Math 563: Theory of Probability I
Meetings: 3:15 pm -- 4:30 pm, TuTh, SW103
Instructor: Chaojie Yuan
E-mail: yuan13@iu.edu
Office Hours: 10am - 11 am TuTh or by appointment, Rawles Hall 425
Course materials will be based on the book:
Patrick Billingsley, Probability and Measure, 3rd edition, Wiley, 1995.
Prerequisites: M463 and M511, the latter of which may be taken concurrently.
Course Content: Covers the analytical foundation of probability and offers a pathway towards research in probability and related fields. We will discuss selected topics in Chapter 1 - 5 from the textbook. Things to be discussed may include: Basic concepts of measure theory and integration, axiomatic foundations of probability theory, Independence, Law of Large Numbers, convergence of distribution functions and characteristic functions, central limit problem, modes of convergence of sequences of random variables, ergodic theorems, Markov chains, and stochastic processes.
Assignments:
There will be an assignment due approximately once per week. Homework will be due every Tuesday. Late submission will not be accepted.
Assignments must be uploaded to Canvas as a single PDF file by the due date. You are encouraged to use Latex to write your solutions. Please make sure that the PDF is easily legible.
It is not trivial to write solutions. You have to write enough to show that you understand the flow of ideas and that you are not jumping to unjustified conclusions. When you use materials we have covered in class, you may use it without proof, as long as you stated what you are using.
You are encouraged to work together on the assignments, but the final writeup must be your own.
Exams: There will be two exams during the term and one final exam. The final exam will be on 12:35-2:35pm Tues., Dec. 14. Two term Exams are most likely in class for a 75-minute period. More will be formalized during the first week of class. The intended Exam dates are listed below:
Exam I: 3:15 pm -- 4:30 pm Tuesday, Oct 5 (during class)
Exam II: 3:15 pm -- 4:30 pm Tuesday, Nov 9 (during class)
Final Exam: 12:35-2:35pm Tuesday, December 14, Location TBD.
Grading Policy:
Term Exams 1 and 2: 15% each for a total of 30%.
Final Exam: 30%
Assignments: 40%