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What Is the Princeton University Mathematics Competition?
The Princeton University Mathematics Competition (PUMaC) is a challenging mathematics competition designed for high school students who enjoy advanced mathematical problem solving. Hosted by students at Princeton University, PUMaC brings together talented young mathematicians for a variety of individual, team, and proof-oriented mathematical events.
A Competition Built Around Mathematical Thinking
PUMaC goes beyond routine classroom mathematics by presenting students with problems that require logical reasoning, creativity, persistence, and the ability to connect different mathematical ideas.
Students encounter problems across areas such as algebra, geometry, combinatorics, number theory, and other areas of mathematics. The competition is particularly appealing to students who enjoy exploring unfamiliar problems and developing their own mathematical approaches.
Why Students Participate in PUMaC
PUMaC provides an opportunity for mathematically motivated high school students to challenge themselves beyond standard school mathematics and experience a more advanced style of mathematical problem solving.
Preparing for PUMaC can help students strengthen skills that are valuable across many mathematics competitions, including AMC, AIME, ARML, HMMT, USAMTS, and other advanced mathematics contests.
PUMaC encourages students to think creatively, recognize mathematical patterns, communicate ideas clearly, and approach unfamiliar problems with confidence. These skills can provide a strong foundation for students interested in higher-level mathematics and future STEM studies.
PUMaC Past Papers & Practice Resources
Prepare for the Princeton University Mathematics Competition with past papers and practice resources. Working through previous PUMaC problems can help students strengthen mathematical reasoning, develop creative problem-solving strategies, explore advanced topics, and become familiar with the style and difficulty of high-level mathematics competitions.
Explore PUMaC Past Papers & Practice Problems
Access PUMaC past papers and practice materials through ProfVed. Use these resources to work through challenging problems in algebra, combinatorics, geometry, number theory, individual finals, and team competition rounds while building advanced mathematical problem-solving skills.
Topics Covered in PUMaC
PUMaC problems draw from a broad range of mathematics and are designed to test reasoning, creativity, and the ability to apply mathematical ideas to challenging problems. Students should build strong fundamentals while developing deeper problem-solving skills.
Algebra
Equations, inequalities, polynomials, sequences, functions, identities, algebraic manipulation, and advanced problem-solving techniques.
Geometry
Euclidean geometry, triangles, circles, angles, similarity, transformations, coordinate geometry, and geometric reasoning.
Number Theory
Divisibility, primes, modular arithmetic, congruences, Diophantine equations, integer properties, and number-theoretic arguments.
Combinatorics
Counting techniques, permutations, combinations, recurrences, pigeonhole principle, configurations, and logical counting arguments.
Probability
Basic probability, counting-based probability, conditional probability, expected value, and probability problems requiring creative reasoning.
Advanced Problem Solving
Multi-step problems that combine different mathematical concepts and require insight, logical reasoning, creativity, and persistence.
Preparation Tip: PUMaC is not simply about memorizing formulas. Students benefit from practicing unfamiliar problems, exploring multiple approaches, and learning how to communicate mathematical reasoning clearly.
Registration & Important Dates
Planning to participate in the Princeton University Mathematics Competition (PUMaC)? Students, coaches, and teams should monitor the official PUMaC registration information carefully because registration deadlines are strictly enforced.
The official PUMaC website currently lists Saturday, November 21, 2026 as the competition date.
The detailed 2026 registration schedule has not yet been published on the official PUMaC website.
Check the official PUMaC registration page for the confirmed 2026 deadline before applying.
Who Can Participate?
PUMaC is designed for high school students. The Main Competition accepts full teams as well as individual applicants, subject to the competition's eligibility requirements.
How Registration Works
PUMaC registration is handled through the official PUMaC registration system. Coaches generally create or log in to a coach account and submit the required team or individual application.
Registration policies, acceptance decisions, payment information, and deadlines can vary by competition year. Students and coaches should therefore verify the current information before submitting an application.
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