課程名稱 |
代數導論優二 Honors Algebra (Ⅱ) |
開課學期 |
100-2 |
授課對象 |
理學院 數學系 |
授課教師 |
林惠雯 |
課號 |
MATH2110 |
課程識別碼 |
201 49460 |
班次 |
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學分 |
3 |
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 |
天數101天數101 |
備註 |
需先修過代數導論優一且成績及格,代數導論優可抵必修代數導論. 總人數上限:50人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1002honors_algebra |
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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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
1. Module theory:
Free modules, Structure theorem for finitely generated modules over a PID, Tensor product, Projective modules, Injective modules, Flat modules.
2. Field theory:
Field extensions, the fundamental theorem of Galois theory, finite fields,solution by radicals, Lindermann-Weierstrass theorem, Hilbert theorem 90, Galois resolvent.
3. Introduction to the representation theory of finite groups:
Linear representations, character theory, the theory of induced characters.
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課程目標 |
Fundamental to all areas of mathematics, algebra provides the cornerstone for the student's development. In this course, in addition to the basic concepts, advanced material will be introduced. We would like to give students an insight into more advanced algebraic topics. |
課程要求 |
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預期每週課後學習時數 |
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Office Hours |
備註: 星期三 12:20 ~ 1:20 |
指定閱讀 |
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參考書目 |
Textbook :
N. Jacobson, Basic Algebra I , 2nd edition
References :
M. Artin, Algebra, 2nd edition
Dummit-Foote, Abstract Algebra
Serge Lang, Undergraduate Algebra, 3rd edition
Jean-Pierre Serrre, Linear representations of finite groups |
評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
Homework and quiz |
35% |
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2. |
Middle examination |
35% |
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3. |
Final examination |
30% |
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週次 |
日期 |
單元主題 |
第1週 |
2/20,2/23 |
Basic properties of modules/Free modules |
第2週 |
2/27,3/01 |
Direct sum and tensor product of modules/Matrices over a PID |
第3週 |
3/05,3/08 |
Modules over a PID/Invariance theorem |
第4週 |
3/12,3/15 |
Applications of invariance theorem/Projective modules |
第5週 |
3/19,3/22 |
Injective moules/Flat modules |
第6週 |
3/26,3/29 |
Finite extensions and simple extensions/Algebraic extensions |
第7週 |
4/02,4/05 |
Geometric construction/溫書假 |
第8週 |
4/09,4/12 |
Splitting fields/Separable extensions |
第9週 |
4/16,4/19 |
Galois extensions /Fundamental theorem of Galois theory |
第10週 |
4/23,4/26 |
期中考/Examples |
第11週 |
4/30,5/03 |
Abelian extensions/Kummer extensions |
第12週 |
5/07,5/10 |
Solution by radicals/Lindemann-Weierstrass theorem |
第13週 |
5/14,5/17 |
Finite fields/Hilbert theorem 90 |
第14週 |
5/21,5/24 |
Galois resolvent/Generalities on linear representations |
第15週 |
5/28,5/31 |
Character theory(I)/Character theory(II) |
第16週 |
6/04,6/07 |
Examples/Group algebra |
第17週 |
6/11,6/14 |
Induced characters (I)/Induced characters (II) |
第18週 |
6/18, 6/21 |
/期末考 |
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