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Introduction to Discrete Mathematics via Logic and Proof

  • Calvin Jongsma
Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Calvin Jongsma
    Pages 1-99
  3. Calvin Jongsma
    Pages 101-147
  4. Calvin Jongsma
    Pages 149-204
  5. Calvin Jongsma
    Pages 205-253
  6. Calvin Jongsma
    Pages 255-296
  7. Calvin Jongsma
    Pages 297-342
  8. Calvin Jongsma
    Pages 343-417
  9. Calvin Jongsma
    Pages 419-466
  10. Back Matter
    Pages 467-482

About this book

Introduction

This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with mathematical logic and proof, this approach suits not only a discrete mathematics course, but can also function as a transition to proof. Its unique, deductive perspective on mathematical logic provides students with the tools to more deeply understand mathematical methodology—an approach that the author has successfully classroom tested for decades.

Chapters are helpfully organized so that, as they escalate in complexity, their underlying connections are easily identifiable. Mathematical logic and proofs are first introduced before moving onto more complex topics in discrete mathematics. Some of these topics include:

  • Mathematical and structural induction
  • Set theory
  • Combinatorics
  • Functions, relations, and ordered sets
  • Boolean algebra and Boolean functions
  • Graph theory

Introduction to Discrete Mathematics via Logic and Proof will suit intermediate undergraduates majoring in mathematics, computer science, engineering, and related subjects with no formal prerequisites beyond a background in secondary mathematics.

Keywords

Sentential logic Propositional logic Predicate logic Mathematical induction Peano arithmetic Set theory Boolean algebra

Authors and affiliations

  • Calvin Jongsma
    • 1
  1. 1.Dordt UniversitySioux CenterUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-25358-5
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-25357-8
  • Online ISBN 978-3-030-25358-5
  • Series Print ISSN 0172-6056
  • Series Online ISSN 2197-5604
  • Buy this book on publisher's site