Foundations of Logic and Mathematics: Applications to Computer Science and Cryptography

This modern introduction to the foundations of logic and mathematics answers many questions that usually remain unanswered: Why is the truth table for logical implication so unintuitive? Why are there no recipes to design proofs? Where do these numerous mathematical rules come from? What issues in l [...]
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This modern introduction to the foundations of logic and mathematics answers many questions that usually remain unanswered: Why is the truth table for logical implication so unintuitive? Why are there no recipes to design proofs? Where do these numerous mathematical rules come from? What issues in logic, mathematics, and computer science still remain unresolved? And the perennial question: In what ways are we going to use this material? 'Foundations of Logic and Mathematics' takes into account not only theory, but also treats in some detail applications that have substantial impact on everyday life---for example, financial loans and mortgages, bar codes (Universal Product Codes), public-key cryptography (Rivest--Shamir--Adelman codes), and transportation networks. Topics covered: truth tables, propositional and predicate calculi, set theory, theory and practice of basic arithmetic, cardinality, well-formed sets, completeness and incompleteness of various logic, number theory, combinatorics, and graph theory. One of the key strengths of the presentation is the continuous thread from logic to applications, without gaps. Thus, material that is necessary for logical coherence---omitted from most texts---is found here.