Complexity Theory (CAS CS 535)

The capabilities and fundamental limits of efficient computation: which problems are inherently hard, and how resources such as time, space, randomness and interaction affect what can be computed.

Introduction to Sequential Decision Making (CDS DS 592)

Design and analysis of algorithms for sequential decision making, focused on bandits and statistical learning theory: UCB, EXP3, linear and contextual bandits, and function approximation.

Multimodal Machine Learning (CAS CS 598)

Representation, fusion, alignment and generation across modalities such as vision, language and signals, including multimodal transformers, interaction and quantification, with a semester-long team research project.

Algorithmic Mechanism Design (CDS DS 574)

Computational perspectives applied to economic problems, and economic techniques applied to computer science: welfare-maximizing auctions, equilibria, and mechanism design for social good.

Algorithms for Machine Learning (CAS CS 599 E1)

Seminar on efficient algorithms for building modern machine learning models at scale: adaptive gradient methods, dimensionality reduction, retrieval, attention and state space models, and model compression.

Bayesian Methods in Computer Science (CS 677)

Bayesian methods for modeling uncertainty in data, including Bayesian deep learning, alongside classical ML models such as regression and decision trees.

Modeling with Uncertainty and Data 2 (MATH 404, with lab)

Mathematical statistics: estimation, inference, regression, multivariate and Bayesian statistics, Kalman filtering, and time series.

Modeling with Dynamics and Control 2 (MATH 438, with lab)

Calculus of variations, optimal control and Pontryagin's maximum principle, stochastic differential equations, and uncertainty quantification.

Introduction to Deep Learning (CS 474)

Theory and practice of deep learning.

Mathematics of Deep Learning (MATH 522)

Mathematics behind how deep neural networks are formulated and designed, including their stability and generalizability, and statistical learning theory such as Rademacher complexity and VC dimension.

Modeling with Uncertainty and Data 1 (MATH 402, with lab)

Probability and stochastic processes: random variables, limit theorems, martingales, Markov and Poisson processes, and information theory.

Modeling with Dynamics and Control 1 (MATH 436, with lab)

Dynamical systems, bifurcation theory, control theory, and partial differential equations.

Reinforcement Learning (CS 401R)

Introduction to reinforcement learning: fundamentals such as Q-learning, policy iteration, policy evaluation, value-based and model-based methods, and on-policy versus off-policy learning.

Algorithm Design and Optimization 2 (MATH 322, with lab)

Optimization: linear programming and the simplex method, convex optimization, Lagrangian methods, and unconstrained and global optimization.

Mathematical Analysis 2 (MATH 346, with lab)

Theory of integration (Riemann and Lebesgue), complex analysis, calculus on curves and surfaces, and spectral calculus.

Matrix Analysis (MATH 570)

Special classes of matrices, canonical forms, matrix and vector norms, eigenvalue localization, and matrix functions.

Algorithm Design and Optimization 1 (MATH 320, with lab)

Algorithm analysis, approximation theory, and recursive algorithms, with some overlap with data structures and algorithms.

Mathematical Analysis 1 (MATH 344, with lab)

Vector spaces, linear maps, inner product spaces, spectral theory, metric space topology, and convex analysis.

Data Structures and Algorithms (CS 235)

Fundamental data structures and algorithms, including algorithm analysis, recursion, sorting and searching, trees and hashing.

Theory of Analysis 1 (MATH 341)

Rigorous treatment of single-variable calculus and the real number system.