Math/Stat 632 Introduction to Stochastic Processes

Spring 2016 Lecture 004

This is the course homepage that also serves as the syllabus for the course.

I will use the class email list to send out corrections, announcements, please check your wisc.edu email from time to time.

Textbook:

Rick Durrett: Essentials of Stochastic Processes. Available on Prof. Durrett's website. Note that you do not need to purchase a book. We will cover most of the topics in the text.

Course description:

The course consists of Chapters 1-4 from Durrett's book: discrete time Markov chains, Poisson processes, renewal processes, and continuous time Markov chains. I also hope to cover at least a portion of chapter 5, martingales. Time permitting, we may cover some extra topics.

Prerequisites:

Calculus, linear algebra, and an introduction to probability (at the level of Math 431) are sufficient. However, the material in this class is sophisticated, so a degree of intellectual maturity and a willingness to work hard are required. For this reason some 500-level work in mathematics is recommended for background, preferably in analysis (521). Students must have enough mathematical maturity to be comfortable following proofs in the textbook and in the lectures, and must also be able to construct proofs of their own on homeworks and tests.

Exams:

There will be two midterm examinations and a final. Make sure to reserve those dates on your calendar.

• Midterm exam 1: Wed, Feb 24

• Midterm exam 2: Wed, April 13

• Final exam: Tuesday, May 10, 2:45PM - 4:45PM

No calculators, cell phones, or other gadgets will be permitted in exams and quizzes, only pencil and paper.

Piazza

We will be using Piazza for class discussion. The system is catered to getting you help fast and efficiently from classmates. I encourage you to post your questions on Piazza. The students (and instructors) from the other three sections of 431 will have access to the same page, and can answer questions. If you have any problems or feedback for the developers, email team@piazza.com.

Evaluation

Course grades will be based on homework and quizzes (20%), two midterm exams (2x20%), and a comprehensive final exam (40%).

The final grades will be determined according to the following scale:

A: [100,89), AB: [89,87), B: [87,76), BC: [76,74), C: [74,62), D: [62,50), F: [50,0].

There will be no curving in the class, but the instructor reserves the right to modify the final grade lines.

Learn@UW

We will use the Learn@UW website of the course to post homework assignments and other documents.

Homework

Homework assignments will be posted on the Learn@UW site of the course. It is your responsibility to get this information. Homework will be due Fridays at the beginning of the class.

• No late homework will be accepted. The lowest score will be dropped.

• Homework is collected at the beginning of the class on the due date.

• You can also submit your solution to the grader directly, but it has to arrive by 12:05am on the due date.

Other Instructions for homework

• • Observe rules of academic integrity. Handing in plagiarized work, whether copied from a fellow student or off the web, is not acceptable. Plagiarism cases will lead to sanctions.

  • Working in groups on homework assignments is strongly encouraged; however, every student must write their own assignments.

  • Organize your work neatly. Use proper English. Write in complete English or mathematical sentences. Answers should be simplified as much as possible. If the answer is a simple fraction or expression, a decimal answers from a calculator is not necessary. For some exercises you will need a calculator to get the final answer.

  • Answers to some exercises are in the back of the book, so answers alone carry no credit. It's all in the reasoning you write down.

  • Put problems in the correct order and staple your pages together.

  • Do not use paper torn out of a binder.

  • Be neat. There should not be text crossed out.

  • Recopy your problems. Do not hand in your rough draft or first attempt.

  • Papers that are messy, disorganized or unreadable cannot be graded.

  • I strongly encourage you to type up your solutions (perhaps using Latex)

Quizzes

No make-up quizzes will be given. The lowest quiz score will be dropped.

Quizzes will be given at the beginning of Wednesday lectures.

The Math Club provides interesting lectures and other math-related events. Everybody is welcome.