Directed study - Spring 2020

Mentor: Wai-Tong (Louis) Fan

Office: Rawles Hall 225

Email: waifan@iu dot edu

Meetings: Friday 1:00-2:30pm and 4-4:30pm (tentative)

Course description This is an independent study with guidance, not a regular course. Students will learn essential techniques in probability and gain a bit experience about mathematical research.

Pre-requisites Students taking (or have taken) graduate level probability (M563 and M564 at IU). Basic knowledge about discrete-time Markov chains and continuous-time Markov chains (M463 and M464 at IU).

Expectation

• During each week, each student will present for about 30 mins and submit a type up in Latex.

  • The content of the presentation is student's choice. Mentor will offer directions and recommend options of reading materials.

  • The type up can be about exercises assigned by the mentor, but most importantly it helps students to organize and enhance their learning outcome in the longer term.

• At the end of the course, each student will submit a final report to the mentor for grading, and a final presentation in slides. The report is an enhancement and organization of the weekly type up.

• Students are expected to be proactive and hard working, with access to guidance in study. Students are expected to keep on improving based on feedback.

Evaluation Course grades will be based on regular meetings and assignments, as well as the written report.

Logistics (Spring 2019)

• Weekly group meetings: ~30 mins presentation for each student

• Dropbox: students will frequently type up their work (exercises assigned by the mentor) in Latex. Mentor will grade and give specific feedback to the write up.

• Students in the group are highly encouraged to meet among themselves to discuss and help each other.

Reading materials

• Reading assignments and exercises will be from a combination of books and articles.

• These materials are recommended by the mentor based on the student's background and interest.

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Other resource

The following website provides some quick info about basic concepts in probability:

https://www.probabilitycourse.com/courses.php

For example, see Chapter 7 (Limit theorems and convergence of random variables).