The Art of Proof

Basic Training for Deeper Mathematics

Authors:

ISBN: 978-1-4419-7022-0 (Print) 978-1-4419-7023-7 (Online)

Table of contents (21 chapters)

previous Page of 2
  1. Front Matter

    Pages i-xxi

  2. The Discrete

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-12

      Integers

    3. No Access

      Book Chapter

      Pages 13-23

      Natural Numbers and Induction

    4. No Access

      Book Chapter

      Pages 25-31

      Some Points of Logic

    5. No Access

      Book Chapter

      Pages 33-45

      Recursion

    6. No Access

      Book Chapter

      Pages 47-54

      Underlying Notions in Set Theory

    7. No Access

      Book Chapter

      Pages 55-64

      Equivalence Relations and Modular Arithmetic

    8. No Access

      Book Chapter

      Pages 65-72

      Arithmetic in Base Ten

  3. The Continuous

    1. Front Matter

      Pages 73-73

    2. No Access

      Book Chapter

      Pages 75-83

      Real Numbers

    3. No Access

      Book Chapter

      Pages 85-93

      Embedding Z in R

    4. No Access

      Book Chapter

      Pages 95-105

      Limits and Other Consequences of Completeness

    5. No Access

      Book Chapter

      Pages 107-112

      Rational and Irrational Numbers

    6. No Access

      Book Chapter

      Pages 113-119

      Decimal Expansions

    7. No Access

      Book Chapter

      Pages 121-129

      Cardinality

    8. No Access

      Book Chapter

      Pages 131-131

      Final Remarks

  4. Further Topics

    1. Front Matter

      Pages 133-133

    2. No Access

      Book Chapter

      Pages 135-139

      Continuity and Uniform Continuity

    3. No Access

      Book Chapter

      Pages 141-144

      Public-Key Cryptography

    4. No Access

      Book Chapter

      Pages 145-150

      Complex Numbers

    5. No Access

      Book Chapter

      Pages 151-160

      Groups and Graphs

    6. No Access

      Book Chapter

      Pages 161-165

      Generating Functions

    7. No Access

      Book Chapter

      Pages 167-171

      Cardinal Number and Ordinal Number

previous Page of 2