描述
课程须知
1.一对一定制辅导：个性定制，专属辅导，弹性时间，高效高质
2. 3-8人小班辅导：小组教学，针对辅导，及时反馈，性价比高
3.线上辅导班：克服地域，网络授课，节约时间，课程回放
课程大纲
| Fundamentals(新秀组） | Advanced Complementaries(专业组） | |
| Number Theory | Prime factorization; Number of divisors, Sum of divisors,
Product of divisors; LCM and GCD |
Prime factorization; Number of divisors, Sum of divisors, Product of divisors;
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
(Induction and iteration Method) |
Function Composition and Functional Equations (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;
The law of Cosine and the law of Sine) |
Basics in Geometry( Polygon; Area Method; 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,
Permutation and Combinations) |
Counting Principles (Sum Rules, Product Rules, Permutation and Combinations) |
| Classical probability theory | Geometric probability; Conditional Probability; Bayes Theorem | |
| Logic reasoning (Pigeon Hole's Principle;
Winning Strategy; Prove by contradiction; Principles of Inclusion and Exclusion) |
Logic reasoning (Pigeon Hole's Principle; Winning Strategy; 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 |
参赛须知
【个人能力挑战 Individual Contest】
10道简答问题被分为5组，每15分钟发下一组2道题，选手要在短暂的时间内迅速解答给出最简答案(挑战难度:3星，时长1小时40分钟)。
【团队能力挑战 Team Contest】
✔团队力量 Power Round
以团队为单位，解答一道多步证明题，并且要求答案和数学证明或解答过程都清晰明了(挑战难度:5星，时长60分钟)。
✔团队协作 Team Round
以团队为单位，解答10道简答题，给出最简洁的数字答案(挑战难度:4星，时长30分钟)。
✔分组接力 Relay Round
（1）每个团队被分为3组，编号为A、B、C；
（2）每组分到不同的题目，C组题目的一个关键条件是B组解出的答案，B组题目的一个关键条件是A组解出的答案。因此，后一组成员需要获得前一组成员的答案后才能解题；C组提交最终答案给监考人员
（3）每轮限时10分钟，5分钟内提交正确答案，得10分；10分钟提交正确答案，得5分。错误答案不给分。团队最高得分20分（挑战难度系数：2星，接力共两轮，总时长25分钟）。
