Logic, Mathematics, and Computer Science Modern Foundations with Practical Applications /

• Main Author: Nievergelt, Yves (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2015.
• Edition: 2nd ed. 2015.
• Subjects: Mathematics.; Mathematical logic.; Number theory.; Mathematical Logic and Foundations.; Mathematical Logic and Formal Languages.; Number Theory.

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 Logi...

Table of Contents:

• Preface
• 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
• 8. Solutions to Some Odd-Numbered Exercises
• References
• Index.