Probability
Theory
(MATH/STAT 235A, Fall 2007)

Instructor: Roman
Vershynin e-mail: vershynin at math dot ucdavis dot edu Office hours: M 2-3, F 1-2 in 2218 MSB. No office
hours: the week of December 3.
Extra office hours: Monday, December
10, 2-3.
TA: Chengwu Shaoe-mail: cshao@math.ucdavis.edu Office hours: T 2-3 in 3139 MSB. Meeting: MWF 10-10:50am in 1062 Bainer. Wednesday, December 5 is the last day of this class. Course description: This is the graduate probability sequence, A in Fall and B in Winter. Basics of measure theory will be covered at a reasonably fast pace. Note that we offer a separate measure theory course MATH 206 in alternate years. The core content of the course (A and B): fundamentals on random variables and convergence, laws of large numbers and central limit theorems. If time permits, martingales will also be included. Note that Markov Chains course MATH 280 will be given this Fall by Prof. Morris. |

Textbook:
Allan Gut, Probability: a Graduate
Course. Springer, 2005. ISBN 978-0-387-22833-4.

Prerequisites:
Undergraduate Real Analysis (MAT 125B) and undergraduate Probability
Theory (MATH 131 or STA 131A). Graduate Analysis (MATH 201 A,B,C) would
be
a big plus.

Notes:

Assessment:

- Quiz. Solutions.

- Homework (50%), weekly. See
below.

- Midterm
(25%). Solutions. Due November 7
before the class. Late midterm will not be
accepted. Under valid
and documented circumstances (medical,
jury duty, and such) midterm's weight will be added to final's weight.

- Final
(25%). Solutions. Due December 13 by
NOON. Please put your work in my department
mailbox. Late exams will not be accepted.

Homework:

Assigned every
Wednesday
and collected next Wednesday before the class. The problems are from
the textbook, unless otherwise stated. You can discuss the problems
with other students, but please write down the solutions individually.
Late homework: 10% penalty is imposed on the homework turned in on
Wednesdsay after the class, 20% penalty on Friday until 5pm, 100%
penalty after.

- Homework 1. Due October 10. Solutions. Chapter 1, Section 6, Problems 2, 3, 4, 7, 9 (first two inequalities).
- Homework 2. Due October 17. Solutions. Chapter 1, Section 6, Problems 5, 11, 12, 13. In Problem 11, you can use the inclusion-exclusion formula without proof. Alternatively, you can use the simple fact (to proved on Friday) that whenever events are independent, then their complements are also independent.
- Homework 3. Due October 24. Solutions.
- Homework 4. Due October 31. Solutions.

- Midterm: see above, under "Assessment".
- Homework 5. Due November 14. Solutions.
- Homework 6. Due November 28. Solutions.
- Final: see above, under "Assessment".

Web:
www.math.ucdavis.edu/~vershynin/teaching/2007-08/235A/235A.html