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 6 PM or 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.

Unfortunately, there will not be after-pizza talks from March 27 to May 29. Practice will end at 6 PM, though students are welcome to stay and ask questions of any mathematical nature.

Here is a tentative schedule for the spring semester of 2016. 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
January 17 Polynomials
Solving Polynomials
Handout / Solutions
Misha Lavrov: Rational Approximations
January 24 Not Solving Polynomials
Handout / Solutions
Christopher Cox: Hat-Guessing Games
January 31 Practice math contest (2008 AMC 12)
Art of Problem Solving link
Misha Lavrov: The Golden Ratio
February 7 Misc. Algebra
Complex numbers
Handout / Solutions
David Roe: The p-adic Numbers
February 14 Arithmetic and geometric series
Handout / Solutions
Misha Lavrov: Counting Roots and Intersections
February 21 Practice math contest (St. Petersburg, 2004)
Selected problems / Solutions
Kevin Carde: The Laurent Phenomenon
February 28 Writing Proofs
Handout / Solutions
Misha Lavrov: Cutting up Squares
March 6 Induction
Handout / Solutions
Misha Lavrov: Ramsey Theory
March 13 Games
Handout / Solutions
March 20 Practice math contest (1998 ARML Power Round)
Contest / Solutions
Misha Lavrov: The Game of Nim
March 27 Practice math contest (ARML Individual Round)
"Office hours" with Misha et al.
April 3 Probability
(Victor and Misha)
Handout / Solutions
April 10 Foundations
Handout / Solutions
April 17 Random Variables
Handout / Solutions
April 24
May 1 ARML Team selection test
Let me know if you can't make this!
May 8 ARML Preparation
May 15
May 22
May 29
June 3-4 ARML Competition at Penn State University


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

This website also has the complete schedule for ARML practices in the fall 2015 semester.

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

Last updated April 18, 2016. Misha Lavrov <mlavrov@andrew.cmu.edu>