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Delftse Foundations of Computation

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Delftse Foundations of Computation

Delftse Foundations of Computation is a textbook for a one quarter introductory course in theoretical computer science. It includes topics from propositional and predicate logic, proof techniques, set theory and the theory of computation, along with practical applications to computer science. It has no prerequisites other than a general familiarity with computer programming.

Computer ScienceEngineering
Author
Stefan Hugtenburg & Neil Yorke-Smith
Publisher
Delft University of Technology
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Information Technology
Read online Download PDF (open licence)
Contents· 85 sections
  1. 01: Logic
  2. 1.01: Propositional Logic
  3. 1.1.01: Propositions
  4. 1.1.02: Logical operators
  5. 1.1.03: Precedence rules
  6. 1.1.04: Logical equivalence
  7. 1.1.05: More logical operaters
  8. 1.1.06: Implications in English
  9. 1.1.07: More forms of implication
  10. 1.1.08: Exclusive or
  11. 1.1.09: Universal operators
  12. 1.1.10: Classifying propositions
  13. 1.02: Boolean Algebra
  14. 1.2.01: Basics of Boolean Algebra
  15. 1.2.02: Substitution Laws
  16. 1.2.03: Simplifications
  17. 1.2.04: More rules of Boolean Algebra
  18. 1.03: Logic Circuits
  19. 1.3.01: Logic Gates
  20. 1.3.02: Combining Gates to Create Circuits
  21. 1.3.03: From Circuits to Propositions
  22. 1.3.04: Disjunctive Normal Form
  23. 1.3.05: Binary Addition
  24. 1.04: Predicate Logic
  25. 1.4.01: Predicates
  26. 1.4.02: Quantifiers
  27. 1.4.03: Operators
  28. 1.4.04: Tarskis world and formal structures
  29. 1.4.05: Logical equivalence
  30. 1.05: Deduction
  31. 1.5.01: Arguments
  32. 1.5.02: Valid arguments and proofs
  33. 1.5.03: Proofs in predicate logic
  34. 1.06: Logic
  35. 02: Proof
  36. 2.01: A Little Historial Background
  37. 2.02: 3.2.C Examples
  38. 2.03: Mathematical Proof
  39. 2.3.01: How to write a proof
  40. 2.3.02: Some terminology
  41. 2.04: Proof by Contradiction
  42. 2.05: Mathematical Induction
  43. 2.5.01: How to write a proof by induction
  44. 2.5.02: Examples
  45. 2.5.03: More examples
  46. 2.06: Strong Mathematical Induction
  47. 2.07: Application - Recursion and Induction
  48. 2.7.01: Recursive factorials
  49. 2.7.02: Towers of Hanoi
  50. 2.7.03: Binary trees
  51. 2.08: Recursive Definitions
  52. 2.09: Invariants
  53. 03: Sets Functions and Relations
  54. 3.01: Basic Concepts
  55. 3.1.01: Elements of sets
  56. 3.1.02: Set-builder notation
  57. 3.1.03: Operations on sets
  58. 3.1.04: Visualising sets
  59. 3.1.05: Sets of sets
  60. 3.1.06: Mathematical induction revisited
  61. 3.1.07: Structural Induction
  62. 3.02: 4.2 The Boolean Algebra of Sets
  63. 3.2.01: Set Complement
  64. 3.2.02: Link between logic and set theory
  65. 3.03: Programming with Sets
  66. 3.3.01: Representing sets
  67. 3.3.02: Computing with sets
  68. 3.04: Functions
  69. 3.4.01: Formalizing the notion of functions
  70. 3.4.02: Operations on functions
  71. 3.4.03: Properties of functions
  72. 3.4.04: First-class objects
  73. 3.05: Programming with Functions
  74. 3.5.01: Functions as first-class objects
  75. 3.06: Counting Past Infinity
  76. 3.6.01: Cardinality
  77. 3.6.02: Counting to infinity
  78. 3.6.03: Uncountable sets
  79. 3.6.04: A final note on infinities
  80. 3.07: Relations
  81. 3.7.01: Properties of relations
  82. 3.7.02: Equivalence relations
  83. 3.08: Relational Databases
  84. 04: Looking Beyond
  85. 4.01: Further Reading