Synopses & Reviews
Prepare for success in mathematics with DOING MATHEMATICS: AN INTRODUCTION TO PROOFS AND PROBLEM SOLVING! By discussing proof techniques, problem solving methods, and the understanding of mathematical ideas, this mathematics text gives you a solid foundation from which to build while providing you with the tools you need to succeed. Numerous examples, problem solving methods, and explanations make exam preparation easy.
About the Author
Steven Galovich is Professor of Mathematics at Lake Forest College. Dr. Galovich's specializations are algebraic number theory and algebra, and his interests include the nature of mathematics, Fermat's Last Theorem, and the history of mathematics. In 1988, he won the Carl B. Allendoerfer Award for expository writing presented by the Mathematical Association of America for the paper "Products of sines and cosines" published in Mathematics Magazine.
Table of Contents
Chapter I. SOLVING PROBLEMS. 1. How to Solve It. 2. Understanding the Problem. Chapter II. THINKING LOGICALLY. 3. Propositional Calculus. 4. Sets. 5. Predicates and Quantifiers. Chapter III. PROVING THEOREMS. 6. Direct Proof. 7. Indirect Proof. 8. Mathematical Induction. 9. Case Analysis. 10. Attacking the Problem/Proof. 11. Looking Back. Chapter IV. SETS AND RELATIONS. 12. Sets and Set Operations. 13. Relations. 14. Functions. 15. Equivalence Relations. 16. Number Systems and Well-Defined Operations. 17. The Real and Complex Numbers. Chapter V. CARDINALITY. 18. Equinumerous Sets. 19. Finite Sets. 20. Denumerable Sets. 21. Uncountable Sets. 22. Cardinality and the Cantor-Bernstein Theorem. Chapter VI. DISCRETE STRUCTURES. 23. Fundamental Combinatorial Principles. 24. Permutations and Combinations. 25. Binomial Coefficients and the Binomial Theorem. 26. Recurrence Relations. 27. Algebraic Properties of the Integers. Chapter VII. DOING MATHEMATICS. 28. Controlling Your Thinking. 29. Attitudes and Beliefs. 30. Problems.