This text for the first or second year undergraduate in mathematics logic computer science
or social sciences introduces the reader to logic proofs sets and number theory. It also
serves as an excellent independent study reference and resource for instructors. Adapted from
Foundations of Logic and Mathematics: Applications to Science and Cryptography © 2002
Birkh¿user this second edition provides a modern introduction to the foundations of logic
mathematics and computers science developing the theory that demonstrates construction of all
mathematics and theoretical computer science from logic and set theory. The focuses is on
foundations with specific statements of all the associated axioms and rules of logic and set
theory and provides complete details and derivations of formal proofs. Copious references to
literature that document historical development is also provided. Answers are found to 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?
Additionally the selection of topics presented reflects many major accomplishments from the
twentieth century and includes applications in game theory and Nash's equilibrium Gale and
Shapley's match making algorithms Arrow's Impossibility Theorem in voting to name a few. From
the reviews of the first edition: ...All the results are proved in full detail from first
principles...remarkably the arithmetic laws on the rational numbers are proved step after
step starting from the very definitions!...This is a valuable reference text and a useful
companion for anybody wondering how basic mathematical concepts can be rigorously developed
within set theory. -MATHEMATICAL REVIEWS Rigorous and modern in its theoretical aspect
attractive as a detective novel in its applied aspects this paper book deserves the attention
of both beginners and advanced students in mathematics logic and computer sciences as well as
in social sciences. -Zentralblatt MATH
