MS&E 316: Discrete Mathematics and Algorithms (CME 305)
Introduction to theoretical foundations of discrete mathematics and algorithms. Emphasis on providing mathematical tools for combinatorial optimization, i.e. how to efficiently optimize over large finite sets and reason about the complexity of such problems. Topics include: graph theory, minimum cut, minimum spanning trees, matroids, maximum flow, non-bipartite matching, NP-hardness, approximation algorithms, spectral graph theory, and Laplacian systems. Prerequisites:
CS 161 is highly recommended, although not required.
Last offered: Winter 2022
MS&E 319: Matching Theory
The theory of matching with its roots in the work of mathematical giants like Euler and Kirchhoff has played a central and catalytic role in combinatorial optimization for decades. More recently, the growth of online marketplaces for allocating advertisements, rides, or other goods and services has led to new interest and progress in this area. The course starts with classic results characterizing matchings in bipartite and general graphs and explores connections with other branches of mathematics, including game theory and algebraic graph theory. Those results are complemented with models and algorithms developed for modern applications in market design, online advertising, and ride sharing. May be repeated for credit. Prerequisite: 212,
CS 261, or equivalent.
Last offered: Spring 2022
| Repeatable
for credit
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.
Terms: Spr
| Units: 3
Instructors:
Blanchet, J. (PI)
MS&E 322: Stochastic Calculus and Control
Ito integral, existence and uniqueness of solutions of stochastic differential equations (SDEs), diffusion approximations, numerical solutions of SDEs, controlled diffusions and the Hamilton-Jacobi-Bellman equation, and statistical inference of SDEs. Applications to finance and queueing theory. Prerequisites: 221 or
STATS 217:
MATH 113, 115.
Last offered: Winter 2023
MS&E 323: Stochastic Simulation
Emphasis is on the theoretical foundations of simulation methodology. Generation of uniform and non-uniform random variables. Discrete-event simulation and generalized semi-Markov processes. Output analysis (autoregressive, regenerative, spectral, and stationary times series methods). Variance reduction techniques (antithetic variables, common random numbers, control variables, discrete-time, conversion, importance sampling). Stochastic optimization (likelihood ratio method, perturbation analysis, stochastic approximation). Simulation in a parallel environment. Prerequisite: MS&E 221 or equivalent.
Terms: Win
| Units: 3
Instructors:
Glynn, P. (PI)
MS&E 324: Stochastic Methods in Engineering (CME 308, MATH 228)
The basic limit theorems of probability theory and their application to maximum likelihood estimation. Basic Monte Carlo methods and importance sampling. Markov chains and processes, random walks, basic ergodic theory and its application to parameter estimation. Discrete time stochastic control and Bayesian filtering. Diffusion approximations, Brownian motion and an introduction to stochastic differential equations. Examples and problems from various applied areas. Prerequisites: exposure to probability and background in analysis.
Terms: Spr
| Units: 3
MS&E 325: Optimal Transport in Operations Research, Statistics, and Economics
Current stochastic models, motivated by a wide range of applications in engineering, business, and science, as well as the design and analysis of associated computational methods for performance analysis and control of such stochastic systems.
Last offered: Winter 2020
MS&E 326: Advanced Topics in Applied Data Science
Advanced Topics in Applied Data Science
| Repeatable
for credit
(up to 99 units total)
MS&E 328: Foundations of Causal Machine Learning
Theoretical foundations of modern techniques at the intersection of causal inference and machine learning. Topics may include: semi-parametric inference and semi-parametric efficiency, modern statistical learning theory, Neyman orthogonality and double/debiased machine learning, theoretical foundations of high-dimensional linear regression, theoretical foundations of non-linear regression models, such as random forests and neural networks, adaptive non-parametric estimation of conditional moment models, estimation and inference on heterogeneous treatment effects, causal inference and reinforcement learning, off-policy evaluation, adaptive experimentation and inference.
Terms: Aut
| Units: 3
Instructors:
Syrgkanis, V. (PI)
MS&E 332: Security and Risk in Computer Networks
Risk management of large scale computing and networking systems with respect to security, data integrity, performance collapse, and service disruption. Qualitative and analytical basis for assessment, modeling, control, and mitigation of network risks. Stochastic risk models. Contact process. Random fields on networks. Virus and worm propagation dynamics and containment. Denial of service attacks. Intruder detection technologies. Distributed network attacks and countermeasures. Disaster recovery networks. Network protection services and resource placement. Autonomic self-defending networks. Economics of risk management. Emphasis is on analytics and quantitative methods.
Last offered: Winter 2021
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