Princeton University Mathematics Competition普林斯顿大学数学竞赛（简称：PUMaC）自2006年起由Princeton University Math Club普林斯顿大学数学俱乐部全权举办，并由普林斯顿大学的学生进行组织。
该竞赛是一项面向国际高中生的世界范围内最顶尖的数学学科竞赛，每年都将汇聚世界各地热爱数学的优秀中学生，共同分享数学学科的乐趣，并进行专业竞技，角逐各大奖项。
PUMaC旨在激励并培养高中生对数学学科的兴趣和热爱，让学生接触到创造性思维和严谨的应用技能。同时，帮助学生们享受解决问题的乐趣，并发现传统意义上枯燥和深奥问题中所蕴含的趣味。
PUMaC普林斯顿大学数学竞赛备赛辅导课程大纲
1、Number Theory
Essential Topics（1）：Prime factorization
Extended Details (Divison A and Beyond)：
—Number of factors
—Sum/Product of factors
—LCM and GCD
—Euclidean Algorithm and Bézout's Theorem
Essential Topics（2）：Congruence and Modular Algebra
Extended Details (Divison A and Beyond)：
—Chinese Remainder Theorem(CRT)
—Euler’s Theorem/Fermat's Little Theorem
—Wilson's Theorem
Essential Topics（3）：Diphantine Equations
Extended Details (Divison A and Beyond)：
—*Pell's Equation and Approximation Method
2、Algebra
Essential Topics（1）：Resursive Sequences
Extended Details (Divison A and Beyond)：
—Characteristic Equation Method
—Conjecture and Mathematical Induction Proof
Essential Topics（2）：Functions and Equations
Extended Details (Divison A and Beyond)：
—Gaussian/Floor function
—Functional Equations
Essential Topics（3）：Inequalities and Extreme Value Problems
Extended Details (Divison A and Beyond)：
—Cauchy inequality
—Jensen's inequality
—Weighted AM-GM Inequality
—Rearrangement Inequality and Chebyshev Inequality
Essential Topics（4）：Polynomials
Extended Details (Divison A and Beyond)：
—Fundamental Theorem of Algebra (Polynomial Factorization)
—Generalized Remainder's Theorem
—Rational Root Theorem
—Vieta's Theorem and Newton's Sums
Essential Topics（5）：Complex numbers
Extended Details (Divison A and Beyond)：
—De Moivre's Theorem and Roots of unity
—Rotation, Translation and Complex Vector Method
3、Geometry
Essential Topics（1）：Basic Geometry (Triangles and Polygons)
Extended Details (Divison A and Beyond)：
—The Law of Sines, The Law of Cosines
—Area Method and Heron's formula
—Centers of triangle
—Menelaus's theorem, Ceva's theorem, Stewart Theorem
Essential Topics（2）：Circles
Extended Details (Divison A and Beyond)：
—Inscribed and circumscribed polygon/Circle, Cyclic Quadrilateral
—Ptolemy's theorem, Butterfly Theorem, Simson's Theorem
Essential Topics（3）：Basic Analytic Geometry
Extended Details (Divison A and Beyond)：
—Ellipse, *Parabola and Hyperbola
Essential Topics（4）：Basic Solid Geometry
Extended Details (Divison A and Beyond)：
—*Euler's Polyhedron Formula
4、Combinatorics
Essential Topics（1）：Basic Counting Principle
Extended Details (Divison A and Beyond)：
—Basic Counting Principle
Essential Topics（2）：Permutations and Combinations
Extended Details (Divison A and Beyond)：
—Advanced problems in combinatorics
Essential Topics（3）：Logic reasoning
Extended Details (Divison A and Beyond)：
—Pigeonhole principle
Essential Topics（4）：*Baisc Graph Theory
Extended Details (Divison A and Beyond)：
—Ramsey's Theory
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