Instructor: Professor Roman Vershynin     e-mail: vershynin at math dot ucdavis dot edu     Office hours: M 3:30-4:30 in 2218 MSB. No class: Monday, March 17. TA: Chengwu Shao     e-mail: cshao@math.ucdavis.edu     Office hours: T 1-2 in 3139 MSB. Meeting: MWF 10-10:50am in 1062 Bainer. Course description: Central Limit Theorem and martingales will be the focus of this course. We will first cover convergence in distribution, characteristic functions, and central limit theorems. We then proceed to conditional expectation and martingale theory.

Textbooks:

• Rick Durrett, Probability: Theory and Examples. Duxbury Press, Belmont, CA, 1996. xiii+503 pp. ISBN: 0-534-24318-5.
  The lectures will mostly follow Chapters 2 and 4 of this book. It is not necessary to buy the book though. A copy will be on reserve in Shields Library.
  
• Allan Gut, Probability: a Graduate Course. Springer, 2005. ISBN 978-0-387-22833-4.

Prerequisites: Undergraduate Real Analysis (MAT 125B) and the one quarter of graduate Probability Theory (MATH/STAT 235A). Familiarity with operations with complex numbers will be required (the first few weeks of undergraduate Complex Analysis). Graduate Analysis (MATH 201 A,B,C) would be a big plus.

Notes: Lecture notes typeset by Edward D. Kim and made public by his courtesy. Neither he nor R. Vershynin is accepting responsibility for their accuracy.

Assessment:

• Homework (30%), weekly. See below.
  
• Midterm (30%). Due February 13 before the class. Solutions.
  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 (40%). Solutions. Due Friday, March 21, at 12:00 noon in my mailbox (in MSB, first floor). Late exams will not be accepted. Only individual work on the exam.

Homework:
Assigned every Wednesday and collected next Wednesday before the class. You can discuss the problems with other students, but please write down the solutions individually. Late homework will not be accepted. One homework with the lowest score will be dropped.

• Homework 1. Due January 16. Solutions.
  
• Homework 2. Due January 23. Solutions.
  
• Homework 3. Due January 30. Solutions.
• Homework 4. Due February 6. Solutions.
  
• Midterm. See above in "Assessment".
• Homework 5. Due February 20. Solutions.
  
• Homework 6. Due February 27. Solutions.
• Homework 7. Due March 5. Solutions.
  
• Homework 8. Due  March 12. Solutions. The solution of Problem 3 is corrected. Independence is needed there.
  
• Final. See above in "Assessment".

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