Math 561: Theory of Probability I (Spring 2016)
Goals and topics
This is the first half of the basic graduate course in probability theory. The goal of this course is to understand the basic tools and language of modern probability theory. We will start with the basic concepts of probability theory: random variables, distributions, expectations, variances, independence and convergence of random variables. Then we will cover the following topics: (1) the basic limit theorems (the law of large numbers, the central limit theorem and the large deviation principle); (2) martingales and their applications. If time allows, we will give a brief introduction to Brownian motion.
Logistics
| Instructor | Partha Dey |
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| Contact | By email psdey@illinois.edu with subject line: "Math 561:" |
| Class | TR 11:00am -12:20pm in 7 Illini Hall |
| Website | learn.illinois.edu |
| Office | 341A Illini Hall |
| Office Hrs | Wednesdays and Thursdays 1pm-1:50pm or by appointment made via e-mail |
| TA | Qu Lu, Office hours and place: TBA. |
| Textbook | Richard Durrett: Probability: Theory and Examples (Free Online edition v4.1). This is the single most relevant text for the course. The style is deliberately concise. Many of the homework problems are from there. The 4th version is published by Cambridge University Press, 2010 (ISBN-13: 978-0521765398). It is okay to use another edition for studying. Some other relevent books: P. Billingsley Probability and Measure (3rd Edition). Chapters 1-30 contain a more careful and detailed treatment of some of the topics of this semester, in particular the measure-theory background. Recommended for students who have not done measure theory. R. Leadbetter et al A Basic Course in Measure and Probability: Theory for Applications is a new book giving a careful treatment of the measure-theory background. |
| Prerequisite | The prerequisite for Math 561 is Math 540 - Real Analysis I. We will review measure theory topics as needed. Math 541 is nice to have, but not necessary. |
Exams and Grades
| Homework Policy | Solving a lot of problems is an extremely important part of learning probability. Homework will be assigned weekly on Thursdays, to be handed in at the start of next Tuesday lectures. You can collect the graded homework from the TA during his office hour. You are encouraged to work together on the homework, but I ask that you write up your own solutions and turn them in separately. Late homework will not be graded. If for some reason you've done a homework but can't turn it in in class, you should turn it in to my mailbox in 250 AH before class, or ask a classmate to turn it in for you, or send it via email before class. Because of this strict policy on late homework, I will drop your two lowest scores. Please talk to the instructor in cases of emergency. |
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| Homework Philosophy | Mathematics is something that you learn by doing: doing homework problems, and explaining them to each other. If, after thinking and talking about homework problems, you get stuck or have questions, I will be happy to help. You'll have a high probability of doing well in this class by combining all of these resources: classes, textbook, homework, office hours, and discussions with classmates. | ||||||||
| Scribing | Every day one student will be assigned to scribe the lecture note in LaTeX using the template file. | ||||||||
| Exams | There will be one in-class midterm exam on Thursday, March 3. It will be technically comprehensive, but emphasizing recent material up to the most recent graded and returned homework assignment. Exam problems will be similar to homework problems. The final take home exam will cover the most important topics of the whole course and will be assigned on the last day of the class. |
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| Exam Policy | Make-up exams will be given only for medical or other serious reasons. If you discover that you cannot be at an exam, please let me know as soon as possible, so that we can make other arrangements. You must work completely on your own during exams. I make my exams fair and similar to homework, so as long as you use the resources provided, you should do fine. If you have difficulties of any kind or fall behind in the course, please come talk to me as soon as possible. | ||||||||
| Grading Policy | Grades will be computed by a weighted average:
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Homeworks (updated weekly here)
- Teacher: Partha Dey