Global Arc

This course will cover topics in Extremal Combinatorics including ones motivated by questions in other areas like Computer Science, Information Theory, Number Theory and Geometry. The subjects that will be covered include Graph powers, the Shannon capacity and the Witsenhausen rate of graphs, Szemeredi's Regularity Lemma and its applications in graph property testing and in the study of sets with no 3 term arithmetic progressions, the Combinatorial Nullstellensatz and its applications, the capset problem, Containers and list coloring, and related topics as time permits.

Wiener measure. Stochastic differential equations. Markov diffusion processes. Linear theory of stationary processes. Ergodicity, mixing, central limit theorem for stationary processes. If time permits, the theory of products of random matrices and PDE with random coefficients will be discussed. Prerequisite: MAT385.

This course gives a mathematical introduction to machine learning. It is not about proving theorems in machine learning, but rather a unified understanding of the models and algorithms used in machine learning. It begins with a simple introduction to supervised and unsupervised learning, including regression, classification, density estimation, clustering, and dimension reduction. Simple models such as linear regression, support vector machines, and k-means will be introduced, followed by focus on deep learning.

This course will teach some of the fundamental concepts needed to succeed in the calculus sequence, and develop students' mathematical writing and presentation skills. It is comprised of lectures, precepts, and writing workshops.Written work will be assigned weekly, and a final project will be due at the end of the summer.

MAT 210 will survey the main ideas of calculus in a single variable incorporating an introduction to formal mathematical proofs. The course will place equal emphasis on theory (how to construct formal mathematical definitions and rigorous, logical proofs) and on practice (concrete computational examples involving integration and infinite sequences and series). This course provides a more theoretical foundation in single variable calculus than MAT104, intended to prepare students better for a first course in real analysis (MAT215), but it covers all the computational tools needed to continue to multivariable calculus (MAT201 or MAT203).