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Discrete lecture 01
This document outlines the syllabus for a course on discrete mathematics. It discusses course policies, grading schemes, recommended textbooks, and provides an overview of topics covered in the course including logic and sets, elementary number theory, proofs, counting and combinatorics, graph theory, and trees. The overview section describes applications of these topics in computer science and technology.
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Discrete lecture 01
- 1.
- 2. Agenda Course policies Quick Overview 2
- 3. Grading Scheme Quize + Assignments 12 Midterm 18 Final 30 Total 60 3
- 4. Recommended Books “Discrete Mathematics with Application” by Susana. K.H. Rosen, Discrete Mathematics and its Applications, (5th Edition), McGraw Hill 1999. “Discrete Mathematical Structures” by B. Kalman Prentice Hall (1996). 4
- 5. Grading (cont’d) Exams/Quizzes can be from the following: Current lecture Material covered in any previous lecture Reading assignments From any assigned homework. 5
- 6. Academic Dishonesty Any form of cheating on exams/assignments/quizzes is subject to a penalty. Assignment Copy may lead to zero in all assignments. 6
- 7. Introduction Discrete mathematics describes processes that consist of a sequence of individual steps. This contrasts with calculus, which describes processes that change in a continuous fashion. Whereas the ideas of calculus were fundamental to the science and technology of the industrial revolution, the ideas of discrete mathematics underlie the science and technology of the computer age 7
- 8.
- 9. What Is DiscreteMathematics? Definition Discrete Mathematics Discrete Mathematics is a collection of mathematical topics that examine and use finite or countably infinite mathematical objects. 9 9
- 10. Quick Overview -Topics Logic and Sets Make notions you’re already used to from programming a little more rigorous (operators) Fundamental to all mathematical disciplines Useful for digital circuits, hardware design Elementary Number Theory Get to rediscover the old reliable number and find out some surprising facts Very useful in crypto-systems 10
- 11. Quick Overview -Topics Proofs (especially induction) If you want to debug a program beyond a doubt, prove that it’s bug-free Proof-theory has recently also been shown to be useful in discovering bugs in pre-production hardware Counting and Combinatorics Compute your odds of winning lottery Important for predicting how long certain computer program will take to finish Useful in designing algorithms 11 11
- 12. Quick Overview -Topics Graph Theory Many clever data-structures for organizing information and making programs highly efficient are based on graph theory Very useful in describing problems in Databases Operating Systems Networks EVERY CS DISCIPLINE!!!! Trees Data structures for organizing information and 12 making programs efficient
- 13. What is ofIntegers & Real Set Discrete Mathematics –6 Numbers – 5b CS-708 13
- 14.
- 15. Statement – 8a CS-708 15
- 16. Examples – 8b CS-708 16
- 17. Truth Values ofPropositions – 8c CS-708 17
- 18. Examples – 9a CS-708 18
- 19. Statements & TruthValues – 9b T T F F CS-708 19
- 20. Example – 10b CS-708 20
- 21. Understanding Statements – 11c CS-708 21
- 22. Example – 11b CS-708 22
- 23. Compound Statement –12a CS-708 23
- 24. Symbolic Representation – 13a CS-708 24
- 25. Logical Connectives –14a CS-708 25
- 26. Examples – 14b CS-708 26
- 27. Translating from Englishto Symbols – 15 CS-708 27
- 28. Translating from Englishto Symbols – 16a CS-708 28
- 29. Translating from Englishto Symbols – 16 CS-708 29
- 30. Translating from Englishto Symbols – 17a CS-708 30
- 31. Translating from Englishto Symbols – 17b CS-708 31
- 32. Negation – 19 CS-708 32
- 33. Truth Table for~p – 20 CS-708 33
- 34. Conjunction – 21 CS-708 34
- 35. Truth Table forp ^ q – 22 CS-708 35
- 36. Disjunction – 23 CS-708 36
- 37. Truth Table forp q – 15 CS-708 37
- 38.
- 39. Truth Table for~p^q - 2 CS-708 39
- 40. Truth Table for~p^q – 2a CS-708 40
- 41. Truth Table for~p^q – 2b CS-708 41
- 42. Truth Table for~p^q – 2c CS-708 42
- 43. ~p ^ (qv~ r) – (2 - 3a) CS-708 43
- 44. ~p ^ (qv~ r) – 2 - 3b CS-708 44
- 45. ~p ^ (qv~ r) – 2 - 3c CS-708 45
- 46. ~p ^ (qv~ r) – 2 - 3d CS-708 46
- 47. Truth Table for~p (p v~ q) – 2 - v 3e CS-708 47
- 48. Truth Table for(pvq) ^~ (p^q) – 2 - 4a CS-708 48
- 49. Truth Table for(pvq) ^~ (p^q) – 2 - 4c CS-708 49
- 50. Truth Table for(pvq) ^~ (p^q) – 2 - v v 4e CS-708 50
- 51. Truth Table for(pvq) ^~ (p^q) – 2 -4f CS-708 51
- 52. Exclusive OR –2 - 5 CS-708 52
- 53. Symbols for ExclusiveOR – 2 - 5a CS-708 53
- 54. Logical Equivalence –2 - 6 CS-708 54
- 55. Double Negation ~(~p)≡ p – 2 - 7 CS-708 55
- 56. Examples – 2- 12 CS-708 56
- 57. Example – 2- 17c CS-708 57
- 58. Example – 2- 17e CS-708 58
- 59. De Morgan’s Laws– 2 - 9 CS-708 59
- 60. De Morgan’s Laws– 2 - 9a CS-708 60
- 61. Proof – 2- 16 CS-708 61
- 62. Proof – 2- 16d CS-708 62
- 63. Application – 2- 10 CS-708 63
- 64. Exercise – 2- 19 CS-708 64
- 65. Tautology – 2- 21 CS-708 65
- 66. Example – 2- 21a CS-708 66
- 67. Contradiction – 2- 22 CS-708 67
- 68. Example – 2- 22a CS-708 68
- 69. Exercise – 2- 23 CS-708 69
- 70. Exercise – 2- 24 CS-708 70
- 71. Laws of Logic– 2 - 25 CS-708 71
- 72. Laws of Logic– 2 - 25a CS-708 72
- 73. Laws of Logic– 2 - 25b CS-708 73
- 74. Laws of Logic– 2 - 25c CS-708 74
- 75. Laws of Logic– 2 - 25d CS-708 75
- 76. Application - 1 CS-708 76
- 77.
- 78. Simplifying a Statement– 3 CS-708 78
- 79. Distributive Law inReverse – 4 CS-708 79
- 80.
- 81. Exercise - 5a CS-708 81