| Description | Table of Contents | Order Information |
How to Read and Do Proofs
Description
This book is designed to reduce the time and frustration involved in learning how to read, think about, understand, and "do" mathematical proofs and also to provide a description of other mathematical "thinking processes". In Part 1 of the book, the various techniques used in virtually all proofs, independent of subject matter, are identified and described. 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. In Part 2 of the book, other mathematical thinking process such as the following are described and illustrated with many examples:
- Generalization
- Unification
- Converting visual images to symbolic form and vice versa
- Creating definitions
- Abstraction and axiomatic systems
This book is suitable as a text for an undergraduate transition-to-advanced-math course, as a supplement to any course involving proofs, or for self-guided reading (especially for Ph.D. students in math-related areas such as Statistics, Computer Science, Physics, Engineering, Finance, Economics, and Business). Students can view videos of my lectures for each of the first 15 chapters at:
http://bcs.wiley.com/he-bcs/Books?action=resource&bcsId=8432&itemId=1118164024&resourceId=33036.You can find a review of this book at the bottom of http://shepherd.com/book/how-to-read-and-do-proofs, which is a page on the website https://shepherd.com/.
Table of Contents
| PART 1: PROOFS |
| 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 |
| 12. Induction |
| 13. Either/Or |
| 14. Max/Min Methods |
| 15. Summary |
| PART 2: OTHER MATHEMATICA THINKING PROCESSES |
| 16. Generalization |
| 17. Creating Mathematical Definitions |
| 18. Axiomatic Systems |
| APPENDICES |
| 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 |
Order Information
| Title: | How to Read and Do Proofs |
| Edition/Year: | Sixth Edition, 2014 |
| Author: | Daniel Solow |
| ISBN #: | 978-1-118-16402-0 |
| Publisher: | John Wiley and Sons, Inc. |
| http://www.wiley.com |
Daniel Solow
- Deaprtment of Operations
- Weatherhead School of Management
- Case Western Reserve University
- Cleveland, OH 44106
