Art of Problem Solving
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The Art of Problem Solving began as a set of two books coauthored by Richard Rusczyk and Sandor Lehoczky. The books, which are about 750 pages together, are for students who are interested in mathematics or compete in mathematics competitions.
Volume 1: The Basics is appropriate for students just beginning in math contests, while Volume 2: and Beyond is for more advanced students. Both books feature hundreds of problems from actual mathematics competitions, such as the American Mathematics Competitions (AMC), the United States of America Mathematical Olympiad (USAMO), the Mandelbrot Competition, Mu Alpha Theta, Mathematics and Informatics Quarterly magazine, and the International Mathematical Olympiad (IMO).
Although the books discuss many topics that occur frequently in mathematics contests (and, perhaps, in problem solving in general), they are not just a collection of tricks. Instead, the books teach students to learn and understand methods, which allows them to solve a wide variety of problems beyond the types presented in the books.
The Art of Problem Solving is now also a website (http://www.artofproblemsolving.com). It features many resources for students and teachers interested in math, including:
- an online forum (http://www.artofproblemsolving.com/Forum/index.php) for students and instructors to discuss topics in problem solving, as well as share and solve mathematics problems.
- free "Math Jams (http://www.artofproblemsolving.com/Community/AoPS_Y_Math_Jams.php)", called this because they are improvisational problem solving sessions guided by Art of Problem Solving instructors.
- inexpensive online classes (http://www.artofproblemsolving.com/Classes/AoPS_C_About.php) covering a variety of mathematical topics, including algebra, combinatorics, geometry, inequalities, and number theory. The classes include 18-24 hours of interactive classes, challenge sets, and extra practice problems.
- a collection of articles (http://www.artofproblemsolving.com/Resources/AoPS_R_Articles.php) relating to math (such as "The Calculus Trap") and links to other sites with mathematical content