Download presentation

Presentation is loading. Please wait.

Published byKelton Bleckley Modified over 4 years ago

1
CS 345 Lecture 1 Introduction and Math Review

2
CS 345 Instructor – Qiyam Tung TA – Sankar Veeramoni

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

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)

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

25
Contradiction (example 1 cont’d)

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

28
Contradiction (cont’d)

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 – http://www.cs.arizona.edu/classes/cs345/summer14/ Syllabus – http://www.cs.arizona.edu/classes/cs345/summer14/syllabus.html

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)

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

59
Contradiction (example 1 cont’d)

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

62
Contradiction (cont’d)

64
Extra 1

65
Extra 2

66
Extra 3

67
Extra 4

68
Extra 5

Similar presentations

Presentation is loading. Please wait....

OK

MATH 224 – Discrete Mathematics

MATH 224 – Discrete Mathematics

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google