Logic,Mathematics,and Computer Science: Modern Foundations with Practical Applications
Authors: Yves Nievergelt
ISBN-10: 1493932225
ISBN-13: 9781493932221
Edition 版本: 2nd ed. 2015
Released: 2015-10-14
Pages: 391 pages
Book Description
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 Birkhӓuser,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.
Book Description
Frontmatter
1. Propositional Logic: Proofs from Axioms and Inference Rules
2. First-Order Logic: Proofs with Quantifiers
3. Set Theory. Proofs by Detachment,Contraposition,and Contradiction
4. Mathematical Induction: Definitions and Proofs by Induction
5. Well-Formed Sets: Proofs by Transfinite Induction with Already Well-Ordered Sets
6. The Axiom of Choice: Proofs by Transfinite Induction
7. Applications: Nobel-Prize Winning Applications of Sets,Functions,and Relations
Backmatter
