数学课程

course description

The Mathematics course is a unique opportunity for students interested in examining mathematical concepts rarely offered at the high school level. This proof-oriented program will fuse lectures, problem sessions, demonstrations, and exploratory research to engage students in topics such as:

 

- Discrete mathematics part will include: Combinatorics (enumerative, algebraic and geometric), Generating functions and partitions, Graph theory, Probability, Combinational game theory.

 

- Algebra and number theory part will include: Linear algebra, Prime and factorization algorithms, Congruencies and quadratic reciprocity, Galois theory, Geometry of numbers.

 

- Geometry and topology part will include: Euclidean and non-Euclidean geometries, Geometric transformations, Algebraic geometry, Point-set topology, Knot theory.

课程介绍

数学课程为那些有兴趣研究数学概念的学生提供一个独特的机会。本课程是以证据为导向的，并将融合讲座、问题讨论会、演示和探索性研究，让学生了解以下主题：

 

- 离散数学部分，包括：组合学（枚举、代数和几何）、母函数和划分、图论、概率论、组合博弈论。

 

- 代数和数论部分，包括：线性代数，素数和因式分解算法，同余和二次互易，伽罗瓦理论，数的几何。

 

- 几何和拓扑部分，包括：欧几里德几何和非欧几里德几何、几何变换、代数几何、点集拓扑、纽结理论。

 

课程时间：7月10日-7月30日

入学资格：

- 在线申请

- GPA 3.3以上

- 个人essay

- 推荐信

- 托福

截止日期：4月1日