课程大纲代数部分多项式，代数手法进阶，数列，二次数列进阶, 不等式进阶Rearrngement Inequality, Cauchy-Schwarz, Jensonʼs Inequlity and more几何欧氏几何的处理手法，共点和共线，多边形和圆，radical axis, 射影几何入门，三角函数进阶，解析几何，solving geometric problems using vectors, solving geometric problems in complex plane.立体几何进阶数论 类费布拉奇数列和质数分解的几个有趣结论模运算进阶 Eulerʼs Toteint Function, Fermatʼs Christmas Theorem, Fermatʼs little Theroem快速筛数 Quadatic Residue, Lifting the Exponent Lemma排列组合二项式系数的运算 Vandermondeʼs identity几种常见的排列组合思维方法，图论入门Probability and Expectation随机过程 Markov ChainRoots of Unity Filter知识综合运用数形结合，构造函数，竞赛技巧和总复习