Last updated: 12/10/2008.
Topics already covered:
1. Monday, 08/25:
Basic information about the course.
Section 2.1: Sets. Power sets.
2. Wednesday, 08/27:
Section 2.2: Set operations: intersection, union, and more.
De Morgan's laws.
3. Friday, 08/29:
Section 2.2: More on set operations. Characteristic functions and membership tables.
Section 2.3: Functions.
4. Wednesday, 09/03:
Section 2.3: Functions (continued).
Section 4.1: Mathematical induction.
Discussion on Homework 1.
5. Friday, 09/05:
Section 4.1: Mathematical induction (continued).
Quiz 1 - see the answer key.
6. Monday, 09/08:
Section 4.1: Mathematical induction (continued).
Section 4.2: Strong induction.
7. Wednesday, 09/10:
Section 4.2: Strong induction.
Discussion on Homework 2.
8. Friday, 09/12:
Section 5.1: Basics of counting.
Quiz 2 - see the answer key.
9. Monday, 09/15:
Section 5.1: Basics of counting. Inclusion-Exclusion Principle.
Section 5.2: The Pigeonhole Principle.
10. Wednesday, 09/17:
Section 5.2: The Pigeonhole Principle (continued).
Section 5.3: Permutations and combinations.
Discussion on Homework 3.
11. Friday, 09/19:
Section 5.3: Permutations and combinations.
Section 5.4: Binomial coefficients.
Quiz 3 - see the answer key.
12. Monday, 09/22:
Section 5.4: Binomial coefficients. The binomial theorem.
13. Wednesday, 09/24:
Section 5.4: Binomial coefficients. Some useful identities.
Section 5.5: Generalized permutations and combinations.
Discussion on Homework 4.
14. Friday, 09/26:
Section 5.5: Generalized permutations and combinations.
15. Monday, 09/29:
Section 5.5: Generalized permutations and combinations (conclusion).
Section 6.1: Discrete probability: an introduction.
16. Wednesday, 10/01:
Section 6.2: More on probability theory.
Discussion on Homework 5.
17. Friday, 10/03:
Section 6.2: More on probability theory.
18. Monday, 10/06:
Discussion on the midterm.
19. Wednesday, 10/08:
The midterm.
20. Friday, 10/10:
Brief review of the midterm.
Section 6.2: More on probability theory. Conditional probability. Independence.
21. Monday, 10/13:
Section 6.3: Bayes's Theorem.
Section 6.2: The notion of a random variable. Bernoulli trials.
22. Wednesday, 10/15:
Section 6.2: Bernoulli trials.
Section 6.4: Expected values.
Discussion on Homework 6.
23. Friday, 10/17:
Section 6.4: Expected values and their properties.
Binomial and geometric random variables.
24. Monday, 10/20:
Section 6.4: Properties of binomial and geometric random variables. Variance.
Independent random variables.
25. Wednesday, 10/22:
Section 6.4: Variance. Independent random variables.
Examples.
Discussion on Homework 7.
26. Friday, 10/24:
Section 6.4: Further examples. Covariance.
27. Monday, 10/27:
Section 7.1: Recurrence relations.
28. Wednesday, 10/29:
Section 7.2: Solving linear homogeneous recurrence relations.
29. Friday, 10/31:
Section 7.2: Solving linear homogeneous recurrence relations.
30. Monday, 11/03:
Section 7.2: Solving linear recurrence relations (homogeneous or otherwise).
Section 7.5: Inclusion-Exclusion.
31. Wednesday, 11/05:
Section 7.2: Solving linear non-homogeneous recurrence relations.
Section 7.5: Inclusion-Exclusion.
Discussion on Homework 9.
32. Friday, 11/07:
Section 7.5: Inclusion-Exclusion.
33. Monday, 11/10:
Section 7.5: Inclusion-Exclusion. Inclusion-Exclusion for probabilities
Section 7.6: Applications of Inclusion-Exclusion.
34. Wednesday, 11/12:
Section 7.6: Applications of Inclusion-Exclusion.
Derangements. The hat-check problem. The number of onto functions.
Discussion on Homework 10.
35. Friday, 11/14:
Section 7.6: Applications of Inclusion-Exclusion. The number of onto functions (continued).
Section 8.1: Relations.
36. Monday, 11/17:
Discussion on Midterm 2.
37. Wednesday, 11/19:
Midterm 2.
38. Friday, 11/21:
Brief review of the midterm.
Section 8.1: Relations.
39. Monday, 12/01:
Section 8.1: Relations. Reflexivity, symmetry, and transitivity. Examples.
Discussion on Homework 11.
40. Wednesday, 12/03:
Section 8.1: Relations. Operations on relations. Examples.
41. Friday, 12/05:
Section 8.3: Representing relations as matrices.
42. Monday, 12/08:
Section 8.3: Representing relations as matrices.
Discussion on Homework 12.
43. Wednesday, 12/10:
Review for the final.
Coming up:
44. Thursday, 12/11:
Review for the final (1-1:50, AH 145).