課程資訊
課程名稱
 代數二
ALGEBRA(Ⅱ) 
開課學期
 98-2 
授課對象
 理學院  數學研究所  
授課教師
 陳榮凱 
課號
 MATH7106 
課程識別碼
 221 U3840 
班次
  
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
 新201新204 
備註
 研究所數學組基礎課。
總人數上限：50人 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/982Algebra 
課程簡介影片
 
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課程大綱
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課程概述

Field Theory:
Algebraic extensions.
Galois groups
Cyclotomic extension and cyclic extensions.
Radical extensions.
Transcendental extensions.

Cmooutative Ring Theory:
Integral extensions, Dimension theory, Dedekind Domain, Hilbert's Nullstellensatz.

Some further topics:
a few topics from the follwoing list: Lie groups and Lie algebra, homological algebra, algebraic groups

 

課程目標
 We would like to provide a solid foundation for students who are interested in advanced studies in the fields related to algebra, such as algebraic number theory, algebraic geometry and representation theory.  
課程要求
 Grading scheme:
1. Homework 30%
2. Midterm 30%
3. Final Examination 40%
 
預期每週課後學習時數
  
Office Hours
  
指定閱讀
 1. Hungerford, Algebra, GTM 73 (Textbook)
2. Lang, Algebra, GTM 211
3. Herstein, Noncommutative rings
4. Atiyah, MacDonald, Introduction to commutative algebra
5. Artin, Algebra, Prentice Hall
 
參考書目
 1. Hungerford, Algebra, GTM 73 (Textbook)
2. Lang, Algebra, GTM 211
3. Herstein, Noncommutative rings
4. Atiyah, MacDonald, Introduction to commutative algebra
5. Artin, Algebra, Prentice Hall
 
評量方式
(僅供參考)
    
課程進度
週次
日期
單元主題
Week 1
 2/22,2/25  Field Extensions 
Week 2
 3/01,3/04  Algebraic Closed Fields and Algebraic Closure 
Week 3
 3/08,3/11  Finite Dimensional Galois Extension 
Week 4
 3/15,3/18  Algebraic Galois Extension and Normal Extension 
Week 5
 3/22,3/25  Galois Group of a Polynomial, Cyclotomic Extension 
Week 6
 3/29,4/01  No class this week! 
Week 7
 4/05,4/08  Cyclotomic Extensions 
Week 8
 4/12,4/15  Cyclic Extensions, Radical Extensions 
Week 9
 4/19,4/22  Separable and Purely Inseparable Extensions 
Week 10
 4/26,4/29  Transcendental Extensions