Western PA ARML

About the team

Western PA ARML is a program for high school students interested in mathematics and in math competitions. At weekly practices, students learn math that isn't normally part of the high school curriculum, focusing on problem-solving techniques. At the end of May, we send a team of 15 students to participate in the ARML competition.

We welcome students of all abilities to attend our practices. The only requirement is being excited about math!

Practice schedule

Practices are held throughout the year every Sunday from 4 PM to 7 PM at Carnegie Mellon University in Porter Hall, room A20. (Porter Hall is in the northwestern corner of the CMU campus, and is most easily accessible via Frew St.)

The typical ARML practice begins with a short lesson on a mathematical technique, followed by a problem-solving session until around 5:30 PM. After a break for pizza, one of the coaches or a guest will give a talk on a topic not necessarily related to competition math, showcasing the infinite variety of mathematics.

A tentative schedule for the fall semester of 2015 is provided. Check back for up-to-date information about the topics that will be covered in practices, the speakers for the after-pizza talks, and handouts from previous practices.

Date Topic Subtopic After-pizza talk
September 13 Number Theory
(Joseph and Misha)
Joseph: Modular arithmetic
Handout / Solutions
Misha Lavrov: Perfect Numbers
September 20 Misha: Divisibility
Handout / Solutions
Misha Lavrov: What's the Biggest Number?
September 27 Joseph: Fermat's little theorem
Handout / Solutions
Christopher Cox: The Math of Juggling
October 4 Misha: Diophantine equations
Handout / Solutions
Misha Lavrov: Mathematical Games
October 11 Practice math contest
AMC 12A 2006 / AIME I 2006 / USAMO 2006
Mor Harchol-Balter: Markov Chains
October 18 Geometry
(David and Pranav)
Misha: The area method
Handout / Solutions
Misha Lavrov: Tangle Theory
October 25 Misha & David: Circles
Slides (from 2013)
Misha Lavrov: Euler's Formula
November 1 Pranav: Triangle geometry
November 8 Pranav: Coordinate geometry
Handout / Solutions
Misha Lavrov: What is computation?
Link to the poem
November 15 Practice math contest
AMC 12A 2007 / AIME I 2007 / USAMO 2007
November 22 Combinatorics
(Victor and Misha)
Victor: Permutations and binomials
Handout / Solutions
David Sisson: Differential Geometry
November 29 Practice math contest
AMC 10B 2008 / AIME II 2008
December 6 Misha: Counting strategies
Handout / Solutions
Misha Lavrov: A Grid Problem
December 13 Victor: Recursions
Handout / Solutions


The team captain is Gabe Ren <gaberen@gmail.com>, a senior at North Allegheny Senior High School.

Our faculty sponsor is Po-Shen Loh, a professor in the math department at CMU.

If you have any comments or questions or would like to know more about ARML, please don't hesitate to email any of the coaches!

Previous years of ARML

On this website, you can also find old practice materials from 2012, 2013, and 2014.

Last updated December 28, 2015. Misha Lavrov <mlavrov@andrew.cmu.edu>