2018-19 Catalog

Covers the basic algebraic, geometric, and topological properties of normed linear spaces, inner-product spaces, and linear maps. Emphasis is placed both on rigorous mathematical development and on applications to control theory, data analysis and partial differential equations.

This class studies mathematical optimization from the viewpoint of convexity. Topics covered include duality and representation of convex sets; linear and semidefinite programming; connections to discrete, network, and robust optimization; relaxation methods for intractable problems; as well as applications to problems arising in graphs and networks, information theory, control, signal processing, and other engineering disciplines.

The course will start with a quick reminder on probability spaces, discrete and continuous random variables. It will cover the following core topics: branching processes, Poisson processes, limit theorems, Gaussian variables, vectors, spaces, processes and measures, the Brownian motion, Gaussian learning, game theory and decision theory (finite state space), martingales (concentration, convergence, Doob's inequalities, optional/optimal stopping, Snell's envelope), large deviations (introduction, if time permits).

This course develops core principles for the analysis and design of algorithms. Basic material includes mathematical techniques for analyzing performance in terms of resources, such as time, space, and randomness. The course introduces the major paradigms for algorithm design, including greedy methods, divide-and-conquer, dynamic programming, linear and semidefinite programming, randomized algorithms, and online learning.

Social networks, the web, and the internet are essential parts of our lives and we all depend on them every day, but do you really know what makes them work? This course studies the "big" ideas behind our networked lives. Things like, what do networks actually look like (and why do they all look the same)? How do search engines work? Why do memes spread the way they do? How does web advertising work? For all these questions and more, the course will provide a mixture of both mathematical analysis and hands-on labs. The course assumes students are comfortable with graph theory, probability, and basic programming.

This course will cover popular methods in machine learning and data mining, with an emphasis on developing a working understanding of how to apply these methods in practice. The course will focus on basic foundational concepts underpinning and motivating modern machine learning and data mining approaches. We will also discuss recent research developments

Registration is limited to graduate students in the CMS department only. This course is a research seminar course covering topics at the intersection of mathematics, computation, and their applications. Students are asked to attend one seminar per week (from any seminar series on campus) on topics related to computing and mathematical sciences. This course is a requirement for first-year PhD students in the CMS department.

Research in the field of computing and mathematical science. By arrangement with members of the staff, properly qualified graduate students are directed in research.