دانلود کتاب How to read and do proofs: an introduction to mathematical thought processes

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Title Page......Page 5
Copyright......Page 6
Contents......Page 7
Preface to the Student......Page 9
Preface to the Instructor......Page 11
Acknowledgments......Page 14
Part I: Proofs......Page 17
1: The Truth of It All......Page 19
2: The Forward-Backward Method......Page 27
3: On Definitions and Mathematical Terminology......Page 43
4: Quantifiers I: The Construction Method......Page 59
5: Quantifiers II: The Choose Method......Page 71
6: Quantifiers III: Specialization......Page 87
7: Quantifiers IV: Nested Quantifiers......Page 99
8: Nots of Nots Lead to Knots......Page 111
9: The Contradiction Method......Page 119
10: The Contrapositive Method......Page 133
11: The Uniqueness Methods......Page 143
12: Induction......Page 151
13: The Either/Or Methods......Page 163
14: The Max/Min Methods......Page 173
15: Summary......Page 181
Part II: Other Mathematical Thinking Processes......Page 195
16: Generalization......Page 197
17: Creating Mathematical Definitions......Page 215
18: Axiomatic Systems......Page 237
Appendix A: Examples of Proofs from Discrete Mathematics......Page 255
Appendix B: Examples of Proofs from Linear Algebra......Page 269
Appendix C: Examples of Proofs from Modern Algebra......Page 287
Appendix D: Examples of Proofs from Real Analysis......Page 305
Glossary of Math Terms and Symbols......Page 323
References......Page 332
Index......Page 334