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!
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 Handout |
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 Handout |
Emily: Short math contest Nov. 2013 Mandelbrot Regional + National |
| February 26 | Probability Handout |
C.J.: The sum 1 + 1/4 + 1/9 + 1/16 + ... | |
| March 5 | Expected Values and Recursion Handout |
Annie: Short math contest ARML 2001 Individual Round |
|
| March 12 | Markov Chains Handout |
Misha: Towers of Hanoi | |
| March 19 | C.J.: Practice math contest | ||
| March 26 | Emily and Annie: Graph Theory Handout |
Andrew: Short math contest 2006 Euclid Contest |
|
| April 2 | Calculus (Misha) |
Asymptotic Calculus Handout |
Misha: Counting beads on necklaces |
| April 9 | Optimization Problems Handout |
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!
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.