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Foundations of Logic and Mathematics

Applications to Computer Science and Cryptography

  • Yves Nievergelt

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Theory

    1. Front Matter
      Pages 1-1
    2. Yves Nievergelt
      Pages 3-53
    3. Yves Nievergelt
      Pages 55-96
    4. Yves Nievergelt
      Pages 97-158
    5. Yves Nievergelt
      Pages 159-221
    6. Yves Nievergelt
      Pages 223-262
  3. Applications

    1. Front Matter
      Pages 263-263
    2. Yves Nievergelt
      Pages 265-302
    3. Yves Nievergelt
      Pages 303-359
    4. Yves Nievergelt
      Pages 361-398
  4. Back Matter
    Pages 399-415

About this book

Introduction

This modem introduction to the foundations of logic, mathematics, and computer science answers frequent questions that mysteriously remain mostly unanswered in other texts: • Why is the truth table for the logical implication so unintuitive? • Why are there no recipes to design proofs? • Where do these numerous mathematical rules come from? • What are the applications of formal logic and abstract mathematics? • What issues in logic, mathematics, and computer science still remain unresolved? Answers to such questions must necessarily present both theory and significant applica­ tions, which explains the length of the book. The text first shows how real life provides some guidance for the selection of axioms for the basis of a logical system, for instance, Boolean, classical, intuitionistic, or minimalistic logic. From such axioms, the text then derives de­ tailed explanations of the elements of modem logic and mathematics: set theory, arithmetic, number theory, combinatorics, probability, and graph theory, with applications to computer science. The motivation for such detail, and for the organization of the material, lies in a continuous thread from logic and mathematics to their uses in everyday life.

Keywords

Arithmetic Boolean algebra Computer Science DES Logic Number Theory cardinality cryptography ksa proof set theory

Authors and affiliations

  • Yves Nievergelt
    • 1
  1. 1.Department of MathematicsEastern Washington UniversityCheneyUSA

Bibliographic information