## 核心能力 Competence

Ability to handle continuity phenomena and approximations.

Ability to operate with symbols and digits.

Ability to visualize space, shape, and images.

Ability of using computer to do mathematics.

Ability to apply stochastic mathematics.

Ability to handle large amount of data.

Ability to do mathematics relating to discrete models.

Ability to do independent studies of mathematics.

Abilities to use computer as a tool.

## 課程概述 Course Description

In this course, we begin by discussing linear equations and matrices. We then proceed to introduce the basic concepts of linear algebra. Topics include vector spaces, linear transformations, bases and dimension, determinants, eigenvalues and eigenvectors, and diagonalizability.

## 課程學習目標 Course Objectives

• 掌握線性代數的基本性質與理論
• 透過簡單的例子讓學生對一些重要定理有更深入地暸解
• 培養學生獨立思考與證明的能力
• ## 課程進度 Progress Description

進度說明 Progress Description
1Introduction to vector spaces
2Vector spaces and subspaces
3Vector spaces, subspaces and linear independence
4Linear independence, linear combinations and span
5Linear combinations, span, bases and dimensions
6Bases, dimensions and linear transformations
7Linear transformations
8Linear transformations and null spaces
9Linear transformations and matrices
10Invertible linear transformations and isomorphic vector spaces
11Product spaces, quotient spaces and dual spaces
12Product spaces, quotient spaces and dual spaces
13Solving systems of linear equations
14Polynomials
15Eigenvalues, eigenvectors and invariant subspaces
16Eigenvalues, eigenvectors and invariant subspaces
17Eigenspaces and diagonal matrices
18Final examination
以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

## 有關課程其他調查 Other Surveys of Courses

1.本課程是否規劃業界教師參與教學或演講? 否
Is there any industry specialist invited in this course? How many times? No
2.本課程是否規劃含校外實習(並非參訪)? 否
Are there any internships involved in the course? How many hours? No
3.本課程是否可歸認為學術倫理課程? 否
Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics? No
4.本課程是否屬進入社區實踐課程? 否
Is this course recognized as a Community engagement and Service learning course? Which community will be engaged? No