Course: MATH 171, Stochastic Processes, Winter 2017
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: 22 March 2017

Instructor: Steven Heilman, heilman(@-symbol)ucla.edu
Office Hours: Fridays, 830AM-1030AM, MS 5634
Lecture Meeting Time/Location: Monday, Wednesday and Friday, 11AM-1150AM, MS 5117
TA:Yuming Zhang, yzhangpaul(@-symbol)math.ucla.edu
TA Office Hours: Tuesdays 10AM-11AM, Fridays 2PM-3PM, MS 6153
Discussion Session Meeting Time/Location: Tuesdays, 11AM-1150AM, MS 5117
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, February 3, 11AM-1150AM, Perloff 1102
Second Midterm: Monday, February 27, 11AM-1150AM, Royce 190
Final Exam: Friday, March 24, 3PM-6PM, MS 5117
Other Resources: An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Email Policy:

• My email address for this course is heilman(@-symbol)ucla.edu
• It is your responsibility to make sure you are receiving emails from heilman(@-symbol)ucla.edu , and they are not being sent to your spam folder.
• Do NOT email me with questions that can be answered from the syllabus.

• Late homework is not accepted.
• If you still want to turn in late homework, then the number of minutes late, divided by ten, will be deducted from the score. (The time estimate is not guaranteed to be accurate.)
• The lowest two homework scores will be dropped. This policy is meant to account for illnesses, emergencies, etc.
• Do not submit homework via email.
• There will be 8 homework assignments, assigned weekly on Tuesday and turned in at the beginning of the discussion section on the following Tuesday.
• A random subset of the homework problems will be graded each week. However, it is strongly recommended that you try to complete the entire homework assignment.
• You may use whatever resources you want to do the homework, including computers, textbooks, friends, the TA, etc. However, I would discourage any over-reliance on search technology such as Google, since its overuse could degrade your learning experience. By the end of the quarter, you should be able to do the entire homework on your own, without any external help..
• All homework assignments must be written by you, i.e. you cannot copy someone else's solution verbatim.
• Homework solutions will be posted on Friday after the homework is turned in.

• The final grade is weighted as the larger of the following two schemes. Scheme 1: homework (15%), the first midterm (20%), the second midterm (25%), and the final (40%). Scheme 2: homework (15%), largest midterm grade (35%), final (50%). The grade for the semester will be curved. However, anyone who exceeds my expectations in the class by showing A-level performance on the exams and homeworks will receive an A for the class.
• We will use the MyUCLA gradebook.
• If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
• You must attend the final exam to pass the course.

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

Advice on succeeding in a math class:

• Review the relevant course material before you come to lecture. Consider reviewing course material a week or two before the semester starts.
• When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
• Come to class with questions, so you can get more out of the lecture. Also, finish your homework at least two days before it is due, to alleviate deadline stress.
• Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes. Also, consider typesetting your homework. Here is a template .tex file if you want to get started typesetting.
• If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

• HW0 HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 (Solutions are on CCLE)

• Exam 1 Solution Exam 2 Solution Final Solution

• Math 171 Lecture Notes