Course: MATH 171, Stochastic Processes, Fall 2016
Prerequisite: Math 33A and Math 170A (or Statistics 100A). It is helpful, though not required, to take Math 170B before this course or concurrently with this course.
Course Content: A stochastic process is a collection of random variables. These random variables are often indexed by time, and the random variables are often related to each other by the evolution of some physical procedure. Stochastic processes can then model random phenomena that depend on time. We will study Markov chains, Martingales, Poisson Processes, Renewal Processes, and Brownian Motion
Last update: 15 October 2016

Instructor: Steven Heilman, heilman(@-symbol)
Office Hours: Fridays, 10AM-12PM, MS 5634
Lecture Meeting Time/Location: Monday, Wednesday and Friday, 9AM-950AM, MS 5147
TA: Fangbo Zhang, fb.zhangsjtu(@-symbol)
TA Office Hours: Tuesdays 2PM-3PM, MS 6153
Discussion Session Meeting Time/Location: Thursdays, 9AM-950AM, TBD
Required Textbook: Rick Durrett, Essentials of Stochastic Processes, 2nd edition. (The book is freely available online).
Other Textbooks (not required): Markov Chains and Mixing Times, Levin, Peres and Wilmer. (This book is freely available online; see also the errata.) This book is a bit more comprehensive and a bit more advanced in the topics that are covered, but I still highly recommend it. It also focuses more on Markov Chains.
First Midterm: Friday, October 21, 9AM-950AM, PAB 1434A
Second Midterm: Monday, November 14, 9AM-950AM, Public Affairs 2270
Final Exam: Thursday, December 8, 8AM-11AM, Boelter 5440
Other Resources: An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Email Policy:

Exam Procedures: Students must bring their UCLA ID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the UCLA Student Guide to Academic Integrity. If you are an OSD student, I would encourage you to discuss with me ways that I can improve your learning experience; I would also encourage you to contact the OSD office to confirm your exam arrangements at the beginning of the quarter.
Exam Resources: Here is a page containing practice exams for another 171 class. Here is a page containing practice exams for a class similar to a 171 class. Here is a page containing practice exams for a class similar to a 171 class. Occasionally these exams will cover slightly different material than this class, or the material will be in a slightly different order, but generally, the concepts should be close if not identical.

Homework Policy: Grading Policy:

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
0 Sep 22: First discussion section. No homework due Sep 23: A.1, A.2, Review of Probability
1 Sep 26: A.3, Review; Law of Large Numbers Sep 28: Central Limit Theorem Sep 29: Homework 0 (ungraded) Sep 30: 1.1, Markov Chains
2 Oct 3: 1.1, Examples of Markov Chains Oct 5: 1.3, Classification of States Oct 6: Homework 1 due Oct 7: 1.4, Stationary Distributions
3 Oct 10: 1.5, Limiting Behavior Oct 12: 1.7, Proofs of Limiting Behavior Oct 13: Homework 2 due Oct 14: 1.7, Proofs of Limiting Behavior
4 Oct 17: 1.10, Infinite State Spaces Oct 19: 5.1, Conditional Expectation Oct 20: No homework due Oct 21: Midterm #1
5 Oct 24: 5.2, Martingale Examples Oct 26: 5.3, Gambling Strategies Oct 27: Homework 3 due Oct 28: 5.4, Applications
6 Oct 31: 2.1, Exponential Distribution Nov 2: 2.2, Poisson Process Nov 3: Homework 4 due Nov 4: 2.2, Poisson Process
7 Nov 7: 2.2, Poisson Process Nov 9: 2.3, Compound Poisson Process Nov 10: Homework 5 due Nov 11: No class
8 Nov 14: Midterm #2 Nov 16: 2.4, Transformations Nov 17: Homework 6 due Nov 18: 2.4, Transformations
9 Nov 21: 3.1, Laws of Large Numbers Nov 23: Homework 7 due. 3.2, Queueing Theory Nov 24: No class Nov 25: No class
10 Nov 28: 6.6, Brownian Motion Nov 30: 6.6, Brownian Motion Dec 1: Homework 8 due Dec 2: Review of course

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