printer friendly pageMATH 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
(up to 99 units total)
Instructors:
Fox, J. (PI)
MATH 235B: Modern Markov Chain Theory
This is a graduate-level course on the use and analysis of Markov chains. Emphasis is placed on explicit rates of convergence for chains used in applications to physics, biology, and statistics. Topics covered: basic constructions (metropolis, Gibbs sampler, data augmentation, hybrid Monte Carlo); spectral techniques (explicit diagonalization, Poincaré, and Cheeger bounds); functional inequalities (Nash, Sobolev, Log Sobolev); probabilistic techniques (coupling, stationary times, Harris recurrence). A variety of card shuffling processes will be studies. Central Limit and concentration.
Last offered: Winter 2016
| Repeatable
for credit
(up to 99 units total)
MATH 235C: Topics in Markov Chains
Classical functional inequalities (Nash, Faber-Krahn, log-Sobolev inequalities), comparison of Dirichlet forms. Random walks and isoperimetry of amenable groups (with a focus on solvable groups). Entropy, harmonic functions, and Poisson boundary (following Kaimanovich-Vershik theory).
Last offered: Spring 2016
| Repeatable
for credit
(up to 99 units total)
MATH 236: Introduction to Stochastic Differential Equations
Brownian motion, stochastic integrals, and diffusions as solutions of stochastic differential equations. Functionals of diffusions and their connection with partial differential equations. Random walk approximation of diffusions. Prerequisite: 136 or equivalent and differential equations.
Terms: Win
| Units: 3
Instructors:
Papanicolaou, G. (PI)
MATH 237A: Topics in Financial Math: Market microstructure and trading algorithms
Introduction to market microstructure theory, including optimal limit order and market trading models. Random matrix theory covariance models and their application to portfolio theory. Statistical arbitrage algorithms.
Terms: Spr
| Units: 3
| Repeatable
10 times
(up to 30 units total)
Instructors:
Papanicolaou, G. (PI)
MATH 238: Mathematical Finance (STATS 250)
Stochastic models of financial markets. Forward and futures contracts. European options and equivalent martingale measures. Hedging strategies and management of risk. Term structure models and interest rate derivatives. Optimal stopping and American options. Corequisites:
MATH 236 and 227 or equivalent.
Terms: Win
| Units: 3
Instructors:
Papanicolaou, G. (PI)
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