Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
MAT 135B: Stochastic Processes
Approved: 2006-05-01 (revised 2023-06-01, J. Gravner and A. Soshnikov)
Suggested Textbook: (actual textbook varies by instructor; check your
instructor)
Lecture Notes for Introductory Probability by Janko Gravner, freely available at https://www.math.ucdavis.edu/~gravner/MAT135A/resources/lecturenotes.pdf
Prerequisites:
MAT 135A; (MAT 022A or MAT 027A or MAT 067 or BIS 027A).
Suggested Schedule:
|
Lecture(s) |
Sections |
Comments/Topics |
|
2 Lectures |
9 |
Convergence in probability |
|
2 Lectures |
10 |
Moment generating functions |
|
4 Lectures |
11 |
Computing probabilities and expectations by conditioning |
|
10 Lectures |
12-16 |
Discrete time Markov chains. Branching processes |
|
3 Lectures |
17 |
Selected applications |
|
3 Lectures |
18 |
Poisson process |
Additional Notes:
Sample exams, homework problems, and some additional resources are
available at
https://www.math.ucdavis.edu/~gravner/MAT135A/resources
Further potential topics that could be covered if time permits include:
martingales; renewal theory; random walks; and Brownian motion.
Learning Goals:
This is a second course in probability. The focus is on random processes
that evolve over time. Upon completing the course, students will know
how to compute limits of random variables. They will know how to compute
the moment generating function of a random variable and find
large-deviation bounds for sums of independent random variables. They
will know how to find the stationary distribution of Markov chain and
find the extinction probability of a branching process.
AS A CAPSTONE:
Students will develop and deepen their understanding of stochastic
processes in this second course of the MAT 135 sequence. While learning
about random processes that evolve over time, they will gain mastery of
this specialization and improve their ability to communicate mathematics
at the capstone level, commensurate with that expected of one with an
undergraduate degree in mathematics.
Assessment:
The grade is decided by homework, quizzes, midterms and a final exam.