MATH 136: Stochastic Processes (STATS 219)
Introduction to measure theory, Lp spaces and Hilbert spaces. Random variables, expectation, conditional expectation, conditional distribution. Uniform integrability, almost sure and Lp convergence. Stochastic processes: definition, stationarity, sample path continuity. Examples: random walk, Markov chains, Gaussian processes, Poisson processes, Martingales. Construction and basic properties of Brownian motion. Prerequisite:
STATS 116 or
MATH 151 or equivalent. Recommended:
MATH 115 or equivalent.
http://statweb.stanford.edu/~adembo/math136/
Terms: Aut

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Dembo, A. (PI)
;
Hui, Y. (TA)
MATH 159: Discrete Probabilistic Methods
Modern discrete probabilistic methods suitable for analyzing discrete structures of the type arising in number theory, graph theory, combinatorics, computer science, information theory and molecular sequence analysis. Prerequisite:
STATS 116/
MATH 151 or equivalent.
Terms: not given this year, last offered Autumn 2016

Units: 3

Grading: Letter or Credit/No Credit
MATH 171: Fundamental Concepts of Analysis
Recommended for Mathematics majors and required of honors Mathematics majors. Similar to 115 but altered content and more theoretical orientation. Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology. Prerequisite: 61CM or 61DM or 115 or consent of the instructor. WIM
Terms: Aut, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 227: Partial Differential Equations and Diffusion Processes
Parabolic and elliptic partial differential equations and their relation to diffusion processes. First order equations and optimal control. Emphasis is on applications to mathematical finance. Prerequisites:
MATH 136/
STATS 219 (or equivalents) and
MATH 131P +
MATH 115/171 or
MATH 173 or
MATH 220.
Terms: not given this year, last offered Winter 2015

Units: 3

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: not given this year, last offered Spring 2017

Units: 3

Grading: Letter or Credit/No Credit
MCS 100: Mathematics of Sports (STATS 50)
The use of mathematics, statistics, and probability in the analysis of sports performance, sports records, and strategy. Topics include mathematical analysis of the physics of sports and the determinations of optimal strategies. New diagnostic statistics and strategies for each sport. Corequisite:
STATS 60, 110 or 116.
Terms: Spr

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
DiCiccio, C. (PI)
;
Hwang, J. (PI)
ME 472: Computational Modeling of Radiative Transfer
Overview of physical modeling and computational methods for radiation heat transfer in participating media. Review of surface transfer. Radiation hydrodynamics and the radiative transfer equation. Constitutive relations for transport coefficients of participating media. Formal solution and onedimensional transfer. Moment methods: diffusion and spherical harmonics. The discrete ordinates method: spatial and angular discretization, false scattering and ray effects, the finite volume method, parallelization. Monte Carlo ray tracing: ray tracing, Monte Carlo simulations, surface transfer, transfer in participating media, variance reduction techniques, parallelization. Additional topics covered time permitting: spectral modeling, collimated sources, transient radiative transfer, reverse raytracing. Prerequisites:
ME 300C or equivalent;
STATS 116 or equivalent; undergraduate heat transfer;
ME 352A strongly recommended but not required.
Terms: not given this year, last offered Winter 2016

Units: 3

Grading: Letter (ABCD/NP)
MS&E 135: Networks
This course provides an introduction to how networks underly our social, technological, and natural worlds, with an emphasis on developing intuitions for broadly applicable concepts in network analysis. The course will include: an introduction to graph theory and graph concepts; social networks; information networks; the aggregate behavior of markets and crowds; network dynamics; information diffusion; the implications of popular concepts such as "six degrees of separation", the "friendship paradox", and the "wisdom of crowds".
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Ugander, J. (PI)
;
Ciurea Ilcus, S. (TA)
;
Pham, O. (TA)
...
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Instructors:
Ugander, J. (PI)
;
Ciurea Ilcus, S. (TA)
;
Pham, O. (TA)
;
Ragain, S. (TA)
;
Zhou, B. (TA)
MS&E 226: "Small" Data
This course is about understanding "small data": these are datasets that allow interaction, visualization, exploration, and analysis on a local machine. The material provides an introduction to applied data analysis, with an emphasis on providing a conceptual framework for thinking about data from both statistical and machine learning perspectives. Topics will be drawn from the following list, depending on time constraints and class interest: approaches to data analysis: statistics (frequentist, Bayesian) and machine learning; binary classification; regression; bootstrapping; causal inference and experimental design; multiple hypothesis testing. Class lectures will be supplemented by datadriven problem sets and a project. Prerequisites:
CME 100 or
MATH 51; 120, 220 or
STATS 116; experience with R at the level of CME/
STATS 195 or equivalent.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Johari, R. (PI)
;
Choi, J. (TA)
;
Ragain, S. (TA)
;
Samaniego de la Fuente, S. (TA)
;
Schmit, S. (TA)
;
Walsh, D. (TA)
;
Zhang, T. (TA)
MS&E 321: Stochastic Systems
Topics in stochastic processes, emphasizing applications. Markov chains in discrete and continuous time; Markov processes in general state space; Lyapunov functions; regenerative process theory; renewal theory; martingales, Brownian motion, and diffusion processes. Application to queueing theory, storage theory, reliability, and finance. Prerequisites: 221 or
STATS 217;
MATH 113, 115. (Glynn)
Terms: Spr

Units: 3

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