Resources for mathematics competitions

The Art of Problem Solving hosts this AoPSWiki as well as many other online resources for students interested in mathematics competitions. Look around the AoPSWiki. Individual articles often have sample problems and solutions for many levels of problem solvers. Many also have links to books, websites, and other resources relevant to the topic.

Training Websites

AMC Problem Trainer: https://amctrainer.com/play

Free eBook of Mathematical Formulas and Strategies

130+ page free eBook of Mathematical Formulas and Strategies: https://www.omegalearn.org/thebookofformulas

Math Courses

Introduction To Number Theory: https://thepuzzlr.com/math-courses

Free AMC 8 Bootcamp covering all the essential concepts: https://thepuzzlr.com/courses/amc-8-bootcamp/

List of Resources

Elementary: https://www.omegalearn.org/elementary-competition-math

Middle: https://www.omegalearn.org/middle-competition-math

High: https://www.omegalearn.org/high-competition-math

Everything you need to know for the AMC 8: https://thepuzzlr.com/courses/amc-8-bootcamp/

AMC 8 Fundamentals Class: https://www.omegalearn.org/amc8-fundamentals

AMC 8 Video Solutions Playlist: https://www.youtube.com/watch?v=TRGPF3BxujE&list=PLbhMrFqoXXwmwbk2CWeYOYPRbGtmdPUhL

AMC/MATHCOUNTS Class: https://www.omegalearn.org/amc8-advanced

Math Competition Classes

Art of Problem Solving hosts classes that are popular among many of the highest performing students in the United States. AoPS Problem Series.

Math Competition Problems

Problem Books

Many mathematics competitions sell books of past competitions and solutions. These books can be great supplementary material for avid students of mathematics.

ARML has four problem books covering most ARML as well as some NYSML competitions. However, they are generally difficult to find. Some can be ordered here.
MOEMS books are available here at AoPS.
MATHCOUNTS books are available here at AoPS.
AMC books are available here at AoPS.
Mandelbrot Competition books are available here at AoPS.

Problems Online

Art of Problem Solving maintains a very large database of math contest problems. Many math contest websites include archives of past problems. The List of mathematics competitions leads to links for many of these competition homepages. Here are a few examples:

Introductory Problem Solvers

Mu Alpha Theta.org hosts past contest problems.
Noetic Learning Challenge Math - Problem Solving for the Gifted Elementary Students .
Elias Saab's MathCounts Drills page.
Alabama Statewide High School Mathematics Contest homepage.
The South African Mathematics Olympiad here includes many years of past problems with solutions.
Beestar.org - Weekly problem solving challenges and honor roll ranking, Grade 1 - 8

Intermediate Problem Solvers

AoPS math contest problems and solutions
Past USAMTS problems can be found at the USAMTS homepage.
Ivana Alexandrova's Weekly Math Problems for High School Students contains good problems that will make you think and that will teach you new skills and material
The Kalva site is one of the best resources for math problems on the planet. (Currently offline. Mirror can be found at this page)
Past Colorado Mathematical Olympiad (CMO) problems can be found at the CMO homepage.
Past International Mathematical Talent Search (IMTS) problems can be found here
Brilliant is a website where one can solve problems to gain points and go to higher levels.
Clevermath Is similar to above

Olympiad Problem Solvers

AoPS math contest problems and solutions
Math and CS Research is a math and computer science publication with articles and problem sets on a wide range of topics.
Past USAMTS problems can be found at the USAMTS homepage.
The Kalva site is one of the best resources for math problems on the planet. (Currently offline - but a few mirrors are available, e.g here.)
Nick's Mathematical Puzzles -- Challenging problems with hints and solutions.
Canadian Mathematical Olympiad are hosted here by the Canadian Mathematical Society.
Problems of the All-Soviet-Union math competitions 1961-1986 - Many problems, no solutions. [Site no longer exists. Site has been replaced by a web capture]
Past International Mathematical Talent Search (IMTS) problems can be found here
Olympiad Math Madness - Stacks of challenging problems, no solutions. [Site no longer exists. Site has been replaced by a web capture]

Articles

Time Management
Pros and Cons of Math Competitions by Richard Rusczyk.
Establishing a Positive Culture of Expectation in Math Education by Sister Scholastica Award winner Darryl Hill.
Stop Making Stupid Mistakes by Richard Rusczyk.
What Questions Really Are the Stupid Questions? by Richard Rusczyk.
Learning Through Teaching
How to Write a Math Solution by Richard Rusczyk and Mathew Crawford.
Inequalities by Dr. Kiran Kedlaya
Olympiad Inequalities by Thomas J. Mildorf
Olympiad Number Theory: An Abstract Perspective by Thomas J. Mildorf
Number Theory by Naoki Sato
Olympiad Number Theory Through Challenging Problems by Justin Stevens
Barycentric Coordinates in Olympiad Geometry by Max Schindler and Evan Chen
Lifting the Exponent (LTE) by Amir Hossein Parvardi
The uvw Method by Mathias Bæk Tejs Knudsen
The Chinese Remainder Theorem by Evan Chen
Contest Reflections by Wanlin Li

A Huge List of Links

AoPS Course Recommendations

Art of Problem Solving Course Recommendations
Do you still have trouble deciding which course? Go to the above link and click contact us at the bottom of the Course Map section to ask for personal recommendations!