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 Shao     e-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:  

• Interpretation of set theory in probability theory

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