Elsevier S & T

The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs

Cupillari, Antonella

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Table of contents
  • Contentsix
  • List of Symbolsv
  • Prefacexi
  • Chapter 1. Introduction and Basic Terminology1
  • Chapter 2. General Suggestions5
  • Chapter 3. Basic Techniques to Prove If/Then Statements9
  • Direct Proof12
  • Related Statements19
  • Proof by Contrapositive (AKA Proof by Contradiction or Indirect Proof)22
  • How to Construct the Negation of a Statement25
  • Chapter 4. Special Kinds of Theorems35
  • "If and Only If" or "Equivalence Theorems"35
  • Use of Counterexamples45
  • Mathematical Induction48
  • Existence Theorems58
  • Uniqueness Theorems61
  • Equality of Sets68
  • Equality of Numbers78
  • Composite Statements81
  • Limits91
  • Chapter 5. Review Exercises103
  • Chapter 6. Exercises Without Solutions107
  • Chapter 7. Collection of Proofs115
  • Chapter 8. Solutions for the Exercises at the End of the Sections and the Review Exercises123
  • Solutions for the Exercises at the End of the Sections124
  • Solutions for the Review Exercises151
  • Chapter 9. Other Books on the Subject of Proofs and Mathematical Writing173
  • Index177
  • A Guide to Selecting a Method of Proof180
Book details
  • Vendor Elsevier S & T
  • SKU 9780120885091
  • ISBN-13 9780080537900
  • Author Cupillari, Antonella
  • Edition 3rd
  • Category Mathematics
  • Subject Set Theory

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The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.

* The "List of Symbols" has been extended.
* Set Theory section has been strengthened with more examples and exercises.
* Addition of "A Collection of Proofs"