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STOCHASTIC COMPUTATIONAL METHODS

MATH 717
과목 설명

Introduction to computational methods that use stochastic algorithms and/or methods that are applied to random or stochastic mathematical problems. The main emphasis will be placed on learning practical tools, while some aspects of theoretical foundations will also be covered (e.g., basic error analysis for numerical solution of stochastic differential equations (SDEs), and basic convergence of Monte Carlo methods). Topics include Monte Carlo methods, Bayesian inference and Bayesian sampling, simulation of Markov chains, numerical analysis for SDEs, data assimilation / state estimation, stochastic optimization methods and random sketching. Applications to science, engineering, finance, data science, and other practical problems also included.

선수과목

Graduate/professional standing or declared in Mathematics Visiting International Student Program (graduate or dissertator)

충족 요건

This course does not satisfy any prerequisites.

학점

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개설 시기

미보고

평점
4

0.9% 과거 데이터 대비

수료율
100%

과거 데이터 대비 변화 없음

A 비율
100%

5% 과거 데이터 대비

학급 규모
25

-10.71% 과거 데이터 대비

Cumulative Grade Distribution

강사 (2026 Summr)

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유사 과목

METHODS OF COMPUTATIONAL MATHEMATICS II

COMPSCI/MATH 715

Introduction to spectral methods (Fourier, Chebyshev, Fast Fourier Transform), finite element methods (Galerkin methods, energy estimates and error analysis), and mesh-free methods (Monte-Carlo, smoothed-particle hydrodynamics) for solving partial differential equations. Applications from science and engineering. Applications from science and engineering. Students are strongly encouraged to have programming skills (e.g.COMP SCI 200), undergraduate numerical analysis (e.g.MATH/​COMP SCI  514orCOMP SCI 412), analysis (MATH 322and521) and linear algebra (e.g.MATH 341or equiv.)

INTRODUCTION TO COMPUTATIONAL STATISTICS

COMPSCI/STAT 471

Classical statistical procedures arise where closed-form mathematical expressions are available for various inference summaries (e.g. linear regression; analysis of variance). A major emphasis of modern statistics is the development of inference principles in cases where both more complex data structures are involved and where more elaborate computations are required. Topics from numerical linear algebra, optimization, Monte Carlo (including Markov chain Monte Carlo), and graph theory are developed, especially as they relate to statistical inference (e.g., bootstrapping, permutation, Bayesian inference, EM algorithm, multivariate analysis).

STOCHASTIC PROGRAMMING

COMPSCI/ISYE 719

Stochastic programming is concerned with decision making in the presence of uncertainty, where the eventual outcome depends on a future random event. Topics include modeling uncertainty in optimization problems, risk measures, stochastic programming algorithms, approximation and sampling methods, and applications. Students are strongly encouraged to have knowledge of linear programming (e.g.,MATH/​COMP SCI/​I SY E/​STAT  525) and probability and statistics (e.g.,MATH/​STAT  431). Knowledge of integer optimization (MATH/​COMP SCI/​I SY E  728) is helpful, but not required.

STOCHASTIC ANALYSIS

MATH 735

Foundations of continuous time stochastic processes, semimartingales and the semimartingale integral, Ito's formula, stochastic differential equations, stochastic equations for Markov processes, application in finance, filtering, and control. The course relies on measure theoretic probability theory that can be reviewed at the beginning of the semester.

DATA-DRIVEN DYNAMICAL SYSTEMS, STOCHASTIC MODELING AND PREDICTION

MATH 616

An introduction to data-driven dynamical systems, including mathematical theory, methodology, numerical algorithms, applications and the use of a programming language to solve related coding problems. Topics include stochastic toolkits for dynamical systems and data science, linear Gaussian processes, nonlinear stochastic systems, elementary stochastic differential equations, data assimilation, parameter estimation, forecasting and prediction.