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ZX|Mathematics Academy

Club Leader: G11 Gamma Jacky Wang 王嘉昊, Jeffrey Chen 陈冠吉, G11 Zeta Steven Shi 石宸宇

Club Day: Monday, Wednesday, Thursday

Club Room: Normal classroom

Club Supervisor: Amy Wang


Achievement:

1) Post or Poster

2) Speech

3) Video


Club Activities Planned for 2023-24 S1:

每周一: ZX线上课,BS线下课,石宸宇讲Algorithm in Mathematics。

以下是大纲:

  • 引入

  • 时间复杂度

  • 二进制与位运算

  • 快速幂

  • 数论

  • 基础数论知识

  • 欧几里得算法 gcd ~ 最大公约数

  • 扩展欧几里得算法 exgcd ~ (同余)乘法逆元 ~ 二元一次方程

  • Lucas 定理 ~ (同余)组合数

  • 中国剩余定理 ~ 解同余方程组

  • 筛法 ~ [1,n] 中质数个数

  • Miller Rabin 算法 ~ 快速判断质数

  • Pollard rho 算法 ~ 快速求因子

  • 欧拉定理 Euler theorem

  • 原根 primitive root

  • Cipolla 算法 ~ 求解二次剩余

  • BSGS 算法 ~ 求解模意义下离散对数

  • 代数

  • 矩阵快速幂 ~ 线性递推数列

  • 快速傅里叶变换 FFT ~ 处理卷积 & 多项式乘法


每周三: ZX线下课,BS线上课,陈冠吉讲数学竞赛。

以下是大纲:

  • Counting and Probability

  • Basic Counting and Probability

  • Geometric Probability

  • Recursive Method

  • Number Theory

  • Basic Number Theory

  • Chinese Remainder Theorem

  • Euler’s Theorem and Fermat's Little Theorem

  • Geometry

  • Basic information

  • Circle Property & Cyclic Quadrilaterals

  • Centers of Triangles

  • Algebra

  • Basic information

  • Logarithmic

  • Trigonometric

  • Complex number


每周四: ZX线下课,BS线上课,王嘉昊讲高数。

以下是大纲:

3.3 Chaos Theory

4.2 Boolean Algebra

4.3 Modulus Theory

4.4 Group Theory

4.5 Abstract Algebra

5.1 Continuity & Discontinuity

5.2 Cryptography

5.3 Graph Theory

6.1 Numerical Analysis

6.2 Game Theory

6.3 Information Theory

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