A Cool Brisk Walk Through Discrete Mathematics

by Stephen Davies

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A Cool Brisk Walk Through Discrete Mathematics - and its companion site "allthemath" - are completely-and-forever-free-and-open-source educational materials dedicated to the mathematics that budding computer science practitioners actually need to know. They feature the fun and addictive teaching of award-winning lecturer Dr. Stephen Davies of the University of Mary Washington in Fredericksburg, Virginia!

Description from LibreTexts.

Publisher
University of Mary Washington
Subjects
Mathematics, Combinatorics and Discrete Mathematics
Licence
CC BY-SA 4.0, as LibreTexts states it
Who can read
Teens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Meetup at the Trailhead
  7. 1.0: Introduction
  8. 1.1: Exercises
  9. 2: Sets
  10. 2.0: Introduction
  11. 2.10: Subsets
  12. 2.11: Power sets
  13. 2.12: Partitions
  14. 2.13: Exercises
  15. 2.1: The idea of a set
  16. 2.2: Defining sets
  17. 2.3: Finite and infinite sets
  18. 2.4: Sets are not arrays
  19. 2.5: Sets are not ordered pairs (or tuples)
  20. 2.6: Sets of sets
  21. 2.7: Cardinality
  22. 2.8: Some special sets
  23. 2.9: Combining sets
  24. 3: Relations
  25. 3.0: Introduction
  26. 3.1: The idea of a relation
  27. 3.2: Defining relations
  28. 3.3: Relations between a set and itself
  29. 3.4: Finite and infinite relations
  30. 3.5: Properties of endorelations
  31. 3.6: Functions
  32. 3.7: Properties of functions
  33. 3.8: Exercises
  34. 4: Probability
  35. 4.0: Introduction
  36. 4.1: Outcomes and events
  37. 4.2: Probability measures
  38. 4.3: Philosophical interlude
  39. 4.4: Conditional probability
  40. 4.5: Total probability
  41. 4.6: Bayes’ Theorem
  42. 4.7: Independence
  43. 4.8: Exercises
  44. 5: Structures
  45. 5.0: Introduction
  46. 5.1: Graphs
  47. 5.2: Trees
  48. 5.3: Final word
  49. 6: Counting
  50. 6.0: Introduction
  51. 6.1: The Fundamental Theorem
  52. 6.2: Permutations
  53. 6.3: Combinations
  54. 6.4: Summary
  55. 7: Numbers
  56. 7.0: Introduction
  57. 7.1: What is a “number?”
  58. 7.2: Bases
  59. 7.3: Hexadecimal (base 16)
  60. 7.4: Binary (base 2)
  61. 8: Logic
  62. 8.0: Introduction
  63. 8.1: Propositional logic
  64. 8.2: Predicate logic
  65. 9: Proof
  66. 9.0: Introduction
  67. 9.1: Proof concepts
  68. 9.2: Types of proof
  69. 9.3: Proof by induction
  70. 9.4: Final word
  71. Back Matter
  72. Index
  73. Glossary
  74. Detailed Licensing