## Math 20

### Discrete Probability

Syllabus
Schedule

We will cover most of Chapters 1-8 of the book. Here is a rough sketch of the material covered in each class.

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