Foundations of Logic and Mathematics

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.

This modern introduction to the foundations of logic and mathematics takes into account not only theory, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography, transportation networks). A first college-level introduction to logic, proofs, sets, number theory, and graph theory for undergraduates in mathematics, computer science, and computer information systems. Also serves as an excellent self-study reference and resource for instructors.

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.