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: Introduction to Mathematical Structures and Proofs
  name:
    name part: Gerstein, Larry J.
    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: 2012
    edition: 2nd ed. 2012.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 401 p. online resource.
  abstract: As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor—and the flexible thinking—required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader. The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Solutions for even numbered exercises are available on springer.com for instructors adopting the text for a course. From a review of the first edition: "...Gerstein wants—very gently—to teach his students to think. He wants to show them how to wrestle with a problem (one that is more sophisticated than "plug and chug"), how to build a solution, and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I think students will find appealing. ...I am confident that a student who works through Gerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledge…. Gerstein’s book states quite plainly that the text is designed for use in a transitions course. Nothing benefits a textbook author more than having his goals clearly in mind, and Gerstein’s book achieves its goals. I would be happy to use it in a transitions course.” —Steven Krantz, American Mathematical Monthly>.
  table of contents: Preface to the Second Edition -- Preface to the First Edition -- 1. Logic -- 2. Sets -- 3. Functions -- 4. Finite and Infinite Sets -- 5. Combinatorics -- 6. Number Theory -- 7. Complex Numbers -- Hints and Partial Solutions to Selected Odd-Numbered Exercises -- Index.
  note: by Larry J. Gerstein.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical logic
  subject:
    topic: Number theory
  subject:
    topic: Combinatorics
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical Logic and Foundations
  subject:
    topic: Number Theory
  subject:
    topic: Combinatorics
  classification: QA8.9-10.3
  classification: 511.3
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Undergraduate Texts in Mathematics
  identifier: 9781461442653
  identifier: http://dx.doi.org/10.1007/978-1-4614-4265-3
  record info:
    record creation date: 120604
    record change date: 20170227142406.0
    record identifier: 978-1-4614-4265-3