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課程名稱 |
代數導論一
Introduction to Algebra(Ⅰ) |
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開課學期 |
105-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
莊武諺 |
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課號 |
MATH2113 |
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課程識別碼 |
201 49610 |
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班次 |
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學分 |
4 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期一3,4(10:20~12:10)星期四8,9(15:30~17:20) |
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上課地點 |
新204新204 |
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備註 |
教學改善計畫課程有教學助理實施小班輔導。MATH2105代數導論一得用此課替代。
總人數上限：80人
外系人數限制：10人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1051algebra |
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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 |
Groups, symmetry groups, matrix groups, homomorphisms, isomorphisms, group actions, cyclic groups, quotient groups, normal subgroups, Lagrange theorem, isomorphism theorems, composition series, Holder program, alternating groups, Cayley theorem, the class equation, conjugacy classes in permutation groups, Sylow theorem, finitely generated abelian groups, semidirect products, classifications of groups of low orders.
Ring theory, integral domain, ideals, ring isomorphism theorems, ideals generated by subsets, maximal ideals, prime ideals, ring of fractions, Chinese remainder theorem. |
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課程目標 |
The goal of the course is to introduce the basic notions in algebra. |
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課程要求 |
待補 |
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預期每週課後學習時數 |
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Office Hours |
備註： 授課教師與助教每星期均有一小時office hour。詳情請見課程公佈欄:
https://ceiba.ntu.edu.tw/course_admin/bulletin/?op=popup&sn=289812 |
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指定閱讀 |
待補 |
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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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No. |
項目 |
百分比 |
說明 |
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1. |
Quiz |
30% |
共有六次小考。取其中較高的五次成績計算。 |
2. |
Midterm |
45% |
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3. |
Final |
45% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/12,9/15 |
9/12 groups, dihedral groups, symmetry groups.
9/15 中秋節放假 |
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第2週 |
9/19,9/22 |
9/19 symmetry group, group action, subgroup.
9/22 centralizer, normalizer, stabilizer, kernel, cyclic group. |
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第3週 |
9/26,9/29 |
9/26 cyclic group.
9/29 cyclic group, subgroups generated by subsets. 小考一 |
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第4週 |
10/03,10/06 |
10/03 subgroups generated by subsets, quotient groups.
10/06 quotient groups, normal subgroups. |
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第5週 |
10/10,10/13 |
10/10 放假
10/13 normal subgroups, Lagrange theorem. 小考二 |
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第6週 |
10/17,10/20 |
10/17 Lagrange theorem, isomorphism theorem.
10/20 isomorphism theorem. |
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第7週 |
10/24,10/27 |
10/24 composition series, Holder program, alternating groups, group actions.
10/27 group actions, group actions by left multiplications, 小考三 |
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第8週 |
10/31,11/03 |
10/31 Cayley theorem, group actions by conjugation, class equation.
11/3 class equation, conjugacy classes in symmetry group. |
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第9週 |
11/07,11/10 |
11/03 conjugacy classes in symmetry group, Burnside's lemma, automorphism.
11/10 期中考 |
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第10週 |
11/14,11/17 |
自主學習週 |
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第11週 |
11/21,11/24 |
11/21 Sylow theorem I, 發還期中考並檢討。
11/24 Sylow theorem II,III. |
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第12週 |
11/28,12/01 |
11/28 Sylow theorem, Cauchy theorem, groups of order 12.
12/01 finitely generated abelian groups, groups of order 8, 小考四 |
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第13週 |
12/05,12/08 |
12/05 semidirect product, groups of order pq.
12/08 groups of order pq, ring theory. |
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第14週 |
12/12,12/15 |
12/12 integral domains, subrings, ideals. ring isomorphism theorems.
12/15 ring isomorphism theorems, nilpotent elements, nilradical. 小考五 |
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第15週 |
12/19,12/22 |
12/19 ideals generated by subsets, Zorn's lemma and axiom of choice, maximal ideals.
12/22 maximal ideals, prime ideals, ring of fractions. |
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第16週 |
12/26,12/29 |
12/26 Rings of fractions.
12/29 Chinese remainder theorem, 小考六 |
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第17週 |
1/02,1/05 |
1/2 放假
1/5 Chinese remainder theorem.
1/09 期末考 |
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