报名须知

赛事第一阶段：The Power Competition
赛事范围：Power Round Test
赛事环节介绍：Power Round Test（能力测试）:?以证明题为主的测试，各支队伍以团队合作形式答题，作答时间不限，需在截止日期前提交。
注意：参加 The Main Competition的团队和个人也需进行该轮测试。

赛事第二阶段：The Main Competition
赛事范围：Individual Round, Team Round and Live Round
赛事环节介绍：
Individual Round（个人测试）：每位参赛者需参加两项测试，即从代数、组合、几何和数论四个选项中任选两项进行测试，每项测试时间60分钟。该轮测试需个人独立作答。
Team Round（团队测试）：各支队伍将得到作答要求和一套试题，需在约30分钟内（具体时长将在学术活动当天公布）以团队合作形式答题，该轮测试为非证明题。
Live Round（实时测试）：各支队伍同时答题，答题过程中，各支队伍可以通过实时评分系统了解其他队伍的答题进度。

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?？奔溆跋?，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

---

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