CS 345 Lecture 1: Introduction and Math Review

This content encompasses the introduction and mathematical review covered in CS 345 lecture 1, including topics such as sets, sequences, logarithms, logical equivalences, and proofs. It delves into sets theory, mathematical operations, deductive reasoning, and examples like the conjecture of even numbers. The images provided visualize concepts such as sets union, intersection, power sets, summation, and more.

• CS 345
• Math Review
• Sets Theory
• Deductive Reasoning
• Proofs

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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 (contd) 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 (contd) Power Change of base

12. Logical Equivalences De Morgan s Law Propositions Sets

13. 10 minute break

14. Proofs Deductive Contrapositive Inductive

15. Proofs (contd) Contradiction p q ~p p->q ~p V q

16. Proofs (contd)

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

18. Deduction (contd) Conjecture: If x is even, then 5x is even

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

20. Contrapositive (contd) Conjecture: If x^2 is odd, then x is odd

21. Inductive (example) Conjecture:

22. Inductive (contd)

23. Inductive (contd)

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

25. Contradiction (example 1 contd)

26. Contradiction (example 1 contd)

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

28. Contradiction (contd)

29. Contradiction (contd)

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 (contd) 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 (contd) Power Change of base

46. Logical Equivalences De Morgan s Law Propositions Sets

47. 10 minute break

48. Proofs Deductive Contrapositive Inductive

49. Proofs (contd) Contradiction p q ~p p->q ~p V q

50. Proofs (contd)

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