280 Lecture Notes
Math 280 -- Probability Theory (Fall 2013 - Spring 2014) Course Information
Final version of the lecture notes have been posted on Thursday, June 5, 2014.
Assignment 7 is due Friday May 30, 2014.
is now due Monday, June 2, 2014.
Driver, APM 5260, 534-2648MWF:
APM 6432, 534-9068
Office Hours: Tuesday and Thursday from
MWF 11:00 -- 11:50 AM in
APM 7421 -- New Location.
Notes : I will be following these notes throughout the
Resnick, S. A Probability Path, Birkhauser, 1999.
Homework: There will be weekly
homework assignments due at the start of class on
Wenesdays. No late homeworks will be accepted.
You should also routinely login to
(https://ted.ucsd.edu/) account for more
Description: Math 280ABC is the fundamental graduate
probability sequence. It covers measure theoretic probability essential for the
pursuit of research in probability or in fields in which probability is used in
applications. Topics to be covered include:
Measure and integration from a probabilistic perspective.
Basic probabilistic notions of random variables, expectation,
Limit theorems: laws of large numbers, convergence in
distribution, central limit theorems.
Martingale theory: conditional expectation, convergence
theorems, optional stopping.
Stochastic processes: a selection from random walk, Markov
chains, Brownian motion, Markov processes, statistical mechanics, stable
processes, stochastic integration.
Topics 1, 2, and parts of 3 will be covered in Math 280A. The
remainder of topic 3, and topics 4 and 5 will be covered in the subsequent two
quarters of Math 280B, C. The text below will be supplemented with class lecture
Reserved Books: The following books have been put on
reserve at the Science and Engineering Library.
1. Author Resnick, Sidney I
Title A probability path / Sidney I. Resnick
Published Boston : Birkhäuser, c1999
2. Author Billingsley, Patrick
Title Probability and measure / Patrick Billingsley
Published New York : Wiley, c1986
Edition 2nd ed
3. Author Durrett, Richard, 1951-
Title Probability : theory and examples / Richard Durrett
Published Belmont, CA : Thomson, Brooks/Cole, c2005
Edition 3rd ed