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 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 (Misha) |
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 (Joseph) |
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 (Misha) |
Invariants Handout / Solutions |
Misha Lavrov: Cutting up Squares |
| March 6 | Induction Handout / Solutions |
Misha Lavrov: Ramsey Theory | |
| March 13 | Games Handout / Solutions |
Games | |
| 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) Slides |
"Office hours" with Misha et al. | |
| April 3 | Probability (Victor and Misha) |
Strategies Handout / Solutions |
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| April 10 | Foundations Handout / Solutions |
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| April 17 | Random Variables Handout / Solutions |
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| April 24 | |||
| May 1 | ARML Team selection test Let me know if you can't make this! |
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| 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!
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.