# 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.

# 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.

# 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 theory of Turing degrees and the...

# 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.

# 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 are very suboptimal error-correcting...

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

# 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.

# 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.

...

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

# MATH 298. Random Matrices (Spring 2012)

An introduction to random matrix theory. Topics: Wigner matrices, Gaussian and circular ensembles, Dyson's Brownian motion, determinantal processes, orthogonal polynomials, bulk and edge scaling limits, beta ensembles, continuum limits, and various recent applications.

...

# MATH 152: Discrete Mathematics

Plan to attend all of the first class and put the course on your study card immediately. If there are more than 16 applicants, we will give priority to the following:

Current or prospective CS concentrators who plan to take CS 121 and/or 124 and who will take this course instead of CS 20...

# MATH 155r. Combinatorics

An introduction to counting techniques and other methods in finite mathematics. Possible topics include: the inclusion-exclusion principle and Mobius inversion, graph theory, generating functions, Ramsey's theorem and its variants, probabilistic methods.

# MATH 278. Geometry and Algebra of Computational Complexity

In this course, mathematical aspects of computational complexity theory will be broadly covered. We shall start with basics of complexity theory (Turing machines, various notions of complexity and NP completeness), discuss other computation models and intractability results, and explore algebro-... Read more about MATH 278. Geometry and Algebra of Computational Complexity

# MATH 295. Topics in Discrete Probability: Random Structures and Algorithms

An introduction to probabilistic reasoning for random structures, including random graphs, graphical models and Markov Random Fields (MRF). Topics include: large deviations theory and concentration inequalities Theory of random graphs,the moment method. Combinatorial...

Read more about MATH 295. Topics in Discrete Probability: Random Structures and Algorithms

# MATH 286: Random Matrices and Applications

We will cover two topics in random matrix theory.  1. Concentration inequalities.  2. Stochastic flow method.  We will start with a review of basic results in random matrices like local laws and Dyson's Brownian motions.  We will discuss coupling methods in random matrices...