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2021 PUMaC輔導班

 

2020年普林斯頓大學高中數學競賽將推遲至2021年3月正式舉辦,普林斯頓大學高中數學競賽是一項由普林斯頓數學俱樂部發起并組織的國際高中生數學競賽,迄今已成功舉辦14屆。就當前全球疫情形勢,該項賽事本年度將轉為線上舉辦.

班型:3-8人

課時:30小時 ?在線直播互動課程

快速組班:微信:linsitute4

描述

論文代寫
國際競賽流程

報名須知

 

賽事第一階段:The Power Competition
比賽時間:2021年3月18日-3月25日(以美國東部時間為準)
賽事范圍:Power Round Test
賽事環節介紹:Power Round Test(能力測試):?以證明題為主的測試,各支隊伍以團隊合作形式答題,作答時間不限,需在截止日期前提交。
注意:參加 The Main Competition的團隊和個人也需進行該輪測試。
 
 
賽事第二階段:The Main Competition
時間:2021年3月27日(以美國東部時間為準)
賽事范圍:Individual Round, Team Round and Live Round
賽事環節介紹:
Individual Round(個人測試):每位參賽者需參加兩項測試,即從代數、組合、幾何和數論四個選項中任選兩項進行測試,每項測試時間60分鐘。該輪測試需個人獨立作答。
Team Round(團隊測試):各支隊伍將得到作答要求和一套試題,需在約30分鐘內(具體時長將在競賽當天公布)以團隊合作形式答題,該輪測試為非證明題。
Live Round(實時測試):各支隊伍同時答題,答題過程中,各支隊伍可以通過實時評分系統了解其他隊伍的答題進度。
 
 

注意事項:

1. 開課時間:根據學生時間組班
2. 學員須知:
(1)受不同學校開學時間影響,班課具體開學時間可能會有微調,具體時間以班課學員為主
(2)班課時間一經確認不再變更,開課后每課若有超半數學員按時出席,則當天正常上課,如有特殊情況請提前告知協調
3. 線上課程:全程互動直播形式,如有需要可以提供課程錄播服務
4. 快速拼班:聯系小助手 微信: linstitute4


導師簡介

 

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

 

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