課程資訊
課程名稱
基礎數學二
Basic Mathematics(Ⅱ) 
開課學期
99-2 
授課對象
理學院  數學系  
授課教師
康明昌 
課號
MATH5331 
課程識別碼
221 U5690 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期三2,3,4(9:10~12:10) 
上課地點
天數201 
備註
總人數上限:20人 
 
課程簡介影片
 
核心能力關聯
本課程尚未建立核心能力關連
課程大綱
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課程概述

The main themes of this course will be focused on linear algebra, differential equations, and projective geometry.
This is a course designed for students who are not mathematics majors. Students of mathmatics are discouraged to take this course.

We will discuss the interplay between differential equations and linear algebra. Then we will study some basic notions of linear algebra, differential equations, and projective geometry, such as vector spaces, simplifying linear transformations, application of linear algebra in solving differential equations, collineation transformations, some classical theorems in projective geometry. We will discuss some history of mathematics in the 19-th century so that students get some ideas about the contribution of several mathematicians in this period, e.g. Jordan, Weierstrass, Frobenius, Poncelet, etc.

Projective spaces will be introduced via synthetic and analytic methods so that it will not be too abrupt for students who understand geometry only from the plane Euclidean viewpoint. Complex projective spaces will be mentioned and we will try to convince students that, even in geometry, working on the complex numbers is superior to working on the real numbers (although it is not intuitive to visualize complex figures).
 

課程目標
We hope the students will understand how linear algebra arose in the study of differential equations. Moreover, we will help students to understand projective spaces through the language of linear algebra.  
課程要求
Two-semester course on calculus and at least one-semester course on linear algebra (or its equivalent). 
預期每週課後學習時數
 
Office Hours
 
參考書目
Garrity, All the mathematics you missed.
Graham, Knuth and Patashnik, Concrete mathematics.
Samuel, Projective geometry.
 
指定閱讀
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Report  
70% 
 
2. 
attendance 
30% 
 
 
課程進度
週次
日期
單元主題