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Introduction to Proof in Abstract Mathematics
by Andrew Wohlgemuth
The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions.
Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.
Table of Contents for Introduction to Proof in Abstract Mathematics
| 1. Sets and Rules of Inference | | 2. Functions | | 3. Relations, Operations, and the Integers | | 4. Proofs in Analysis | | 5. Cardinality | | 6. Groups | | Appendix 1 Properties of Number Systems | | Appendix 2 Truth Tables | | Appendix 3 Inference Rules | | Appendix 4 Definitions | | Appendix 5 Theorems | | Appendix 6 A Sample Syllabus | | Answers to Practice Exercises | | Index |
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