creation date: 100301
    record change date: 20151116134040.0
    record identifier: 978-0-387-21831-1