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Discrete Mathematics

Discrete Mathematics . Why Are You Studying this Course. This course will develop your mathematical maturity Discrete mathematics provides the mathematical foundations for many computer science courses Data Structures Algorithm Analysis and Design

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Discrete Mathematics

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  1. Discrete Mathematics

  2. Why Are You Studying this Course • This course will develop your mathematical maturity • Discrete mathematics provides the mathematical foundations for many computer science courses • Data Structures • Algorithm Analysis and Design • Database Management Systems and Database Theory • Compiler Construction • Computer Security • Digital Logic Design • Artificial Intelligence

  3. Course Information • Syllabus: • Logic • Sets • Relations • Functions. • Combinatory: counting, permutations, combinations. • Recursion • Probibility • Mathematical Induction • Graph theory: Graphs and Trees

  4. Course Information • Textbook: • Discrete Mathematics and its Applications by Kenneth. H. Rosen, 7th Edition • Discrete Mathematics with Application” by Susana. 4th edition, 2010

  5. How will you master Discrete Structures • “I hear and I forget. I see and I remember. I do and understand” - Chinese proverb

  6. Terminology Discrete - Composed of distinct OR separable/unconnected parts. (Opposite of continuous.) Structures- Objects built up from simpler objects according to some definite pattern.

  7. Introduction • What is discrete mathematics? • Part of mathematics devoted to the study of discrete objects. • Discrete means consisting of distinct or unconnected elements. • As computers are discrete object operating one jumpy, discontinuous step at a time, Discrete Math is the right framework for describing precisely Computer Science concepts.

  8. Introduction • What is discrete mathematics? • In computer science we usually deal with finite, discrete objects. • For example, we cannot store a real number (infinite precision) in a computer but can only store bits (finite precisions). • Definition • Discrete Mathematics is a collection of mathematical topics that examine and use finite or countably infinite mathematical objects.

  9. Problems Solved Using DM

  10. Logic – 7

  11. Statement – 8a

  12. Examples – 8b

  13. Truth Values of Propositions – 8c

  14. Examples – 9a

  15. Statements & Truth Values – 9b T T F F

  16. Example – 10b

  17. Understanding Statements – 11c

  18. Example – 11b

  19. Compound Statement – 12a

  20. Symbolic Representation – 13a

  21. Logical Connectives – 14a

  22. Examples – 14b

  23. Translating from English to Symbols – 15

  24. Translating from English to Symbols – 16a

  25. Translating from English to Symbols – 16

  26. Translating from English to Symbols – 17a

  27. Translating from English to Symbols – 17b

  28. Negation – 19

  29. Truth Table for ~p – 20

  30. Conjunction – 21

  31. Truth Table for p ^ q – 22

  32. Disjunction – 23

  33. Truth Table for p q – 15

  34. Truth Table

  35. Advanced versions of many Internet search engines allow you to use some form of and, or and not to refine the search process. • Imagine that you want to find web pages about careers in mathematics or computer science but not finance or marketing. • With a search engine that uses quotation marks to enclose exact phrases and expresses and as AND, or as OR, and not as NOT, you would write • Careers AND (mathematics OR "computer science") • AND NOT (finance OR marketing).

  36. Truth Table for ~p^q - 2

  37. Truth Table for ~p^q – 2a

  38. Truth Table for ~p^q – 2b

  39. Truth Table for ~p^q – 2c

  40. ~p ^ (q v~ r) – (2 - 3a)

  41. ~p ^ (q v~ r) – 2 - 3b

  42. ~p ^ (q v~ r) – 2 - 3c

  43. ~p ^ (q v~ r) – 2 - 3d

  44. Truth Table for ~p (p v~ q) – 2 - 3e v

  45. Truth Table for (pvq) ^~ (p^q) – 2 - 4a

  46. Truth Table for (pvq) ^~ (p^q) – 2 - 4c

  47. Truth Table for (pvq) ^~ (p^q) – 2 - 4e v v

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