Current classes - Number theory - High school math - College math Everything on this page is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License. More recent notes are available at http://holdenlee.wordpress.com/math-notes/. Number Theory Here are various notes on number theory I've written up on number theory. Update: Please use this googledoc to report typos and for general comments and discussion on the text. I will check it periodically. Proof of prime number theorem for arithmetic progressions: analytic-nt.pdf Algebraic number theory, class field theory, and complex multiplication: ant.pdf I've compiled all my number theory notes in the following open-source textbook. Textbook (NEW: source now on github.) For recent updates, please see the googledoc. Note much of this is still pretty sketchy; I've extracted the more complete parts into the two documents above. Contributions and corrections are welcome; please email me at holdenlee@alum.mit.edu. High school math Gliya geometry curriculum: I wrote lessons on introduction to geometry, angles, congruent triangles, similar triangles, constructions, and the angle bisector theorem. High school math club materials: Materials I used for ERHS math club, 2007-2009. Short-answer based Sums and products, source Number theory, source Triangles Proof-based Box principle, source Extremal, invariance, and induction, source Inequalities Combinatorics Geometry Contests "Pre-test" part 1, part 2 End of year contest, source (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 ? in OMC. Inequalities, Holder and Minkowski, strategies Functional equations (solutions) Week 2 exam Final exam Team contest 2010, Dallas, round 2 (solutions) 2010, Santa Cruz, round 1 (solutions) 2010, Santa Cruz, round 2 (solutions) 2010, Santa Cruz, round 3 (solutions) 2011, Santa Cruz, round 2 2011, Santa Cruz, round 3 I wrote several lectures for Online Math Circle. (All lectures) Lecture 1: The Beauty of Mathematics Lecture 4: Combinatorial Number Theory Lecture 8: Polynomials, Part 1 Lecture 11: Complex Numbers Lecture 13: Polynomials, Part 2 (Polynomials and number theory) Lecture 19: Generating functions Lecture 20 (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. 2012-2013 classes 18.318: Geometric graph theory lecture notes and source 18.404: Theory of computation lecture notes 18.787: Topics in number theory (abelian varieties and p-divisible groups) lecture notes (warning: poorly edited) 18.965: Geometry of manifolds lecture notes Source (may not be updated) Previous classes (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 Some problems with solutions Analysis Real analysis (18.100C), errata Measure theory (18.125), source code, problem sets (Note several sections in the latter half are incomplete.) Differential forms (18.952) psets Geometry Topology (18.901), errata Combinatorics Probabilistic methods (18.997, spring 2011), source code, problem sets Number theory Additive number theory (18.784) final paper on finite field Waring's problem Automorphic forms (18.785) psets
 Last edited 09/20/2014