Here are course notes from classes I've taken in the past. If you find any typos or other errors, please email me at lindrew@stanford.edu, and I'd be happy to fix them as soon as I can. Course notes marked in gray aren't quite at the level of polish I'd like yet -- expect updates in the future. Notes here that are published are done so with the permission of the course staff, but please note that all course content is owned by MIT / Stanford and their professors, while mistakes should be attributed to me (in transcription or interpretation -- they were not checked by instructors).
Relevant information
I take notes using Overleaf and my own LaTeX style package (download it here, see sample project here). These documents are meant to be a close transcription of lecture, plus any additional thoughts that come to me. I hope this makes the material easy to follow, and it also helps me be a more active learner.
Some of these notes are less clean than others, because I was still learning to live-TeX, had trouble following along with the pace of the class while typing, or was just tired. I occasionally go back to previous notes, reviewing the material myself and improving their quality. Thank you for your patience on this front!
I'm aware that some people read my notes to pass an ASE, as a replacement for going to classes, or in preparation for future coursework. I'm flattered, but please don't blame me if I miss anything! Specifically for Stanford grad students, the MATH 205/210/215 A/B notes may be helpful for qual prep, but you should definitely still read textbooks and study past exams as your primary study method.
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Notes from Stanford
- MATH 205A: Real Analysis I, Autumn 2022 (notes)
- MATH 205B: Real Analysis II, Winter 2023 (notes)
- MATH 210A: Modern Algebra I, Autumn 2022 (notes)
- MATH 210B: Modern Algebra II, Winter 2023 (notes)
- MATH 215A: Algebraic Topology, Autumn 2022 (notes)
- MATH 215B: Differential Topology, Winter 2023 (notes)
- MATH 215C: Differential Geometry, Spring 2023 (notes)
- MATH 235: Modern Markov Chains, Winter 2024 (notes)
- CS 228: Probabilistic Graphical Models, Winter 2024 (notes)
- PHYSICS 330: Quantum Field Theory I, Autumn 2022 (notes). I sat in on these lectures but did not actually take the class, so be particularly wary of the accuracy of material here!
Notes from MIT
Classes in each subject are ordered in (reverse) chronological order.
Mathematics
- 18.218: Algebraic Methods in Extremal Combinatorics, Spring 2022 (notes)
- 18.952: Theory of Differential Forms, Spring 2022 (notes)
- 18.677: Topics in Stochastic Processes, Fall 2021 (notes, joint final project with Michael Ren)
- 18.102: Intro to Functional Analysis, Spring 2021 (notes)
- 18.677: Topics in Stochastic Processes, Spring 2021 (notes, my class presentation)
- 18.905: Algebraic Topology I, Fall 2020 (notes)
- 18.676: Stochastic Calculus, Spring 2020 (notes)
- 18.784: Seminar in Number Theory, Spring 2020 (notes, my CI-M paper)
- 18.721: Intro to Algebraic Geometry, Spring 2020 (notes)
- 18.112: Functions of a Complex Variable, Fall 2019 (notes)
- 18.675: Theory of Probability, Fall 2019 (notes)
- 18.212: Algebraic Combinatorics, Spring 2019 (notes)
- 18.218: The Probabilistic Method in Combinatorics, Spring 2019 (notes)
- 18.702: Algebra II, Spring 2019 (notes)
- 18.701: Algebra I, Fall 2018 (notes)
Physics
- 8.04: Quantum Physics I, from OCW (notes)
- 8.06: Quantum Physics III, Spring 2021 (notes)
- 8.251: String Theory for Undergraduates, Spring 2021 (notes)
- 8.333: Statistical Mechanics I, Fall 2020 (notes)
- 8.051: Quantum Physics II, Spring 2020 (notes)
- 8.033: Relativity, Fall 2019 (notes)
- 8.044: Statistical Physics I, Spring 2019 (notes)
- 8.223: Classical Mechanics II, IAP 2019 (notes)
- 8.03: Physics III, Fall 2018 (notes)
Other Notes
- 5.111: Principles of Chemical Science, Spring 2022 (notes)
- 6.004: Computation Structures, Fall 2020 (notes)
- 6.036: Intro to Machine Learning, Fall 2019 (notes)
- 7.012: Introductory Biology, Fall 2018 (handwritten; large file)
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