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: Problems and Proofs in Numbers and Algebra
  name:
    name part: Millman, Richard S.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Shiue, Peter J.
    role:
      role term: author.
  name:
    name part: Kahn, Eric Brendan.
    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: X, 223 p. 9 illus. online resource.
  abstract: Designed to facilitate the transition from undergraduate calculus and differential equations to learning about proofs, this book helps students develop the rigorous mathematical reasoning needed for advanced courses in analysis, abstract algebra, and more. Students will focus on both how to prove theorems and solve problem sets in-depth; that is, where multiple steps are needed to prove or solve. This proof technique is developed by examining two specific content themes and their applications in-depth: number theory and algebra. This choice of content themes enables students to develop an understanding of proof technique in the context of topics with which they are already familiar, as well as reinforcing natural and conceptual understandings of mathematical methods and styles. The key to the text is its interesting and intriguing problems, exercises, theorems, and proofs, showing how students will transition from the usual, more routine calculus to abstraction while also learning how to “prove” or “solve” complex problems. This method of instruction is augmented by examining applications of number theory in systems such as RSA cryptography, Universal Product Code (UPC), and International Standard Book Number (ISBN). The numerous problems and examples included in each section reward curiosity and insightfulness over more simplistic approaches. Each problem set begins with a few easy problems, progressing to problems or proofs with multi-step solutions. Exercises in the text stay close to the examples of the section, allowing students the immediate opportunity to practice developing techniques. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathemat…
  note: by Richard S. Millman, Peter J. Shiue, Eric Brendan Kahn.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Mathematical logic
  subject:
    topic: Number theory
  subject:
    topic: Mathematics
  subject:
    topic: General Algebraic Systems
  subject:
    topic: Number Theory
  subject:
    topic: Mathematical Logic and Foundations
  classification: QA150-272
  classification: 512
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319144276
  identifier: http://dx.doi.org/10.1007/978-3-319-14427-6
  record info:
    record creation date: 150209
    record change date: 20151204154551.0
    record identifier: 978-3-319-14427-6