描述
报名须知
1、 适合人群:目前水平可以晋级AIME的精英学员
2、 假期集中上课
3、 AIME培训班为3-8人小班,满3人开班,40课时。
注意事项:
学员须知:
受不同学校开学时间影响,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
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
线上课程:全程互动直播形式,如有需要可以提供课程录播服务
快速拼班连续顾问
课程大纲
Essential Topics | Extended Details (Divison A and Beyond) | |
Number Theory | Prime factorization | Number of factors |
Sum/Product of factors | ||
LCM and GCD | ||
Euclidean Algorithm and Bézout's Theorem | ||
Congruence and Modular Algebra | Chinese Remainder Theorem(CRT) | |
Euler’s Theorem/Fermat's Little Theorem | ||
Wilson's Theorem | ||
Diphantine Equations | Estimation and Molular Metthod | |
Algebra | Resursive Sequences | Characteristic Equation Method |
Conjecture and Mathematical Induction Proof | ||
Functions and Equations | Gaussian/Floor function | |
*Functional Equations | ||
Inequalities and Extreme Value Problems | Cauchy inequality | |
Jensen's inequality | ||
Weighted AM-GM Inequality | ||
Rearrangement Inequality and Chebyshev Inequality | ||
Polynomials | Fundamental Theorem of Algebra (Polynomial Factorization) | |
Generalized Remainder's Theorem | ||
Rational Root Theorem | ||
Vieta's Theorem and Newton's Sums | ||
Complex numbers | De Moivre's Theorem and Roots of unity | |
Rotation, Translation and Complex Vector Method | ||
Geometry | Basic Geometry (Triangles and Polygons) | 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 | ||
Circles | Inscribed and circumscribed polygon/Circle, Cyclic Quadrilateral | |
Ptolemy's theorem, *Butterfly Theorem | ||
Basic Analytic Geometry | Ellipse, *Parabola and Hyperbola | |
Basic Solid Geometry | *Euler's Polyhedron Formula | |
Combinatorics | Basic Counting Principle | Sum Rules and Product Rules |
Permutations and Combinations | Advanced problems in combinatorics | |
Logic reasoning | Pigeonhole principle |