MATH 233C: Topics in Combinatorics
A topics course in combinatorics and related areas. The topic will be announced by the instructor.
Terms: Spr
| Units: 3
| Repeatable
for credit
Instructors:
Diaconis, P. (PI)
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/
Last offered: Spring 2019
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.
Last offered: Spring 2019
| Repeatable
for credit
(up to 99 units total)
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.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
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.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Win
| Units: 3
Instructors:
Papanicolaou, G. (PI)
;
Perlman, M. (TA)
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.
Last offered: Spring 2019
| Repeatable
10 times
(up to 30 units total)
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.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Win
| Units: 3
Instructors:
Papanicolaou, G. (PI)
;
Guijarro Ordonez, J. (TA)
MATH 243: Functions of Several Complex Variables
Holomorphic functions in several variables, Hartogs phenomenon, d-bar complex, Cousin problem. Domains of holomorphy. Plurisubharmonic functions and pseudo-convexity. Stein manifolds. Coherent sheaves, Cartan Theorems A&B. Levi problem and its solution. Grauert¿s Oka principle. nPrerequisites:
MATH 215A and experience with manifolds.
Last offered: Winter 2011
| Repeatable
for credit
MATH 244: Riemann Surfaces
Riemann surfaces and holomorphic maps, algebraic curves, maps to projective spaces. Calculus on Riemann surfaces. Elliptic functions and integrals. Riemann-Hurwitz formula. Riemann-Roch theorem, Abel-Jacobi map. Uniformization theorem. Hyperbolic surfaces. (Suitable for advanced undergraduates.) Prerequisites:
MATH 106 or
MATH 116, and familiarity with surfaces equivalent to
MATH 143,
MATH 146, or
MATH 147.
Last offered: Autumn 2017
| Repeatable
for credit
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