GRADUATE COURSES IN PROBABILITY (UCSD)

Math 285. The one quarter graduate course, Math 285, on Stochastic Processes introduces beginning Mathematics graduate students and graduate students from other disciplines to some fundamental stochastic processes. For the Mathematics students, this provides valuable preparation and motivation for the more advanced graduate probability sequence, Math 280ABC. For students from other disciplines, the course provides a theoretical base for pursuing applied work involving stochastic models. Math 285 is usually offered in the Spring each year and is an excellent course for Mathematics students to take prior to taking the probability sequence Math 280ABC.

Math 280ABC. The three-quarter graduate sequence, Math 280ABC, covers the fundamentals of the theory of Probability. This sequence is essential preparation for Mathematics students intending to pursue research in Probability and provides rigorous training in the theory and techniques of probability for those intending to apply probability in other areas of mathematics or in areas of application, especially in science, engineering, economics and finance. Knowledge of real analysis at the level of the undergraduate course Math 140AB is essential for success in this sequence. In particular, students should be proficient at writing rigorous proofs. Students who do not have this preparation are encouraged to consider Math 285 instead, which is usually offered every Spring. Students wishing to improve their real analysis preparation before taking Math 280ABC are encouraged to take at least Math 140AB. For further preparation in analysis, the graduate real analysis sequence, Math 240ABC, is an excellent complement to Math 280ABC, especially for Mathematics Ph.D. students. Math 280ABC is a sequence and success in Math 280A is expected for enrolment in Math 280B, and similarly, success in Math 280B is expected for enrolment in Math 280C.

Math 286. The one-quarter graduate course, Math 286, covers Stochastic Integration and Stochastic Differential Equations. Such equations are used to model a variety of random dynamic phenomena in applications. Solutions of these equations are often Markov diffusion processes. Because of this, the theory of stochastic differential equations has strong links to the theory of partial differential equations. Math 286 is usually offered every second year, in alternation with Math 294.

Math 294. The one-quarter graduate course, Math 294, provides an introduction to the mathematics of financial models. Students are introduced to some basic models of finance and the associated mathematical machinery. Key probabilistic concepts of conditional expectation, martingale, change of measure, and martingale representation are covered. Math 294 is usually offered every second year, in alternation with Math 286.

Math 289. The graduate course, Math 289, is a Topics Course in Probability. The topic of this course is chosen by the instructor and typically relates to an area of current research interest. This course may be repeated for credit with advisor consent, as the topic varies. Scheduling of this course is variable.

Math 288. Math 288 is a Seminar in Probability featuring talks on topics of current research interest. Graduate students who attend the weekly seminars may sign up for one unit of credit per quarter, on a P/NP basis.

Catalog descriptions for courses offered in the Mathematics Department can be found by clicking here.