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課程名稱 |
代數一
Algebra(Honor Program)(Ⅰ) |
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開課學期 |
106-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
余正道 |
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課號 |
MATH5178 |
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課程識別碼 |
221 U6520 |
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班次 |
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學分 |
5.0 |
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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 |
星期一2,3,4(9:10~12:10)星期四8,9(15:30~17:20) |
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上課地點 |
天數101天數101 |
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備註 |
此課程研究生選修不算學分。
限學士班學生
總人數上限：44人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1061MATH5178 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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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 |
More the contents, please refer the standard syllabus available in
http://www.math.ntu.edu.tw/sites/default/files/imce/documents/courses/honor_course_ syllabus_2016.pdf |
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課程目標 |
Theory of groups, linear representations of finite groups, applications to fields |
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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 |
每週五 13:20~14:10
每週三 13:30~14:30
每週一 15:00~16:00 備註： Monday: Astro-Math 461,
Wednesday: Astro-Math 430,
Friday: Astro-Math 407 |
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指定閱讀 |
Textbook: Knapp, Basic algebra. Digital 2nd edition. Available on the author's website. |
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參考書目 |
Dummit and Foote, Abstract algebra. 3rd edition. |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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Week 1 |
9/11, 9/14 |
Examples of groups from previous courses, symmetric, dihedral, alternating, cyclic groups |
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Week 2 |
9/18, 9/21 |
Quotient,
relations between group and its quotient (isomorphism theorems),
splitting of quotient (semidirect product) |
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Week 3 |
9/25, 9/28, 9/30 |
End of semidirect product,
Structure of finite abelian groups (statement),
p-groups.
Notice that we have classes on Saturday: [Digression to field extension]. |
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Week 4 |
10/02, 10/05 |
Sylow theorems,
simpleness of A_n,
composition series |
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Week 5 |
10/12 |
Structure of finitely generated abelian groups (proof) |
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Week 6 |
10/16, 10/19 |
Quiz (10/16, 9:10 - 10:00)
[Digression: Modules over PID],
Arbitrary product of groups,
Categories and functors |
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Week 7 |
10/23, 10/26 |
Free groups, free product |
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Week 8 |
10/30, 11/02 |
Midterm.
[Digression: Free groups/products in topology] |
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Week 9 |
11/06, 11/09 |
Characters: finite abelian case,
Schur's lemma, averaging trick.
TA section: Chinese Remainder Theorem |
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Week 10 |
11/13, 11/16 |
Schur orthogonality,
class functions and characters
TA section: irreducible representation of A_4 |
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Week 11 |
11/20, 11/23 |
Group extension.
Quiz 2 |
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Week 12 |
11/27, 11/30 |
[Digression: group cohomology as a derived functor],
induced representation |
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Week 13 |
12/04, 12/07 |
Convolution,
Burnside's theorem
TA section: integral closure of Z |
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Week 14 |
12/11, 12/14 |
Quiz 3.
Hilbert basis theorem,
division algorithm,
Grobner basis |
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Week 15 |
12/18, 12/21 |
Buchberger's criterion,
Grobner basis and elimination,
examples.
TA section: Frobenius reciprocity |
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Week 16 |
12/25, 12/28 |
Final.
[Miscellaneous remarks] some questions left in class, Kunneth, etc. |
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