Math 285J: Applied Probability -- An Introduction
Stochastic processes are necessary ingredients for building
models of a wide variety of phenomena exhibiting time-varying randomness.
Despite being listed as a seminar, this course is intended as an introduction
to probability and stochastic processes for graduate students primarily interested in
applications. If you plan to take only one probability course
in your graduate studies, this course is meant for you.
It may also serve as a complement to a more rigorous course.
Unlike the measure-theory-based MATH 275 sequence, this course
will emphasize modeling, analysis and simulation of applied stochastic
processes as opposed to rigorous proofs (although there will be
some proofs). Time permitting, a range
of applications from biology to economics will be discussed. No background in probability
will be assumed, but the pace will be quite fast and an undergraduate course in probability
will be an asset.
Here is a tentative list of topics to be covered:
- Overview of Basic Probability:
Basic limit laws;
- Introduction to Stochastic (mostly Markov) Processes:
Markov chains and continuous-time Markov processes;
Diffusion processes and numerical methods (if time permits).
- Instructor: Sebastien Roch. To communicate with me, use Piazza.
- Time and place: MWF at 2 in MS 5147
- Office hours: TBA
- Prerequisites: No probability background is required. An undergraduate
course in probability and stochastic processes (e.g. MATH 170) will be useful.
- Texts (not required): Topics covered will be taken mostly from
- Grades will be based on a few homework assignments which may involve simulation.
Piazza: We will use Piazza, a free discussion board.
You should sign up here
with your UCLA email by looking up the class. On Piazza, you can:
You are strongly encouraged to post any questions about course content
or policies here, and to help answer your fellow students questions.
There are things to be kept in mind while using Piazza.
Here are the rules:
- Ask course-related questions
- Collaborate to form a high-quality Wikipedia-style response
- Have a traditional thread-style discussion
- Customize how Piazza notifies you of new posts (e.g., in real time, in daily digests, etc.)
- Posts can be anonymous if you wish.
If you have questions for me of a more personal nature, use
a private post. I will also post course announcements there, so it is important
to check it regularly.
- Do not post solutions to the assignments, although feel free to discuss the problems
without giving away too much.
- Be civilized; refrain from posting offensive, inappropriate, or irrelevant
content. Remember that the whole class, including the professor and the TAs,
are potentital readers to the discussion board.
Use your common sense to determine what constitutes as acceptable content.
- [Mar 30]: Please take the poll on Piazza. It is completely anonymous and it will help me prepare the class.
- [Mar 30]: All future announcements, including homework assignments, will be posted on Piazza.
Last updated: Mar 30, 2012.