基本素養 Basic Literacy

核心能力 Competence

掌握連續與逼進的能力
Ability to handle continuity phenomena and approximations.
處理數字及符號運算的能力
Ability to operate with symbols and digits.
透視形像與空間的能力
Ability to visualize space, shape, and images.
利用計算機處理數學的能力
Ability of using computer to do mathematics.
應用隨機理論的能力
Ability to apply stochastic mathematics.
處理大量數據的能力
Ability to handle large amount of data.
處理離散型數學的能力
Ability to do mathematics relating to discrete models.
獨立研究的能力
Ability to do independent studies of mathematics.
使用計算機的能力
Abilities to use computer as a tool.

課程概述 Course Description

這門課以線性方程及矩陣為開端,再逐一引進線性代數的基本概念,包括向量空間、線性變換、基底與維度、行列式、特徵值與特徵向量以及對角化。
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