Table of Contents

Foreword.Preface to the Student.Preface to the Instructor.Acknowledgments.1. The Truth of It All.2. The Forward-Backward Method.3. On Definitions and Mathematical Terminology.4. Quantifiers I: The Construction Method.5. Quantifiers II: The Choose Method.6. Quantifiers III: Specialization.7. Quantifiers IV: Nested Quantifiers.8. Nots of Nots Lead to Knots.9. The Contradiction Method.10. The Contrapositive Method.11. Uniqueness Methods and Induction.12. Either/or and Max/Min Methods.13. Summary.Appendix A: Examples of Proofs from Discrete Mathematics.Appendix B: Examples of Proofs from Linear Algebra.Appendix C: Examples of Proofs from Modern Algebra.Appendix D: Examples of Proofs from Real Analysis.Solutions to Select Exercises.Glossary.References.Index.

Reviews

"I think that Solow has written an excellent text that I will highly recommend as a supplementary text for several upper division mathematics courses including abstract algebra and mathematical analysis." (Phillip Bean, Mercer University) "His already fine book becomes more usable by having the four subject-targeted appendices." (Richard Delaware, UMKC) "The book covers all the basic proof techniques in a very readable, concise way without overwhelming the student. The organization is great. I like the short chapters highlighting only one concept at a time." (Josephine Hamer, Western Connecticut State University) "Very clear, rigorous, extremely thorough, almost unique in what it tries to do, reaches out to weaker students." (Michael Thaddeus, Columbia University)