Week | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
1 |
Jan 8
Topic 0 |
Jan 9 | Jan 10
Topic 1 |
Jan 11 | Jan 12
Topic 2 Homework 1 due |
2 |
Jan 15
No class |
Jan 16 | Jan 17
Topic 3 Homework 2 due |
Jan 18 | Jan 19
Topics 3-4 |
3 |
Jan 22
Topics 4-5 |
Jan 23 | Jan 24
Topics 5-6 Homework 3 due |
Jan 25 | Jan 26
Topic 6 |
4 |
Jan 29
Topic 7 |
Jan 30 | Jan 31
Topic 8 Homework 4 due |
Feb 1 | Feb 2
Exam 1 |
5 |
Feb 5
Topic 9 |
Feb 6 | Feb 7
Topics 9-10 Homework 5 due |
Feb 8 | Feb 9
Topic 10 |
6 |
Feb 12
Topic 11 |
Feb 13 | Feb 14
Topic 11 Homework 6 due |
Feb 15 | Feb 16
Topic 12 |
7 |
Feb 19
No class |
Feb 20 | Feb 21
Topic 12 Homework 7 due |
Feb 22 | Feb 23
Topic 13 |
8 |
Feb 26
Topic 13 |
Feb 27 | Feb 28
Topic 14 Homework 8 due |
Mar 1 | Mar 2
Exam 2 |
9 |
Mar 5
Topics 14-15 |
Mar 6 | Mar 7
Topic 16 |
Mar 8 | Mar 9
Topic 16 Homework 9 due |
10 |
Mar 12
Topic 17 |
Mar 13 | Mar 14
Topic 18 |
Mar 15 | Mar 16
Topic 18 Homework 10 due |
11 | Mar 19 | Mar 20 | Mar 21
Final Exam 3:00-6:00 PM |
Mar 22 | Mar 23 |
Topic | Pinsky-Karlin | Durrett | |
0 | Review of Math 180A | 1.2-1.5 | Appendix |
1 | Conditional distributions: discrete case | 2.1-2.2 | N/A |
2 | Conditional distributions: continuous case | 2.4 | N/A |
3 | Conditional expectation | 2.3 | N/A |
4 | Covariance and correlation | N/A | N/A |
5 | Variance of sums | N/A | N/A |
6 | Multivariate normal distribution | N/A | N/A |
7 | Introduction to Markov chains | 3.1, 3.3 | 1.1 |
8 | Transition matrices | 3.2 | 1.2 |
9 | First-step conditioning and hitting probabilities | 3.4-3.6 | 1.9 |
10 | Mean hitting times | 3.4-3.6 | 1.10 |
11 | Recurrence and transience | 4.3 | 1.3 |
12 | Stationary distributions | 4.1-4.2 | 1.4-1.5 |
13 | Long-run behavior of Markov chains | 4.4 | 1.6-1.8, 1.11 |
14 | Branching processes | 3.8-3.9 | 1.11 |
15 | Poisson processes: definition and basic properties | 5.1-5.2 | 2.2 |
16 | Poisson processes: times between events | 5.3-5.4 | 2.2 |
17 | Superposition and thinning of Poisson processes | N/A | 2.2.2 |
18 | Inhomogeneous and spatial Poisson processes | 5.5 | 2.3 |