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| Description | Table of Contents | Order Information |
| Homepage | Books |
| This book is designed to reduce the time and frustration
involved in learning how to read, think about, understand, and
"do" mathematical proofs. This goal is accomplished by
identifying and describing the various techniques used in virtually all
proofs, independent of subject matter. Students are taught not only how
to use the techniques, but also when each technique is likely
to be used, based on certain keywords that appear in the statement under
consideration. Students are also taught how to understand a written proof
by learning to identify the sequence of techniques that are used.
This undergraduate-level book is suitable as a text for a transition-to-advanced-math course, as a supplement to any course involving proofs, or for self-guided reading. |
| 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 Selected Exercises |
| Title: | How to Read and Do Proofs |
| Edition/Year: | Fourth Edition, 2005 |
| Author: | Daniel Solow |
| ISBN #: | 0-471-68058-3 |
| Publisher: | John Wiley and Sons, Inc. |
| http://www.wiley.com |