This is a graduate probability course. The textbook is "Probability: Theory and Examples", 3ed, by Richard Durrett. The reference book is "Probability" by Davar Khoshnevisan. Topics to be covered are: Measure theoretic background; Random variables, expectation and independence; Weak Law of Large Numbers; Borel Cantelli Lemmas; Strong Law of Large Numbers; Weak Convergence; Convergence in distribution; Characteristic Functions; Central Limit Theorems for i.i.d. sequences and triangular arrays; Poisson convergence; Martingale;

Office Hours on Monday, Wednesday 12-2 pm at Brink 322, or by appointment fuchang@uidaho.edu

Homework (60%) Roughly speaking, I will assign two homework problems for each leacutre. The first problem may contain several small problems, but are all easy enough. The purpose of the first problem is to help you understanding the basic concepts. The second problem is challenging and requires some deeper understanding. You may however ask me for hint if needed. These problems will be grouped into seven assignments, and are due on the dates specified below. The solutions need to be neatly written, or typed using latex in professional standards. Please double space the text, and leave enough space between problems for me to write comments/corrections/remarks.

Presentation (20%) Each student will be asked to choose a topic, and give a 30-45-minutes presentation on that topic. I will provide you the material for the topic you choose, and you will have at least one week to prepare for your presentation.

Final Exam (20%) There will be a comprehensive final exam at the end of the semester. You may choose to do a (harder) take home final exam instead. You may also choose to do both; in that case, I will use the better score to calculate your finl grade.

Grades are determined by: A=[90,100]; B=[80,90); C=[70,80); D=[60,70); F=[0,60).

Tentative Schedule