Everything on this page is licensed under a Creative) Commons Attribution-ShareAlike 3.0 Unported License. Notes for seminars and talks are available at my blog http://holdenlee.github.io/blog/notes.html
Most of the source code is available either below or on github. To compile the source you’ll need the LaTeX template files (see the readme for instructions).
Please do contact me if you find typos, want to help improve the notes, want source code, etc. I don’t always post/update the source code but I will if you poke me.
Number Theory
I’ve compiled all my number theory notes in the following open-source textbook (shortlink: tiny.cc/ntbook). This version does not contain drafts in progress; for that see the github page.
Source code is available at the dedicated repository https://github.com/holdenlee/number-theory. Contributions and corrections are welcome; send me a pull request or email me at holdenlee@alum.mit.edu.
The number theory notes are made of the following two parts:
- Proof of prime number theorem for arithmetic progressions: tiny.cc/annt
- Algebraic number theory, class field theory, and complex multiplication: tiny.cc/algnt
High school math
- Gliya geometry curriculum:
- I wrote lessons on introduction to geometry, angles, congruent triangles, similar triangles, constructions, and the angle bisector theorem. Some sample sections (called “cells”) follow.
- Angles: roadmap
- Congruent triangles
- Similar triangles
- I wrote lessons on introduction to geometry, angles, congruent triangles, similar triangles, constructions, and the angle bisector theorem. Some sample sections (called “cells”) follow.
- High school math club materials: Materials I used for ERHS math club, 2007-2009.
- Short-answer based
- Proof-based
- Contests
- “Pre-test” part 1, part 2
- End of year contest (the bunny problem has a simpler solution, see AwesomeMath UTD contest)
- AwesomeMath materials (all source files)
- Algebra 3.5, 2010: I taught the second week at Santa Cruz. Notes below.
- Polynomials (solutions) (Note that part of these notes appear in lectures 8 and 13 in OMC.)
- Inequalities, Holder and Minkowski, strategies
- Functional equations (solutions)
- Week 2 exam
- Final exam
- Team contest
- Algebra 3.5, 2010: I taught the second week at Santa Cruz. Notes below.
- I wrote several lectures for Online Math Circle. Source for all lectures
- Lecture 1: The Beauty of Mathematics
- Lecture 4: Combinatorial Number Theory
- Lecture 8: Polynomials, Part 1, solutions
- Lecture 11: Complex Numbers
- Lecture 13: Polynomials, Part 2 (Polynomials and number theory)
- Lecture 18: Generating functions
- Lecture 21 (with Yoni Miller): Principle of Inclusion and Exclusion
- Lecture 23: Rearrangement inequality
College math
Various notes and homeworks I have written up for math subjects. Most of the source is available on github, or given below. (There are also miscellanous notes there that are not listed below.)
See also this googledoc for notes on Part III classes by other students.
Note: the earlier notes are pdfs compiled from Word. I’ve given errata for them since the original word documents are corrupted and uneditable. Now I’ve learned better and use LaTeX instead.
- Algebra
- Linear algebra notes
- Abstract algebra notes (18.701-2)
- Group theory (18.701-2), some problems with solutions
- Analysis
- Real analysis (18.100C), errata
- Measure theory (18.125) (Note several sections in the latter half are incomplete.)
- Functional analysis (source (Part III, Fall 2013) (Ask me for a link to the ShareLaTeX.)
- Distribution theory (source)
- Geometry
- Geometry of manifolds (18.965)
- Topology (18.901), errata
- Combinatorics
- Geometric graph theory (18.318)
- Probabilistic methods (18.997, spring 2011), problem sets
- Extremal and probabilistic combinatorics (Part III, Spring 2014)
- Noise sensitivity source (Part III essay)
- Ramsey theory source (Part III, Fall 2013)
- Arithmetic combinatorics googledoc about notes (Part III, Fall 2013)
- Additive combinatorics and equidistribution source (Part III, Spring 2014)
- Algebraic methods in incidence theory source (Part III, Spring 2014)
- Computer science
- Theory of computation (18.404)
- Number theory
- Additive number theory (18.784) final paper on finite field Waring’s problem
- Automorphic forms (18.785) psets
- Abelian varieties and p-divisible groups (18.787) (warning: poorly edited)
- Elliptic curves source (Part III, Fall 2013)