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Working with definitions, part 2 (Screencast 1.2.1b)

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Published on Jul 19, 2012

More practice with instantiating definitions, this time using a common term from geometry.

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  1. 1

    Statements and Non-Statements (Screencast 1.1.1)

  2. 2

    How do we know if a statement is true? (Screencast 1.1.2)

  3. 3

    Conditional statements (Screencast 1.1.3)

  4. 4

    When are conditional statements true? (Screencast 1.1.4)

  5. 5

    Truth tables for conditional statements (Screencast 1.1.5)

  6. 6

    Working with definitions (Screencast 1.2.1)

  7. Working with definitions, part 2 (Screencast 1.2.1b)

  8. 8

    Direct proofs of conditional statements using know-show tables (part 1) (Screencast 1.2.2)

  9. 9

    Direct proofs of conditional statements using know-show tables, Part 2 (Screencast 1.2.3)

  10. 10

    Writing up a proof outline into a paragraph (Screencast 1.2.4)

  11. 11

    Negations of simple statements (Screencast 2.1.1)

  12. 12

    Truth tables, part 1 (Screencast 2.1.2)

  13. 13

    Truth tables, part 2 (Screencast 2.1.3)

  14. 14

    Truth tables, part 3 (Screencast 2.1.4)

  15. 15

    Truth tables, part 4 (Screencast 2.1.5)

  16. 16

    Truth tables, part 5 (Screencast 2.1.6)

  17. 17

    Tautologies and contraditions, part 1 (Screencast 2.1.7)

  18. 18

    Tautologies and contradictions, part 2 (Screencast 2.1.8)

  19. 19

    Logical equivalence (Screencast 2.2.1)

  20. 20

    Converse and contrapositive (Screencast 2.2.2)

  21. 21

    Negations of conditional statements (Screencast 2.2.3)

  22. 22

    Logical equivalence without truth tables (Screencast 2.2.4)

  23. 23

    Sets and set notation (Screencast 2.3.1)

  24. 24

    Open sentences and truth sets (Screencast 2.3.2)

  25. 25

    Elements, subsets, and set equality (Screencast 2.3.3)

  26. 26

    Set-builder notation (Screencast 2.3.4)

  27. 27

    Quantified statements (Screencast 2.4.1)

  28. 28

    Negating quantified statements (Screencast 2.4.2)

  29. 29

    Integer divisibility (Screencast 3.1.1)

  30. 30

    Direct proof involving divisibility (Screencast 3.1.2)

  31. 31

    Integer congruence (Screencast 3.1.3)

  32. 32

    Reducing an integer modulo n (Screencast 3.1.4)

  33. 33

    Proofs involving integer congruence (Screencast 3.1.5)

  34. 34

    Proof by contraposition (Screencast 3.2.1)

  35. 35

    Proof by Contraposition, part 2 (Screencast 3.2.2)

  36. 36

    Proof of biconditional statements (Screencast 3.2.3)

  37. 37

    Proof of biconditional statements, part 2 (Screencast 3.2.4)

  38. 38

    Constructive proofs (Screencast 3.2.5)

  39. 39

    Proof by contradiction (Screencast 3.3.1)

  40. 40

    Proof by contradiction, part 2 (Screencast 3.3.2)

  41. 41

    Proof by contradiction, part 3 (Screencast 3.3.3)

  42. 42

    Proof by contradiction: Irrationality of sqrt(2) (Screencast 3.3.4)

  43. 43

    Proof by cases, part 1 (Screencast 3.4.1)

  44. 44

    Proof by cases, part 2 (Screencast 3.4.2)

  45. 45

    Proof by cases, part 3 (Screencast 3.4.3)

  46. 46

    Proof using cases, part 4 (Screencast 3.4.4)

  47. 47

    The Division Algorithm (Screencast 3.5.1)

  48. 48

    Using the Division Algorithm to Set up Proof Cases (Screencast 3.5.2)

  49. 49

    The Division Algorithm and Integer Congruence (Screencast 3.5.3)

  50. 50

    Application to Cryptography (Screencast 3.5.4)

  51. 51

    The Traveler and the Strange Staircase (Screencast 4.1.1)

  52. 52

    Mathematical Induction, part 1 (Screencast 4.1.2)

  53. 53

    Mathematical Induction, part 2 (Screencast 4.1.3)

  54. 54

    Mathematical induction: Example with integer division (Screencast 4.1.4)

  55. 55

    Mathematical induction: Example with inequality (Screencast 4.1.5)

  56. 56

    Mathematical induction: Example with calculus (Screencast 4.1.6)

  57. 57

    The Extended Principle of Mathematical Induction

  58. 58

    Extended Principle of Mathematical Induction: Example from computational geometry (Screencast 4.2.2)

  59. 59

    The Second Principle of Mathematical Induction (Screencast 4.2.3)

  60. 60

    Recursively defined sequences (Screencast 4.3.1)

  61. 61

    Proving propositions about Fibonacci numbers (Screencast 4.3.3)

  62. 62

    The Fibonacci sequence (Screencast 4.3.2)

  63. 63

    Proving propositions about Fibonacci numbers (Screencast 4.3.3)

  64. 64

    Sets and set operations (Screencast 5.1.1)

  65. 65

    Operations using infinite sets (Screencast 5.1.2)

  66. 66

    Subsets and set equality (Screencast 5.1.3)

  67. 67

    Cardinality (Screencast 5.1.4)

  68. 68

    Proving subset inclusion (Screencast 5.2.1)

  69. 69

    Proving set equality (Screencast 5.2.2)

  70. 70

    Disjoint sets (Screencast 5.2.3)

  71. 71

    Identities about sets (Screencast 5.3.1)

  72. 72

    Using set identities (Screencast 5.3.2)

  73. 73

    Using set identities, part 2 (Screencast 5.3.3)

  74. 74

    Using set identities, part 3 (Screencast 5.3.4)

  75. 75

    Cartesian products (Screencast 5.4.1)

  76. 76

    Proofs involving Cartesian products (Screencast 5.4.2)

  77. 77

    Functions: The big concepts (Screencast 6.1.1)

  78. 78

    Functions: Terminology (Screencast 6.1.2)

  79. 79

    Function example: Names to initials (Screencast 6.1.3)

  80. 80

    Function example: Counting primes (Screencast 6.1.4)

  81. 81

    Function example: Congruence functions (Screencast 6.1.5)

  82. 82

    Function example: Derivatives (Screencast 6.1.6)

  83. 83

    Function example: Averages (Screencast 6.1.7)

  84. 84

    Non-examples of functions (Screencast 6.1.8)

  85. 85

    Equality of functions (Screencast 6.2.1)

  86. 86

    Functions involving congruences (Screencast 6.2.2)

  87. 87

    Injective functions (Screencast 6.3.1)

  88. 88

    How to prove a function is an injection (Screencast 6.3.2)

  89. 89

    Surjective functions (Screencast 6.3.3)

  90. 90

    How to prove that a function is a surjection (Screencast 6.3.4)

  91. 91

    Compositions of functions (Screencast 6.4.1)

  92. 92

    Proving results involving compositions (Screencast 6.4.2)

  93. 93

    Functions as sets of ordered pairs (Screencast 6.5.1)

  94. 94

    Sets of ordered pairs as functions (Screencast 6.5.2)

  95. 95

    Inverses of functions (Screencast 6.5.3)

  96. 96

    Working with inverse functions (Screencast 6.5.4)

  97. 97

    Relations (Screencast 7.1.1)

  98. 98

    Directed graphs for relations (Screencast 7.1.2)

  99. 99

    Properties of relations (Screencast 7.2.1)

  100. 100

    Equivalence relations (Screencast 7.2.2)

  101. 101

    Equivalence classes (Screencast 7.3.1)

  102. 102

    Properties of equivalence classes (Screencast 7.3.2)

  103. 103

    Partitions (Screencast 7.3.3)

  104. 104

    The integers modulo n (Screencast 7.4.1)

  105. 105

    Modular arithmetic (Screencast 7.4.2)

  106. 106

    Divisibility by 3 test (Screencast 7.4.3)

  107. 107

    Affine ciphers (Screencast 7.4.4)

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