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Birkhäuser - Birkhäuser Mathematics | Foundations of Logic and Mathematics - Applications to Computer Science and Cryptography

Foundations of Logic and Mathematics

Applications to Computer Science and Cryptography

Nievergelt, Yves

2002, XVI, 415 p.

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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.

Content Level » Research

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

Related subjects » Birkhäuser Computer Science - Birkhäuser Mathematics

Table of contents 

Preface * Outline * Part A. Theory * 0. Boolean Algebraic Logic * 1. Logic and Deductive Reasoning * 2. Set Theory * 3. Induction, Recursion, Arithmetic, Cardinality * 4. Decidability and Completeness * Part B. Applications * 5. Number Theory and Codes * 6. Ciphers, Combinatorics, and Probabilities * 7. Graph Theory * Bibliography * Index

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