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91 - 100 of 136 results for: MATH

MATH 233C: Topics in Combinatorics

A topics course in combinatorics and related areas. The topic will be announced by the instructor. NOTE: 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: Spr | Units: 3 | Repeatable for credit
Instructors: Fox, J. (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 235: Modern Markov Chains (STATS 318)

Tools for understanding Markov chains as they arise in applications. Random walk on graphs, reversible Markov chains, Metropolis algorithm, Gibbs sampler, hybrid Monte Carlo, auxiliary variables, hit and run, Swedson-Wong algorithms, geometric theory, Poincare-Nash-Cheeger-Log-Sobolov inequalities. Comparison techniques, coupling, stationary times, Harris recurrence, central limit theorems, and large deviations.
Terms: Win | Units: 3

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. Introduction to stochastic control and Bayesian filtering. Prerequisite: Math 136 or equivalent and basic familiarity with parabolic partial differential equations. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such other courses taken.
Terms: Win | Units: 3

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 2023 | Repeatable 10 times (up to 30 units total)

MATH 238: Mathematical Finance (STATS 250)

Stochastic models of financial markets. Risk neutral pricing for derivatives, hedging strategies and management of risk. Multidimensional portfolio theory and introduction to statistical arbitrage. Prerequisite: Math 136 or equivalent. NOTE: 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 other courses taken.
Terms: Win | Units: 3

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. Prerequisites: MATH 215A and experience with manifolds. NOTE: 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 2021 | Repeatable for credit
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