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MATH 276. Expander Graphs and Number Theory (Spring 2009)

Expander graphs, Ramanujan graphs, and their explicit constructions using representation theory. Topics may include: Lattices in algebraic groups, Property (T), Representation theory of PGL(2,Q-p), Ramanujan conjecture.

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MATH 270. Advanced Probability Theory (Fall 2011)

The axioms of Kolmogorov, convergence and limit theorems, random walks, martingales and Markov processes in discrete time, concentration of measure and large deviations.

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MATH 268x. Graph Limits (Fall 2011)

Introduction to the emerging field of relating large graphs to analytical objects. Topics may include: ultra-limit method and Szemeredi regularity, constant-time algorithms, Borel graphs and measurable equivalence relations, Gromov's sofic groups.

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MATH 256x. The Theory of Error-Correcting Codes (Fall 2013)

The general motivating setup from information theory for error-correcting block codes (as opposed to other kinds such as convolutional, let alone cryptographic: we’re aiming to protect against error, not eavesdropping). Natural languages such as English...

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MATH 253. Introduction to Computability and Randomness (Spring 2011)

An introduction to computability theory and algorithmic randomness. Topics: Turing reducibility, computably enumerable sets, complexity, notions of randomness, and martingales, as well as interactions between computability and randomness.

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MATH 168. Computability Theory (Spring 2013)

An introduction to computability theory (also known as recursion theory). A discussion of the problem of determining what it means for a set or function to be computable, including primitive recursion, Turing machines, and the Church-Turing Thesis. The...

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MATH 162. Introduction to Quantum Computing (Spring 2011)

This course is meant to give an introduction to the fundamental mathematics of quantum computing. Notions from linear algebra, elementary number theory and probability theory are introduced along the way as needed.

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MATH 116. Real Analysis, Convexity, and Optimization (Fall 2013)

This course is meant to give an introduction to the fundamental mathematics of quantum computing. Notions from linear algebra, elementary number theory and probability theory are introduced along the way as needed.

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CS 286r. Topics at the Interface between Computer Science and Economics (Computational Social Choice) (Fall 2011)

This is a rotating topics course that studies the interplay between computation and economics. Topics covered include electronic commerce, computational social choice, computational mechanism design, peer production, prediction markets and reputation...

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CS 286r. Topics at the Interface between Computer Science and Economics (Information, Prediction, and Collective Intelligence) (Fall 2012)

This is a rotating topics course that studies the interplay between computation and economics. Topics covered include electronic commerce, computational social choice, computational mechanism design, peer production, prediction markets and reputation...

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CS 286r. Topics at the Interface between Computer Science and Economics (Matching and Market Design) (Spring 2014)

Markets are the basic mechanism by which resources are allocated to agents. In recent years, computer scientists and economists have re-engineered markets with a particular eye towards efficiency (i.e., that the market optimizes the designer's objective)...

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CS 285. Multi-Agent Systems (Fall 2013)

A multi-agent system is composed of multiple autonomous entities, with distributed information, computational ability, and possibly divergent interests. Multi-agent systems may be cooperative, such as sensor networks and mobile robots in a warehouse, or...

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