報(bào)名須知

賽事第一階段：The Power Competition
賽事范圍：Power Round Test
賽事環(huán)節(jié)介紹：Power Round Test（能力測(cè)試）:?以證明題為主的測(cè)試，各支隊(duì)伍以團(tuán)隊(duì)合作形式答題，作答時(shí)間不限，需在截止日期前提交。
注意：參加 The Main Competition的團(tuán)隊(duì)和個(gè)人也需進(jìn)行該輪測(cè)試。

賽事第二階段：The Main Competition
賽事范圍：Individual Round, Team Round and Live Round
賽事環(huán)節(jié)介紹：
Individual Round（個(gè)人測(cè)試）：每位參賽者需參加兩項(xiàng)測(cè)試，即從代數(shù)、組合、幾何和數(shù)論四個(gè)選項(xiàng)中任選兩項(xiàng)進(jìn)行測(cè)試，每項(xiàng)測(cè)試時(shí)間60分鐘。該輪測(cè)試需個(gè)人獨(dú)立作答。
Team Round（團(tuán)隊(duì)測(cè)試）：各支隊(duì)伍將得到作答要求和一套試題，需在約30分鐘內(nèi)（具體時(shí)長(zhǎng)將在學(xué)術(shù)活動(dòng)當(dāng)天公布）以團(tuán)隊(duì)合作形式答題，該輪測(cè)試為非證明題。
Live Round（實(shí)時(shí)測(cè)試）：各支隊(duì)伍同時(shí)答題，答題過(guò)程中，各支隊(duì)伍可以通過(guò)實(shí)時(shí)評(píng)分系統(tǒng)了解其他隊(duì)伍的答題進(jìn)度。

注意事項(xiàng)：

1. 開課時(shí)間：根據(jù)學(xué)生時(shí)間組班
2. 學(xué)員須知：
（1）受不同學(xué)校開學(xué)時(shí)間影響，班課具體開學(xué)時(shí)間可能會(huì)有微調(diào)，具體時(shí)間以班課學(xué)員為主
（2）班課時(shí)間一經(jīng)確認(rèn)不再變更，開課后每課若有超半數(shù)學(xué)員按時(shí)出席，則當(dāng)天正常上課，如有特殊情況請(qǐng)?zhí)崆案嬷獏f(xié)調(diào)

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課程大綱

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