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How to Read and Do Proofs
Daniel Solow
Table of Contents
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. The Uniqueness Methods
12. Induction.
13. The Either/Or Methods.
14. The Max/Min Methods.
15. 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.
Glossary.
References.
Index.