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, BorelCantelli 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: 24

Grading: Letter or Credit/No Credit
MATH 230B: Theory of Probability II (STATS 310B)
Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 01 laws, RadonNikodym 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: 23

Grading: Letter or Credit/No Credit
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/stat310c/
Terms: Spr

Units: 24

Grading: Letter or Credit/No Credit
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.
Terms: not given this year, last offered Spring 2018

Units: 3

Grading: Letter or Credit/No Credit
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 hypercontractivity, recent breakthrough regarding scaling exponents, and providing exposure to some fundamental longstanding open problems. Course prerequisite: graduatelevel probability.
Terms: not given this year, last offered Autumn 2016

Units: 3

Repeatable for credit

Grading: Letter or Credit/No 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

Grading: Letter or Credit/No 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.
Terms: not given this year, last offered Winter 2017

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 233C: Topics in Combinatorics
A topics course in combinatorics and related areas. The topic will be announced by the instructor.
Terms: not given this year, last offered Spring 2017

Units: 3

Repeatable for credit

Grading: Letter or Credit/No 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 23 years.
http://statweb.stanford.edu/~adembo/largedeviations/
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
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

Grading: Letter or Credit/No Credit
Instructors:
Fox, J. (PI)
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