## MATH 230A: Theory of Probability I (STATS 310A)

Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites:
STATS 116,
MATH 171.

Terms: Aut
| Units: 2-4

## MATH 230B: Theory of Probability II (STATS 310B)

Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 0-1 laws, Radon-Nikodym Theorem, ruin problems, etc. Other topics as time allows selected from (i) local limit theorems, (ii) renewal theory, (iii) discrete time Markov chains, (iv) random walk theory,n(v) ergodic theory. Prerequisite: 310A or
MATH 230A.

Terms: Win
| Units: 2-3

## MATH 230C: Theory of Probability III (STATS 310C)

Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes. Invariance principle, random walks, LIL and functional CLT. Markov and strong Markov property. Infinitely divisible laws. Some ergodic theory. Prerequisite: 310B or
MATH 230B.
http://statweb.stanford.edu/~adembo/stat-310c/

Terms: Spr
| Units: 2-4

## MATH 231: Mathematics and Statistics of Gambling (STATS 334)

Probability and statistics are founded on the study of games of chance. Nowadays, gambling (in casinos, sports and the Internet) is a huge business. This course addresses practical and theoretical aspects. Topics covered: mathematics of basic random phenomena (physics of coin tossing and roulette, analysis of various methods of shuffling cards), odds in popular games, card counting, optimal tournament play, practical problems of random number generation. Prerequisites: Statistics 116 and 200.

Last offered: Spring 2018

## MATH 232: Topics in Probability: Percolation Theory

An introduction to first passage percolation and related general tools and models. Topics include early results on shape theorems and fluctuations, more modern development using hyper-contractivity, recent breakthrough regarding scaling exponents, and providing exposure to some fundamental long-standing open problems. Course prerequisite: graduate-level probability.

Last offered: Autumn 2016
| Repeatable for credit

## MATH 233A: Topics in Combinatorics

A topics course in combinatorics and related areas. The topic will be announced by the instructor.

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Vondrak, J. (PI)

## MATH 233B: Topics in Combinatorics: Polyhedral Techniques in Optimization

A topics course in combinatorics and related areas. The topic will be announced by the instructor.

Last offered: Winter 2017
| Repeatable for credit

## MATH 233C: Topics in Combinatorics

A topics course in combinatorics and related areas. The topic will be announced by the instructor.

Last offered: Spring 2017
| Repeatable for credit

## MATH 234: Large Deviations Theory (STATS 374)

Combinatorial estimates and the method of types. Large deviation probabilities for partial sums and for empirical distributions, Cramer's and Sanov's theorems and their Markov extensions. Applications in statistics, information theory, and statistical mechanics. Prerequisite:
MATH 230A or
STATS 310. Offered every 2-3 years.
http://statweb.stanford.edu/~adembo/large-deviations/

Terms: Spr
| Units: 3

Instructors:
Dembo, A. (PI)

## MATH 235A: Topics in combinatorics

This advanced course in extremal combinatorics covers several major themes in the area. These include extremal combinatorics and Ramsey theory, the graph regularity method, and algebraic methods.

Terms: Spr
| Units: 3
| Repeatable for credit

Instructors:
Fox, J. (PI)

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