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


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.


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