描述
报名须知
团队由 8 名学生组成,团队不必是高中,可以是区域团队或家庭教育团队,但必须来自明确定义的地理区域。从2017年开始,我们不再接受半团队申请,而是接受个人申请主赛(详见下文)。
PUMaC有两个不同的比赛:Power Competition,团队只参加Power Round,以及Princeton University的Main Competition,Power Round是其中的一个部分。(Power Round 是一项基于证明的测试,在比赛前一周发布并在规定的截止日期上交。)团队最多只能注册两场比赛中的一场。
竞赛时间和地点:
动力赛题目将于2023年3月23日线上发布,参赛者需要在3月30日前提交答案。
主赛将于2023年4月1日在位于美国新泽西州的欧林斯顿大学举行。
截止注册:
2023年2月20日星期一下午五点(美东时间)
通知报名结果:
2023年2月24日
注意事项:
1. 开课时间:根据学生时间组班
2. 学员须知:
(1)受不同学校开学时间影响,班课具体开学时间可能会有微调,具体时间以班课学员为主
(2)班课时间一经确认不再变更,开课后每课若有超半数学员按时出席,则当天正常上课,如有特殊情况请提前告知协调
3. 线上课程:全程互动直播形式,如有需要可以提供课程录播服务
4. 快速拼班:联系顾问
导师简介
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