Nestor GuillenDepartment of Mathematics University of California at Los Angeles Office: MS 6903 Email: nestor@math.ucla.edu |
Math 171. Spring 2013.
Stochastic Processes
Lectures: MWF 12:00 - 12:50 pm at MS 5118
Office hours: Mondays, Wednesdays 9-10 am or by appointment.
Main text book: Essentials of Stochastic Processes by Rick Durrett, Second Edition. (NOTE: this book is fully available available online in PDF format, requires UCLA library access).
The goal of this course is to serve as a bridge between undergraduate and graduate level courses in probability. This is done through a complete introduction to one of the central objects of probability theory, the Markov chain.
Markov chains or Markov processes are (random) dynamical systems where the statistics of the future configuration of the system are fully determined by its present state, independently of its past. This "lack of memory" has already been tangentially discussed in Math 170B when studying the Bernoulli and Poisson processes and the random walk or Brownian motion.
The minimum course requirements are: a strong background on calculus, linear algebra, as well as Math 170A and 170B (or equivalent courses). Knowledge of basic combinatorics and ordinary differential equations is a plus. Some degree of mathematical maturity will be expected, and in particular the weekly homeworks will require a great deal of creative problem solving, they will be the single most important activity of this class.
Enrollment: Any questions about class Enrollment are to be taken to the math department office in MS 6356.
Grading scheme: Homeworks: 25% Midterms 1: 15% Midterm 2: 20% Final: 40%. No late homeworks will be accepted! On the other hand, when computing your homework grade average your lowest homework grade will be dropped.
Exam schedule:
Midterm 1: Friday of the fourth week of classes.
Midterm 2: Friday of the eight week of classes
Final: Thursday, June 13, 2013. 8:00 AM - 11:00 AM in MS 5118.
Homeworks
Homework 1. Due April 11th during discussion.