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.
Yves Nievergelt is professor of mathematics at Eastern Washington University. His research interests include applied analysis (mathematics applied to chemistry, medical diagnostic imaging, and physics), complex analysis, and numerical analysis (mathematics of scientific programming).
“This book could be a valuable reference text and would be useful to one who would like to know how basic mathematical primitives can be rigorously developed within basic set theory.” (Rana Barua, Mathematical Reviews, June, 2016)It is quite suitable for a first- or second-year university course where the hand of the lecturer can guide the student through the material. There are fairly comprehensive sets of problems at the end of each chapter … . In summary, the book is a very thorough treatment of the topics … . It is quite suitable as a textbook for an undergraduate course in the logic and mathematics that underpin a computer science course. The exercises are comprehensive.” (Martin Schweitzer, Computing Reviews, computingreviews.com, May, 2016)“This introductory textbook on logic and set theory stands out in that it does notonly present its mathematical content in a thorough and accessible way, but also giving historical and philosophical background … . The book contains many exercises that should serve to further the understanding of the reader … . The book should be accessible to readers with a basic general background in mathematics.” (Merlin Carl, zbMATH 1334.03002, 2016)
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