MIT Course Notes

18.701 🍂 Fall 2025 Algebra I A demanding introduction to abstract algebra and linear algebra, dedicating roughly equal time to each. Begins with group and vector space definitions, and covers topics such as Jordan Normal Form, the Crystallographic Restriction, Sylow's Theorems, Sylvester's Law of Inertia, the Spectral Theorem, and matrix groups. 6.1220 🌸 Spring 2026 Design and Analysis of Algorithms A survey of classic algorithms and data structures (Union-Find, MST, Max Flow, MCMC, and FFT), fundamental elements of algorithmic design (e.g., amortized analysis, hash functions, linear programming), and specialized models of computation (e.g., approximation, streaming, and sublinear algorithms). 6.300 ☀️ Summer 2026 Signal Processing An introduction to Fourier analysis and its applications to audio and images. Topics include Fourier series and transforms, the Discrete Fourier Transform, sampling, convolution, filtering, and noise reduction. Notes taken through Lecture 18 of 22. 18.650 ☀️ Summer 2026 Fundamentals of Statistics A fast-paced introduction to foundational statistical concepts and methods from a mathematical perspective. The original course occasionally handwaves the mathematical detail; these notes fill in some of those gaps. Notes taken through Lecture 25 of 32.