Recommended Links

Here are a bunch of links to other resources of various types, not originally designed by me.

Math Competitions

The following links are to competitions which I think are useful for practice.

• HMMT: the Harvard-MIT Mathematics Tournament. This consists of both a November competition and a Feburary one, with the latter being significantly harder than the former. Since these problems are written by Harvard and MIT students, many of whom were successful competitors themselves, the difficulty of the problems here can far exceed those found in other high school contests. I particularly like the tests from 2003 to 2010; while not as hard as rounds today, they contain some very nice problems.

• Mandelbrot: a contest run by Sam Vandervelde which ended in 2019. While many of the problems are not free, I highly recommend getting the books for some nice AIME practice - many of the problems are very good! In addition, since the contest ended, all problems from 2009 to 2019 are publicly available on the Mandelbrot website, and these offer a good starting point into the archivesof the contest.

• NIMO/OMO: two different competitions hosted on the same site. The NIMO consists of anywhere between five to seven contests a year, the majority of which contain 8 problems to be solved in a 40 minute span. The OMO is a team competition with 30 problems to be solved in the span of a week. These contests are known for having high-quality problems on a consistent basis.

• Stanford Math Tournament: a math tournament run by Stanford students. Many of SMT's problems are quite good, though for best results, see 2011 - 2014. (The A-Star Math Tournament took its place in 2015 and 2016; there are some good questions from those two years as well.)

Problem Sets

These are miscellaneous problem sets that are worth looking at.

• TJHSST Black Book of Problem Solving: Gems (new!): A collection of problems compiled by Thomas Jefferson High School of Science and Technology students. These problems used to be available on the TJ website, it seems, but have unfortunately been taken down. This PDF was extracted from CourseHero, and I am hosting it here so that the problems are more readily available; this is a piece of history that should not be behind an arbitrary paywall.