More geometry advice: Do lots of locus problems to build up your geometric intuition. Geometry: "Geometry Revisited" by Greitzer and Coxeter, Prasolov's "Problems in Plane and Solid Geometry" (available online here), "Episodes in 19th and 20th Century Euclidean Geometry" by Honsberger, my own notes on cross ratios (work in progress, here), "Adventitious Quadrangles: A Geometrical Approach" by Rigby.
Number Theory: LeVeque's book "Fundamentals of Number Theory", Baker's "A Concise Introduction to the Theory of Numbers", Mordell's "Diophantine Equations" (out of print, but it's on Library Genesis), "250 Problems in Elementary Number Theory" by Sierpinski.Ĭombinatorics/CS: Sedgewick's "Algorithms in C" or "Introduction to Algorithms" by CLRS, "Principles and Techniques in Combinatorics", "Problem-Solving Strategies" by Engel, "Enumerative Combinatorics" by Richard Stanley, maybe also "Problems from the Book". The youtube videos by Mathologer, 3Blue1Brown, and Vi Hart are also decent.įor highschool students who want to get good at competitive/basic math: Also, Wikipedia is surprisingly helpful for self-studying math if you learn to skip past the bits that go over your head and come back to them later, and searching Google for "Notes on " usually turns up a decent exposition of any undergraduate or graduate level subject. General advice for beginners: How to Read Math, Calculus Made Easy. This is my (current) reading recommendation list, inspired by emails I've received asking for reading suggestions.
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