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 A19. (Porter Hall is in the northwestern corner of the CMU campus, and is most easily accessible via Frew St. The door is sometimes locked on weekends; call Misha at (919) 702-2400 if you can't get in.)

The typical ARML practice begins with a lesson on a mathematical technique, together by a problem-solving session, which lasts until around 5:30 PM. After a break for pizza, one of the coaches or a guest might give a talk, or we might have a short practice contest lasting about an hour.

A tentative schedule for the spring semester of 2017 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
January 15 Writing Proofs
(C.J. and Misha)
Logic and Definitions I
Handout / Solutions
Misha: Pell's Equation
January 22 Logic and Definitions II
Misha: Short math contest
AMC 10 / Extra Contest / Solutions
January 29 The Pigeonhole Principle
Handout / Solutions
Misha: Probability Paradoxes
February 5 The Extremal Principle
Handout / Solutions
Go home and watch the Superbowl!
February 12 C.J.: Practice math contest
February 19 Combinatorics
(Patrick and Victor)
Counting Techniques
Emily: Short math contest
Nov. 2013 Mandelbrot Regional + National
February 26 Probability
C.J.: The sum 1 + 1/4 + 1/9 + 1/16 + ...
March 5 Expected Values and Recursion
Annie: Short math contest
ARML 2001 Individual Round
March 12 Markov Chains
Misha: Towers of Hanoi
March 19 C.J.: Practice math contest
March 26 Emily and Annie: Graph Theory
Andrew: Short math contest
2006 Euclid Contest
April 2 Calculus
Asymptotic Calculus
Misha: Counting beads on necklaces
April 9 Optimization Problems
David: Short math contest
Problems from SDML 2012-2013
April 16 Easter: no ARML practice
April 23 Andrew and David: 3D Geometry Chris Cox: Sperner's Lemma
April 30 ARML Team Selection Quiz Misha: Cake Cutting
May 7 ARML Preparation
May 14
May 21
May 28
June 2-3 ARML competition at Penn State University


The team captain is Andrew Gu <a1267ab@gmail.com>, a junior at Allderdice 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

This website also has the complete schedule for ARML practices in the fall 2015, spring 2016, and fall 2016 semesters.

There are also old practice materials from 2012, 2013, and 2014.

Last updated April 18, 2017. Misha Lavrov <mlavrov@andrew.cmu.edu>