課程資訊
課程名稱
代數導論一
Introduction to Algebra (Ⅰ) 
開課學期
103-1 
授課對象
電機資訊學院  電機工程學系  
授課教師
李秋坤 
課號
MATH2105 
課程識別碼
201 24210 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期一3,4(10:20~12:10)星期四7,8(14:20~16:20) 
上課地點
新204新204 
備註
總人數上限:80人
外系人數限制:10人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1031MATH2105_tklee1 
課程簡介影片
 
核心能力關聯
核心能力與課程規劃關聯圖
課程大綱
為確保您我的權利,請尊重智慧財產權及不得非法影印
課程概述

*Contents (I, II):
In this course we want to study the basic theory of algebra, containing groups, rings and some basic
field theory with applications.
(A) Basic Group Theory
1. Definition of a Group
2. Examples of Groups
3.Subgroups, Lagrange's Theorem
4. A Counting Principle
5. Normal Subgroups and Quotient Groups
6. Homomorphisms, Cauchy's Theorem
7. Automorphisms
8. Cayley’s Theorem
9. Permutation Groups, Odd and Even Permutations, Cycle Decomposition
10. Another Counting Principle
11. Conjugacy and Sylow's Theorem
12. Finite Abelian Groups
(B) Basic Ring Theory
1. Definitions and Examples
2. Ideals, Homomorphisms, and Quotient Rings
3. The field of Quotients of an Integral Domain
4. PIDs, Euclidean Rings, UFDs
5. Polynomial Rings
(C) Fields
1. Examples of Fields
2. Field Extensions
3. Finite Extensions 4. Constructions with Straightedge and Compass
5. The Elements of Galois Theory
6. Solvability by Radicals
7. Galois Groups over the Rationals 

課程目標
The aim of the course is to study the basic theory of groups, rings, fields and related
applications.  
課程要求
待補 
預期每週課後學習時數
 
Office Hours
 
參考書目
1. Herstein, I. N. Abstract algebra. Third edition. With a preface by Barbara Cortzen and David J.
Winter. Prentice Hall, Inc., Upper Saddle River, NJ, 1996. xviii+249 pp. ISBN: 0-13-374562-7
2. Herstein, I. N. Topics in algebra. Second edition. Xerox College Publishing, Lexington, Mass.-
Toronto, Ont., 1975. xi+388 pp.
3. Dummit, David S.; Foote, Richard M. Abstract algebra. Third edition. John Wiley & Sons,
Inc., Hoboken, NJ, 2004. xii+932 pp.
 
指定閱讀
待補 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
期中考 
35% 
 
2. 
期末考 
35% 
 
3. 
小考 
30% 
兩次小考, 共 30 %。 
 
課程進度
週次
日期
單元主題