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 |
