Presentation is loading. Please wait.

Presentation is loading. Please wait.

CS 345 Lecture 1 Introduction and Math Review. CS 345 Instructor – Qiyam Tung TA – Sankar Veeramoni.

Similar presentations


Presentation on theme: "CS 345 Lecture 1 Introduction and Math Review. CS 345 Instructor – Qiyam Tung TA – Sankar Veeramoni."— Presentation transcript:

1 CS 345 Lecture 1 Introduction and Math Review

2 CS 345 Instructor – Qiyam Tung TA – Sankar Veeramoni

3 Administrivia Webpage – Syllabus –

4

5 Sets Union Intersection

6 Sets (cont’d) Membership Defining sets – Even numbers – Odd numbers

7 Sets Power set

8 Sequences Summation Products

9 Closed form equivalents Triangular numbers Sum of powers of 2

10 Logarithms Product Quotient

11 Logarithms (cont’d) Power Change of base

12 Logical Equivalences De Morgan’s Law – Propositions – Sets

13 10 minute break

14 Proofs Deductive Contrapositive Inductive

15 Proofs (cont’d) Contradiction pq~pp->q~p V q

16 Proofs (cont’d)

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

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

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

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

21 Inductive (example) Conjecture:

22 Inductive (cont’d)

23

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

25 Contradiction (example 1 cont’d)

26

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

28 Contradiction (cont’d)

29

30 Extra 1

31 Extra 2

32 Extra 3

33 Extra 4

34 Extra 5

35 CS 345 Lecture 1 Introduction and Math Review

36 CS 345 Instructor – Qiyam Tung TA – Sankar Veeramoni

37 Administrivia Webpage – Syllabus –

38

39 Sets Union Intersection

40 Sets (cont’d) Membership Defining sets – Even numbers – Odd numbers

41 Sets Power set

42 Sequences Summation Products

43 Closed form equivalents Triangular numbers Sum of powers of 2

44 Logarithms Product Quotient

45 Logarithms (cont’d) Power Change of base

46 Logical Equivalences De Morgan’s Law – Propositions – Sets

47 10 minute break

48 Proofs Deductive Contrapositive Inductive

49 Proofs (cont’d) Contradiction pq~pp->q~p V q

50 Proofs (cont’d)

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

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

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

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

55 Inductive (example) Conjecture:

56 Inductive (cont’d)

57

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

59 Contradiction (example 1 cont’d)

60

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

62 Contradiction (cont’d)

63

64 Extra 1

65 Extra 2

66 Extra 3

67 Extra 4

68 Extra 5


Download ppt "CS 345 Lecture 1 Introduction and Math Review. CS 345 Instructor – Qiyam Tung TA – Sankar Veeramoni."

Similar presentations


Ads by Google