Here are some notable classes that I’ve taken. (G) refers to a graduate-level class.

Math

18.656 (G) Mathematical Statistics: A Non-Asymptotic Approach

Statistical analysis without relying on \(n \to \infty\): every bound is exactly true regardless of the value of \(n\). Results are in the form of concentration bounds \(\mathbb{P}[Z_n > t] \le e^{-cnt}\), bounds on estimation error \(\mathbb{E} \Vert \hat{\theta} - \theta^* \Vert_2^2 \le \frac{c \sigma^2 f(d)}{n}\) under a constraint \(\theta \in \Theta\), etc. Full of deep intuitions from geometry and linear algebra!

6.780 (G) (previously 6.437) Inference and Information

A fun and fast-paced class about inferring parameters from data in both Bayesian and non-Bayesian manners. Lots of information theory as well. Get comfortable with taking expectations and integrals of everything and trying to visualize infinite-dimensional spaces of probability distributions.

18.650 Fundamentals of Statistics

Asymptotic statistical theory (Central Limit Theorem repeatedly) and statistical tests such as the Wald test, t-test, permutation tests, etc.

6.S095 Intermediate Probability Problem Solving

A very fast-paced and problem-solving oriented class that was difficult to keep up with but a great introduction to using probability in practice.

18.705 (G) Commutative Algebra

Rings, ideals, modules, tensor products, Noetherian rings/modules, Dedekind domains, etc. Fun class, though it’s in a tough spot because it would feel much more motivated alongside algebraic geometry or number theory.

18.225 (G) Graph Theory and Additive Combinatorics

Difficult class with a very Olympiad-like flavor and lots of interesting, deep theory within the niche of extremal graph theory and additive combinatorics. My favorite units were probably graph limits, regularity, and Freiman’s theorem.

CS

6.566 (G) (previously 6.858) Computer Systems Security

Survey of security principles and defenses across computer systems, such as memory safety, operating systems, software isolation, symbolic verification, client device security, web security, networks, authentication, etc.

6.830 (G) (previously 6.869) Advances in Computer Vision

Traditional computer vision, e.g. Sobel filters, all the way up to modern-day CNNs and ResNet/robust ImageNet. Comes with lots of very nice and some very creepy machine-generated images.

6.122 (previously 6.046) Design and Analysis of Algorithms

Median finding, hashing, flow networks, linear optimization, randomized algorithms, amortized analysis, computability, the whole grab bag.

6.390 (previously 6.036) Introduction to Machine Learning

(Self-study) Lots of theory with interesting perspectives such as Markov decision processes.

Full Stack App Development

Learn web app development in a stack of your choice: I learned Django, HTML/CSS/JavaScript (jQuery, D3), PostgreSQL.

6.147 Battlecode

Writing instructions for an army of bots. Competitive programming plus strategy. It was also good Java practice.

Economics

14.382 (G) Econometrics

I was in this fast-paced class for the first 5 weeks. Topics like conditional IV, GMM, and bootstrap (but mostly GMM, since everything is GMM).

14.32 Econometrics

First time I learned about a lot of the really interesting applications of econometrics such as determining correlations between sociological variables like race, gender, education, wage etc., as well as ingenious methods such as IV regression (see my blog post about it!).

14.73 The Challenge of World Poverty

Turns solving the problem of poverty into something very analytically tractable. This class is solely responsible for me being interested in economics.

14.75 Political Economics and Economic Development

The impact of colonialism, whether leaders matter, what causes conflict, all through the lens of economic theory: equations and models.

14.13 Psychology and Economics

(Self-study) What are we but partially naive quasihyperbolic discounters?

Business

15.076 Analytics for a Better World

Solving all kinds of optimization problems to make the world better in a very concrete way, using large datasets and powerful optimization tools (including machine learning!).

Physics

Fluid Mechanics

A fun and challenging class where you learn to make friends with differential equations (there is no other choice really).

Modern Physics

A good introduction to special relativity and quantum mechanics.