Math 180B Calendar, Winter 2018

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

Course Topics

Below is a list of the topics that will be covered in Math 180B, together with references to the relevant sections in the textbook by Pinsky and Karlin, and the textbook by Durrett. The material for the first three weeks of the course is not covered as thoroughly in these books as the material on Markov chains and Poisson processes. However, this material can be found in standard books on probability such as A First Course in Probability by Ross (see sections 6.4, 6.5, 7.4, 7.5, and 7.8)


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