| Lecture Number |
Date |
Sections in Text |
Brief Description |
| 1 |
Monday, 3/30 |
1.1 - 1.3 |
Introduction, Set Operations |
| 2 |
Wednesday, 4/1 |
1.4, 2.1 - 2.3 |
Motivation for an Abstract Definition, Probability Measures |
| 3 |
Friday, 4/3 |
2.3 - 2.4 |
Examples of Probability Measures, Infinite Spaces, Independent Events |
| 4 |
Monday, 4/6 |
3.1 - 3.2 |
Counting, Sampling with Order |
| 5 |
Wednesday, 4/8 |
3.2 |
Sampling without Order, Recognizing An Overcount |
| 6 |
Friday, 4/10 |
3.3 - 3.4 |
More Counting!, Binomial Coefficients |
| 7 |
Monday, 4/13 |
3.4 |
Even More Counting!, Inclusion-Exclusion (not in book) |
| 8 |
Wednesday, 4/15 |
- |
Inclusion-Exclusion Examples (Hat-Check Problem, Surjections), Biased Coins |
| 9 |
Friday, 4/17 |
4.1 - 4.3 |
Random Variables, Expected Value |
| 10 |
Monday, 4/20 |
- |
First Exam |
| 11 |
Wednesday, 4/22 |
4.4 |
Calculating Expected Values, Random Variables on Infinite Spaces |
| 12 |
Friday, 4/24 |
4.5 |
Continuous Random Variables, Density Functions |
| 13 |
Monday, 4/27 |
5.1 |
Conditional Probability, Memoryless Property, Craps |
| 14 |
Wednesday, 4/29 |
5.2 |
Conditional Probability Formulas, Bayes' Theorem |
| 15 |
Friday, 5/1 |
5.3, 5.5 |
Urn Models, Independence of Random Varibles |
| 16 |
Monday, 5/4 |
5.5, 6.1 |
Independence, Expected Value of the Sum of Random Variables |
| 17 |
Wednesday, 5/6 |
6.1, 6.3 |
Coupon Collector Problem, Variance |
| 18 |
Friday, 5/8 |
6.3 |
Properties of E(X) and V(X), Calculating Examples |
| 19 |
Monday, 5/11 |
7.1 |
Poisson Distribution |
| 20 |
Wednesday, 5/13 |
7.1, 7.3 |
Expected Value and Variance of the Poisson Distribution, Stirling's Approximation |
| 21 |
Friday, 5/15 |
- |
Second Exam |
| 22 |
Monday, 5/18 |
7.3 |
Normal Distribution, Approximating the Binomial Distribution |
| 23 |
Wednesday, 5/20 |
7.5, 7.6 |
Central Limit Theorem, Law of Large Numbers |
| 24 |
Friday, 5/22 |
- |
Markov Chains |
| - |
Monday, 5/25 |
- |
No Class (Memorial Day) |
| 25 |
Wednesday, 5/27 |
- |
Regular Markov Chains |
| 26 |
Friday, 5/29 |
- |
Absorbing Markov Chains |
| 27 |
Monday, 6/1 |
- |
Review |