Books / Resources

List of Books on Competition Mathematics

The prerequisite for middle school competitive mathematics is to have a solid understanding of middle school algebra and geometry. For easing into competitive mathematics during middle school, it is recommended that students start learning algebra and geometry during elementary school years. Learning high school mathematics during middle school years would definitely provide an added advantage for middle school mathematics competitions.

Provided below are several good books on competitive mathematics for interested students although, by no means, this is a comprehensive list.

1. The Art of Problem Solving, Vol. 1: the Basics by Sandor Lehoczky and Richard Rusczyk, 7th ed., AoPS.

2. The Art of Problem Solving, Vol. 2: and Beyond by Sandor Lehoczky and Richard Rusczyk, 7th ed., AoPS.

3. A Decade of the Berkeley Math Circle: The American Experience Volume I edited by Zvezdelina Stankova and Tom Rike, 2008 ed., American Mathematical Society.

4. A Decade of the Berkeley Math Circle: The American Experience Volume II edited by Zvezdelina Stankova and Tom Rike, February 2015, American Mathematical Society.

5. The Art and Craft of Problem Solving by Paul Zeitz, 2nd ed., Wiley.

6. Mathematics of Choice: Or, How to Count Without Counting by Ivan Morten Niven, 1975 ed., MAA.

7. Counting by Koh Khee Meng and Tay Eng Guan, 2002 ed., World Scientific.

8. Problem-Solving Strategies by Arthur Engel, 1999 ed. Springer.

9. Geometry Revisited by H.S.M. Coxeter and S.L. Greitzer, 9th Printing, MAA.

In general, the Art of Problem Solving books are quite comprehensive for beginners. The introductory series is suitable for middle school students preparing for competitions such as MATHCOUNTS® and the intermediate series is suitable for students preparing for more advanced competitions.

For students interested in especially MATHCOUNTS® training, AoPS MATHCOUNTS trainer is a good resource for problems and solutions.

For a more general source of problems, please see Alcumus.

Zvezdelina Stankova and Tom Rike have introduced diverse topics in mathematics in a very lucid and entertaining way in the series A Decade of the Berkeley Math Circle: The American Experience.

Problems for specific competitions, such as HMMT and PuMAC, can be found on the respective websites.  See the Math Competitions page.

In addition to the above resources, Coach Ken Monks of Lehigh Valley ARML has compiled two lists of formulae and mathematical facts for MATHCOUNTS® and high school math competitions. They can be found here: MathCounts Playbook and High School Playbook.