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CS 345 Lecture 1

CS 345 Lecture 1. Introduction and Math Review. CS 345. Instructor Qiyam Tung TA Sankar Veeramoni. Administrivia. Webpage http://www.cs.arizona.edu/classes/cs345/summer14/ Syllabus http://www.cs.arizona.edu/classes/cs345/summer14/syllabus.html. Sets. Union Intersection.

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CS 345 Lecture 1

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  1. CS 345Lecture 1 Introduction and Math Review

  2. CS 345 • Instructor • Qiyam Tung • TA • SankarVeeramoni

  3. Administrivia • Webpage • http://www.cs.arizona.edu/classes/cs345/summer14/ • Syllabus • http://www.cs.arizona.edu/classes/cs345/summer14/syllabus.html

  4. Sets • Union • Intersection

  5. Sets (cont’d) • Membership • Defining sets • Even numbers • Odd numbers

  6. Sets • Power set

  7. Sequences • Summation • Products

  8. Closed form equivalents • Triangular numbers • Sum of powers of 2

  9. Logarithms • Product • Quotient

  10. Logarithms (cont’d) • Power • Change of base

  11. Logical Equivalences • De Morgan’s Law • Propositions • Sets

  12. 10 minute break

  13. Proofs • Deductive • Contrapositive • Inductive

  14. Proofs (cont’d) • Contradiction

  15. Proofs (cont’d)

  16. Deduction (example) Conjecture: If x is even, then 5x is even

  17. Deduction (cont’d) Conjecture: If x is even, then 5x is even

  18. Contrapositive (example) Conjecture: If x^2 is odd, then x is odd

  19. Contrapositive(cont’d) Conjecture: If x^2 is odd, then x is odd

  20. Inductive (example) Conjecture:

  21. Inductive (cont’d)

  22. Inductive (cont’d)

  23. Contradiction (example 1) Conjecture: There are infinite prime numbers

  24. Contradiction (example 1 cont’d)

  25. Contradiction (example 1 cont’d)

  26. Contradiction (example) Conjecture: The square root of 2 is irrational

  27. Contradiction (cont’d)

  28. Contradiction (cont’d)

  29. Extra 1

  30. Extra 2

  31. Extra 3

  32. Extra 4

  33. Extra 5

  34. CS 345Lecture 1 Introduction and Math Review

  35. CS 345 • Instructor • Qiyam Tung • TA • SankarVeeramoni

  36. Administrivia • Webpage • http://www.cs.arizona.edu/classes/cs345/summer14/ • Syllabus • http://www.cs.arizona.edu/classes/cs345/summer14/syllabus.html

  37. Sets • Union • Intersection

  38. Sets (cont’d) • Membership • Defining sets • Even numbers • Odd numbers

  39. Sets • Power set

  40. Sequences • Summation • Products

  41. Closed form equivalents • Triangular numbers • Sum of powers of 2

  42. Logarithms • Product • Quotient

  43. Logarithms (cont’d) • Power • Change of base

  44. Logical Equivalences • De Morgan’s Law • Propositions • Sets

  45. 10 minute break

  46. Proofs • Deductive • Contrapositive • Inductive

  47. Proofs (cont’d) • Contradiction

  48. Proofs (cont’d)

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