TOPICS IN ELEMENTARY MAHEMATICS

课程名称：

Topics in Elementary Math

课程概述：

内容简介：

Complex numbers have played an instrumental role in the development of modern math. Whether a (pure) mathematician is working with analysis, algebra, combinatorics, geometry, number theory, etc., he/she must have been using complex numbers to some extent. One can thus claim that working with complex numbers or not distinguishes pure mathematicians from their applied counterparts, who are rarely counted as mathematicians in academics.

In this course, we will take a brief glance at the fruitful aspects of complex numbers, particularly from the viewpoint of functions. The course will cover the following five major topics:

1. The algebra of complex numbers;
2. The geometric representation of complex numbers;
3. Introduction to the concept of analytic function;
4. Elementary theory of power series;
5. The exponential and trigonometric functions.

As well as the following bonus topics:

1. Solving cubic equations;
2. Application of complex numbers to Euclidean geometry;
3. Complex numbers in enumeration problems.

Remark: Bilingual lectures. Acquaintance with limits and derivatives highly demanded.

推荐阅读：

1. Ahlfors, Complex Analysis, Ch 1~2【教材】
2. 龚昇，《复变函数概貌》
3. 邓纳姆，《天才引导的历程》（第六章）
4. 蒋声，《从单位根谈起》
5. 常庚哲、伍润生，《复数与几何》
6. 波利亚、舍贵，《数学分析中的问题和定理》（第一章§1）

课程评价：

1. 课堂参与的积极程度与表现情况占20%。
2. 每课的作业占50%。
3. 期末提交研究性小论文一篇，中英文不限。内容围绕本学期课程涉及的专题展开。成绩占30%。