Math 365: Stochastic processes

Instructor	Tanya Leise
Email	tleise at amherst dot edu
Phone	542-5411
Office	SMudd 503
Office hours	Regular hours: Mon 10-10:50am, 1-2pm Tues 11am-1pm Wed 10-10:50am, 1:30-2:30pm Thurs 10-11:20am Fri 10-10:50am, 1:30-2:30pm Feel free to drop in whenever my door is open, or make an appointment
Text	Introduction to Stochastic Processes, 2nd Edition, Gregory Lawler

Course goals:

• Study the theory underlying both discrete-time and continuous-time stochastic processes.
• Learn how to use R and RStudio to simulate the stochastic processes as we learn about them.

Course Topics:

• Markov chains (finite, countable, and continuous-time flavors)
• Poisson processes
• Branching processes
• Martingales
• Brownian motion
• Stochastic integration

Attendance: Class will be chock full of material and activities -- cooperative learning is more effective and more fun than struggling through material on your own. If you do miss a class, it is your responsibility to obtain the material that you missed and to get your assignments handed in to me.

Questions: If you have a question during lecture, please raise your hand and ask it right away. Chances are that other students are wondering the same thing. If a question arises later, feel free to visit my office and we'll work through sample problems until you are comfortable with the mathematics. Always feel free to ask me to slow down as well.

Grading: Your course grade will be based on class participation (15%), two midterm exams (30%), a take-home exam at the end of the semester (20%), regular problem sets and labs (20%), and a final project (15%).

Intellectual Responsibility

• Exams. Your work must be entirely your own, so please follow the guidelines of the honor code. Unless I explicitly allow other aids, you are only allowed whatever implements you need to read and write (no notes or calculators).  Please turn off your cell phone in kindness to your fellow test-takers during in-class exams.
• Homework and other assignments. You may study with other students following these guidelines:

1. If you worked with or received help from any source other than me, you should put a note on the front of your homework saying, "I worked with <names>." Make sure your name stands out as the author of your homework.
2. Working together does not mean that one of you does the first half of the homework set and the other does the second. Everyone should work on every problem.
3. Each student must hand in his or her own problem set. You may not hand in a single packet as the work of multiple people. You must do your own write-up of each problem.
4. Do not copy someone else's solution—you will not learn anything and it is plagiarism. You may discuss problems with others, but then you must be able to work out the solution on your own again and write it down yourself.
5. Sending or receiving a copy of a file that contains student work violates the honor code and will be treated as plagiarism. You may talk with others about strategies for solving a problem in R, but please do not share files.
6. If you are unsure what agrees or does not agree with the precepts of intellectual responsibility in this course, feel free to talk to me about it.

Homework Guidelines

• All problem sets are due at THE START OF CLASS. Late homework will receive half credit for homework handed in after start of class but within 2 class days (e.g., homework due Monday will get half-credit if handed in after the start of class on Monday through Wednesday start of class, and will not accepted after that).
• If you are unable to attend class due to illness or an emergency, let me know as soon as you can and we will work out an appropriate schedule for assignments.
• Your name should be written on all sheets handed in.
• Problem solutions must be written out in the order they were assigned.
• Multiple pages must be stapled or clipped together.
• Homework should be neat. No dog ears. No messy edges from notebook paper.
• Where appropriate, please box or highlight final answers. In general, try to make your answers readable and easy to find. Always keep the grader happy!
• As mentioned elsewhere, no copying!

Course Resources:

Don't struggle alone! You have many options for getting help with this course.

• Me. Feel free to come to my office hours, make an appointment by email or phone, or simply try stopping by my office—you are welcome whenever my door is open. If you have some anxiety about taking math exams, please come see me and we can work together on building your math confidence.

• Homework. Mathematics is learned ACTIVELY, not passively. You can't absorb math through listening or reading, even if you think you understand it all.
• Textbook. I won't go over everything that is contained in the text, and I will try to avoid doing the same examples. Hence your textbook in an important independent source of information and you should read it!
• Lecture notes. Reviewing the notes you take in lecture will give you a chance to see the material again after you have had some time to assimilate it.
• Your classmates. Discussing math with others can help you think through the concepts. Explaining an idea you already understand will deepen your comprehension, and for the concepts that you don't understand well, the explanation of a peer may be more helpful than mine or the textbook's.
• Library and online resources. There are a variety of books covering probability and stochastic processes in the library that you may find it helpful to peruse, which can be very helpful if the textbook doesn't explain a topic in a way that makes sense to you or if you want to see some further examples. There are also many online resources explaining concepts and giving further examples that are easily found by searching for key terms.

To the Math 365 Homework Schedule