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課程名稱 |
代數導論優一
Honors Algebra (Ⅰ) |
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開課學期 |
101-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
陳榮凱 |
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課號 |
MATH2109 |
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課程識別碼 |
201 49450 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一3,4(10:20~12:10)星期四7,8(14:20~16:20) |
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上課地點 |
天數101天數101 |
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備註 |
需修過微積分及線性代數，成績未達B以上需先徵求授課教師同意。代數導論優可抵代數導論。
總人數上限：50人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1011HA1 |
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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 |
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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. Group theory:
Examples and definition and basic properties,
Subgroups,
Quotient Groups,
Homomorphisms,
Group Actions,
Abelian Groups,
Sylow's Theorems
2 Basic Ring Theory
Examples and Definition,
Polynomial Rings,
Irreducible Polynomials
3. Field Theory
Field Extensions,
Galois Groups,
Cyclotomic Extensions,
Fundamental Theorem of Galois Theory
Finite Fields.
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課程目標 |
For those students who are highly motivated and would like to pursuit for advanced studies in mathematics, this course provides a quick tour of abstract algebra starting from scratch. Besides the standard materials, such as group theory and field theory, we would like to exhibit how these concepts appeared in various branches of mathematics.
Even though this course is considered to be part of the Honor Program, any ambitious student not necessarily in the Program is welcome. |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
每週四 13:00~14:00 |
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指定閱讀 |
Textbook:
Dummit-Foote, Abstract Algebra, 3rd edition |
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參考書目 |
References:
M. Artin, Algebra, 2nd edition,
N. Hungerford, Abstract Algebra, An Introduction, 2nd edition
N. Jacobson, Basic Algebra I , 2nd edition
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Final Examination |
35% |
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2. |
Midterm |
30% |
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3. |
Quiz |
20% |
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4. |
Homework and Note |
15% |
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