課程名稱 |
代數導論二 Introduction to Algebra (Ⅱ) |
開課學期 |
103-2 |
授課對象 |
理學院 數學系 |
授課教師 |
李秋坤 |
課號 |
MATH2106 |
課程識別碼 |
201 24220 |
班次 |
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學分 |
3 |
全/半年 |
半年 |
必/選修 |
必修 |
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304新204 |
備註 |
教學改善計畫課程有教學助理實施小班輔導。 總人數上限:80人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1032MATH2106_ |
課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
課程大綱
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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 |
Linear Algebra
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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. |
評量方式 (僅供參考) |
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