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...

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 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 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 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.

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Additive Combinatorics (Lecturer Ben Green) (Fall 2009, one-time course)

CS 229r. Topics in the Theory of Computation (Algorithms for Big Data)

Big data is data so large that it does not fit in the main memory of a single machine, and the need to process big data by efficient algorithms arises in Internet search, network traffic monitoring, machine learning, scientific computing, signal processing, and several other...

AM/ES 121. Introduction to Optimization: Models and Methods

Optimization is the problem of making decisions to maximize or minimize an objective in the presence of complicating constraints. The class will take you on a journey through the theory, methods, and application of linear programming, integer programming, Markov chains, and Markov decision...

ES 250. Information Theory

Fundamental concepts of information theory, Entropy, Kullback-Leibler divergence, Mutual information; typical sequences and their applications, Loss-less data compression, Huffman codes, Elias Codes, Arithmetic Codes, Discrete Memory-less Channels, Channel Coding and Capacity, Differential...

MATH 141. Introduction to Mathematical Logic

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...

CS 124. Data Structures and Algorithms

This course covers the modern theory of algorithms, focusing on the themes of efficient algorithms and intractable problems. The course goal is to provide a solid background in algorithms for computer science students, in preparation either for a job in industry or for more advanced...

CS 136. Economics and Computation

The interplay between economic thinking and computational thinking as it relates to electronic commerce, incentives engineering, and networked systems

CS 221. Computational Complexity

Computational complexity aims to understand the fundamental limitations and capabilities of efficient computation. For example, which computational problems inherently require a huge running time to solve, no matter how clever an algorithm one designs? This most basic question of computational complexity is now understood to be both extremely difficult and of great importance, as demonstrated by all the attention given to the famous P vs. NP question.... Read more about CS 221. Computational Complexity

AM 106/206. (Advanced) Applied Algebra

Introduction to abstract algebra and its applications. Sets, subsets, and partitions; mappings, operations, and equivalence relations; groups, rings, and fields, polynomials, encryption, computer coding, application of modular arithmetic, combinatorial designs, lattices, application of...

AM 107. Graph Theory and Combinatorics

Topics in combinatorial mathematics that find frequent application in computer science, engineering, and general applied mathematics. Specific topics taken from graph theory, enumeration techniques, optimization theory, combinatorial algorithms, and discrete probability.

AM 221. Advanced Optimization

This is a graduate-level course on optimization. The course covers mathematical programming and combinatorial optimization from the perspective of convex optimization, which is a central tool for solving large-scale problems. In recent years convex optimization has had a profound impact on...

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