AoPS Articles

Below are some articles of interest to students of problem solving. We expect to add more occasionally, so come back every once in a while.

How to Write a Solution
Why Discrete Math Is Important
Stop Making Stupid Mistakes
The Calculus Trap
Proofs Without Words Gallery
Building a Successful MATHCOUNTS Program by Jeff Boyd, coach of multiple National Championship teams
Establishing a Positive Culture of Expectation in Math Education by Darryl Hill, Sister Scholastica Award winner and coach of numerous USAMO participants.
What is Problem Solving?
Pros and Cons of Math Competitions
Stupid Questions
Learning Through Teaching
Article about Art of Problem Solving in Focus, the Newsletter of the Mathematical Association of America
Discrete Math Problem Solving for Middle School Students Presented by Dave Patrick at NCTM 2008 in Salt Lake City, UT.
Three Types of Probability
Excerpts from AoPS Introduction Texts
Slideshow used by Richard Rusczyk in his Life After MATHCOUNTS talk at National MATHCOUNTS.

Articles for Olympiad Students

How to Write a Solution
Inequalities by Dr. Kiran Kedlaya
Inequalities by Thomas J. Mildorf
Olympiad Number Theory: An Abstract Perspective by Thomas J. Mildorf
Number Theory by Naoki Sato

Award Winning Papers

Below are papers by Art of Problem Solving Community members that won awards in major high school research competitions. Many readers may find the mathematics in these papers tough to follow; we share them to give students an idea what is expected of top papers in competitions such as the Siemens Competition, the Intel Science Search, and the Davidson Fellows Program.

On the expected winding number of a random walk on the unit lattice by Yi Sun, who won a $75,000 scholarship in the Intel Science Talent Search.
Cayley graphs formed by conjugate generating sets of S_n by Jacob Steinhardt, who won a $40,000 scholarship in the Siemens Competition.
Asymptotic behavior of certain Ducci sequences by Greg Brockman, who won a $25,000 scholarship in the Intel Competition.
Character sums and Ramsey properties of generalized Paley graphs by Nicholas Wage, who won a $25,000 scholarship in the Intel Competition.

Student Papers

Below are papers written by students. If you have a paper you would like to submit for consideration, please contact us. Note that the paper should be in PDF format for submission. We do not expect all papers to be as advanced as the ones below!

A Proof of Heron's Formula by Miles Edwards. An innovative proof of Heron's Formula. This article was published in American Mathematical Monthly.
Powerful Technique for Proving Remarkable Trigonometric Identities by Zach Abel and Fred Sala. A challenging article on trigonometric manipulation and cyclotomic polynomials.
Polyominoes by Amanda Beeson, Thomas Belulovich, Connie Chao, Jon Chu, Eric Frackleton, Li-Mei Lim, Travis Mandel. Learn some cool counting methods by reading the authors' exploration of various classes of polyominoes.
Partitions of Integers by Joseph Laurendi. A variety of problem solving approaches for problems involving partitions.
A Few Elementary Properties of Polynomials by Adeel Khan. Includes many applications to AIME and Olympiad problems.
Predicting Improper Fractional Base Integer Characteristics by Billy Dorminy, written for the Intel International Science and Engineering Fair (ISEF).