Princeton University Mathematics Competition
Encyclopedia
The Princeton University Mathematics Competition (PUMaC) is an annual high school mathematics competition started in 2006. The contest is written, organized, and staffed entirely by Princeton students. In the past, it has been held variously in December, November, and January of the school year. All competitions took place on the campus of Princeton University
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Top-scoring students are invited to participate in the Individual Finals, where finalists are given one hour to complete three proofs. The proofs are graded (by Princeton students) during the Mini-Events, and results are announced a few hours later.
On the day of the competition, no calculators or other computational aids are allowed in any part of the competition. Computers may be used on the Power Test.
) is needed to solve all of the problems, but finding the solutions requires much more ingenuity than is typically required in a high school curriculum. Problems are similar in difficulty to those found on the AIME, ARML, and HMMT individual tests. In the past, Division A students in the top 10 have scored between 20 and 30 points out of 40 on a given subject test.
Notably, in 2010, the all-star A division attracted all of the national championship ARML teams from 2002-2010. Since PUMaC went international starting in 2009, teams from as far away as Beijing and Bulgaria have competed. Since the competition among these teams is very intense, the PUMaC staff organized a B division designed for local high schools. Only teams consisting of students from a single high school are allowed to compete in Division B to ensure that the competition can be fun and winnable for non-powerhouse teams as well.
Participants were also free to explore campus and the surrounding town on their own.
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
.
Format
Teams of eight high school students compete in individual and team events:- The Power Test is distributed by email one week before the competition. It is a proof-based test with statements all relating to a central topic (for example, the 2010 Power Test was about Graph TheoryGraph theoryIn mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
). Teams can work together and use any non-living resources. It is due the morning of the competition and handed in at registration. - Students participate in two individual rounds. Individual tests are offered in four subjects: Algebra, Geometry, Combinatorics, and Number Theory. Students choose any two out of the four, though only the top five scores in any subject test count toward the team's score. In previous years, two versions of each subject test were available: a harder test for Division A students and an easier one for Division B students.
- The Team Test, like the Power Test, is also a collaborative event. However, it is shorter (on the order of 1 hour) and has numerical answers (as opposed to proofs).
Top-scoring students are invited to participate in the Individual Finals, where finalists are given one hour to complete three proofs. The proofs are graded (by Princeton students) during the Mini-Events, and results are announced a few hours later.
On the day of the competition, no calculators or other computational aids are allowed in any part of the competition. Computers may be used on the Power Test.
Difficulty
The Individual tests are designed such that only high school math (not including calculusCalculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
) is needed to solve all of the problems, but finding the solutions requires much more ingenuity than is typically required in a high school curriculum. Problems are similar in difficulty to those found on the AIME, ARML, and HMMT individual tests. In the past, Division A students in the top 10 have scored between 20 and 30 points out of 40 on a given subject test.
Notably, in 2010, the all-star A division attracted all of the national championship ARML teams from 2002-2010. Since PUMaC went international starting in 2009, teams from as far away as Beijing and Bulgaria have competed. Since the competition among these teams is very intense, the PUMaC staff organized a B division designed for local high schools. Only teams consisting of students from a single high school are allowed to compete in Division B to ensure that the competition can be fun and winnable for non-powerhouse teams as well.
Previous Years
The new PUMaC website contains an archives section with test questions and solutions from previous years.| Year | Date of Competition | Director |
|---|---|---|
| 2011 | November 19, 2011 | Minh-Tam Trinh '14 |
| 2010 | November 20, 2010 | Sterling Chu '13 |
| 2009 | November 21, 2009 | Arthur Safira '12 |
| 2008 | January 31, 2009 | Adam Hesterberg '11 |
| 2007 | November 10, 2007 | Nathan Savir '09 |
| 2006 | December 16, 2006 | Nathan Savir '09 |
Mini-Events
The mini-events at PUMaC take place in the afternoon, between lunch and the Awards Ceremony. In 2010, three mini-events were offered:- The Math Bowl, a Quiz bowl-like event where questions are math-related. Question categories included mental math, identifying famous mathematicians based on achievements or biographical details, questions about science and technology, and questions involving the history of Princeton. Sixteen teams participated in a single-elimination bracket.
- A Rubik's CubeRubik's CubeRubik's Cube is a 3-D mechanical puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.Originally called the "Magic Cube", the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 and won the German Game of the Year special award for Best Puzzle that...
event, where participants competed against each other solving a 3x3x3 cube. The winner faced off with former world record holder Shotaro Makisumi '12. - A chess event hosted by the Princeton Chess Club.
Participants were also free to explore campus and the surrounding town on their own.
Related competitions
- The Caltech Harvey Mudd Math Competition
- The Duke University Math Meet
- The Harvard–MIT Mathematics Tournament
External links
- PUMaC, official website (PUMaC 2010)
- PUMaC 2009 website
- PUMaC 2008-09 website
- PUMaC 2007 website
- PUMaC 2006 website