A Spiral Workbook for Discrete Mathematics

by Harris Kwong

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In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values.

Description from LibreTexts.

Publisher
State University of New York at Fredonia
Subjects
Mathematics, Combinatorics and Discrete Mathematics
Licence
CC BY-NC-SA, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. Preface
  7. 1: Introduction to Discrete Mathematics
  8. 1.1: An Overview of Discrete Mathematics
  9. 1.2: Suggestions to Students
  10. 1.3: How to Read and Write Mathematics
  11. 1.4: Proving Identities
  12. 2: Logic
  13. 2.1: Propositions
  14. 2.2: Conjunctions and Disjunctions
  15. 2.3: Implications
  16. 2.4: Biconditional Statements
  17. 2.5: Logical Equivalences
  18. 2.6: Logical Quantifiers
  19. 3: Proof Techniques
  20. 3.1: An Introduction to Proof Techniques
  21. 3.2: Direct Proofs
  22. 3.3: Indirect Proofs
  23. 3.4: Mathematical Induction - An Introduction
  24. 3.5: More on Mathematical Induction
  25. 3.6: Mathematical Induction - The Strong Form
  26. 4: Sets
  27. 4.1: An Introduction to Sets
  28. 4.2: Subsets and Power Sets
  29. 4.3: Unions and Intersections
  30. 4.4: Cartesian Products
  31. 4.5: Index Sets
  32. 5: Basic Number Theory
  33. 5.1: The Principle of Well-Ordering
  34. 5.2: Division Algorithm
  35. 5.3: Divisibility
  36. 5.4: Greatest Common Divisors
  37. 5.5: More on GCD
  38. 5.6: Fundamental Theorem of Arithmetic
  39. 5.7: Modular Arithmetic
  40. 6: Functions
  41. 6.1: An Introduction to Functions
  42. 6.2: Definition of Functions
  43. 6.3: One-to-One Functions
  44. 6.4: Onto Functions
  45. 6.5: Properties of Functions
  46. 6.6: Inverse Functions
  47. 6.7: Composite Functions
  48. 7: Relations
  49. 7.1: Definition of Relations
  50. 7.2: Properties of Relations
  51. 7.3: Equivalence Relations
  52. 7.4: Partial and Total Ordering
  53. 8: Combinatorics
  54. 8.1: What is Combinatorics?
  55. 8.2: Addition and Multiplication Principles
  56. 8.3: Permutations
  57. 8.4: Combinations
  58. 8.5: The Binomial Theorem
  59. 9: Appendices
  60. 9.1: Answers
  61. Back Matter
  62. Index
  63. Index
  64. Glossary
  65. Detailed Licensing