Author	Nievergelt, Yves. author
Title	Foundations of Logic and Mathematics [electronic resource] : Applications to Computer Science and Cryptography / by Yves Nievergelt
Imprint	Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2002
Connect to	http://dx.doi.org/10.1007/978-1-4612-0125-0
Descript	XVI, 415 p. online resource

This modem introduction to the foundations of logic, mathematics, and computer science answers frequent questions that mysteriously remain mostly unanswered in other texts: โข Why is the truth table for the logical implication so unintuitive? โข Why are there no recipes to design proofs? โข Where do these numerous mathematical rules come from? โข What are the applications of formal logic and abstract mathematics? โข What issues in logic, mathematics, and computer science still remain unresolved? Answers to such questions must necessarily present both theory and significant applicaยญ 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 deยญ 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

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

1. Mathematics
2. Data encryption (Computer science)
3. Applied mathematics
4. Engineering mathematics
5. Mathematical logic
6. Number theory
7. Mathematics
8. Mathematical Logic and Foundations
9. Data Encryption
10. Applications of Mathematics
11. Number Theory