課程大綱

	Fundamentals(新秀組）	Advanced?Complementaries(專業組）
Number?Theory	Prime?factorization;?Number?of?divisors,?Sum?of?divisors,	Prime?factorization;?Number?of?divisors,?Sum?of?divisors,?Product?of?divisors;
	Product?of?divisors;	LCM?and?GCD
	LCM?and?GCD
	Euclidean?Algorithm?and?Bezout's?Theorem	Euclidean?Algorithm?and?Bezout's?Theorem
	Congruence?and?Divisibility	Congruence?and?Divisibility
		Chinese?remainder?theorem(CRT),?Fermat’s?little?theorem
		Euler’s?function?and?theorem,?Wilson's?Theorem
		Diophantine?Equations
Algebra	Algebraic?identities?and?Algebraic?manipulations	Algebraic?identities?and?Algebraic?manipulations
	Function?Composition?and?Functional?Equations	Function?Composition?and?Functional?Equations?(Induction?and?iteration?Method)
	(Induction?and?iteration?Method)
	Polynomials?and?Vieta's?Theorem	Polynomials?and?Vieta's?Theorem;?Newton's?Sum;
	Fundamental?inequalities,?Cauchy?inequality	Fundamental?inequalities,?Cauchy?inequality,?other?advanced?inequalities
	Rescursive?Sequence	Rescursive?Sequence;?Characteristic?Equation
Geometry	Basics?in?Geometry(?Polygon;?Area?Method;	Basics?in?Geometry(?Polygon;?Area?Method;?The?law?of?Cosine?and?the?law?of?Sine)
	The?law?of?Cosine?and?the?law?of?Sine)
	Triangles,?Centers?of?triangle	Triangles,?Centers?of?triangle;?Menelaus's?theorem,?Ceva's?theorem,?Stewart?Theorem
	Circles;?Cyclic?Quadrilateral;Power?of?Point?Theorem	Circles;?Cyclic?Quadrilateral;Power?of?Point?Theorem:?Ptolemy's?theorem;?Radical?Axis;
Probability?and?Statistic	Counting?Principles?(Sum?Rules,?Product?Rules,	Counting?Principles?(Sum?Rules,?Product?Rules,?Permutation?and?Combinations)
	Permutation?and?Combinations)
	Classical?probability?theory	Geometric?probability;?Conditional?Probability;?Bayes?Theorem
	Logic?reasoning?(Pigeon?Hole's?Principle;	Logic?reasoning?(Pigeon?Hole's?Principle;?Winning?Strategy;?Prove?by?contradiction;
	Winning?Strategy;	Principles?of?Inclusion?and?Exclusion)
	Prove?by?contradiction;
	Principles?of?Inclusion?and?Exclusion)
		Elementary?Graph?Theory;?Coloring?Problem?and?Labelling?Method
College?Topics		Limit,?Differentiation,?and?simple?Integration,
		Simple?Series?and?convergency?test
		Simple?Group?Theory

參賽須知

【個人能力挑戰 Individual Contest】
10道簡答問題被分為5組，每15分鐘發下一組2道題，選手要在短暫的時間內迅速解答給出最簡答案(挑戰難度:3星，時長1小時40分鐘)。

【團隊能力挑戰 Team Contest】
✔團隊力量 Power Round
以團隊為單位，解答一道多步證明題，并且要求答案和數學證明或解答過程都清晰明了(挑戰難度:5星，時長60分鐘)。

✔團隊協作 Team Round
以團隊為單位，解答10道簡答題，給出最簡潔的數字答案(挑戰難度:4星，時長30分鐘)。

✔分組接力 Relay Round
（1）每個團隊被分為3組，編號為A、B、C；
（2）每組分到不同的題目，C組題目的一個關鍵條件是B組解出的答案，B組題目的一個關鍵條件是A組解出的答案。因此，后一組成員需要獲得前一組成員的答案后才能解題；C組提交最終答案給監考人員
（3）每輪限時10分鐘，5分鐘內提交正確答案，得10分；10分鐘提交正確答案，得5分。錯誤答案不給分。團隊最高得分20分（挑戰難度系數：2星，接力共兩輪，總時長25分鐘）。

以上就是關于【2023 DMM杜克大學數學競賽沖刺班】的解答，如需了解學校/賽事/課程動態，可至翰林教育官網獲取更多信息。

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