Holiday
GEN III綜三 723 T2W3W4
本課程延續上學期近世代數一的研究所程度內容,主要目的為介紹代數相關領域的知識和方法,令學生熟悉代數語言的使用。
Course keywords: Galois Theory, Commutative algebra, Non-commutative algebra, Finite group representation, Homological algebra 一、課程說明(Course Description): 本課程延續上學期近世代數一的研究所程度內容, 主要目的為介紹代數相關領域的知識和方法, 令學生熟悉代數語言的使用。 本課程的預備知識為群,環,體,模的基本理論。 上課將會綜合這些基本知識來介紹並討論各種更深的主題。 二、指定書籍(Text Books): (N. Jacobson) Basic algebra II, Freeman and Company 三、參考書籍(References): 1. (S. Lang) Algebra, GTM 211 Springer-Verlag 1993 2. (T. W. Hungerford) Algebra, GTM 73 Springer-Verlag New York Inc. 1974 3. (M. F. Atiyah and I. G. Macdonald) Introduction to commutative algebra, Addison-Wesley Series in Mathematics 4. (J.-P. Serre) Linear representations of finite groups, GTM 42 Springer-Verlag 四、教學方式(Teaching Method): Lectures, discussions, also problem sections 五、教學內容(Syllabus): 1. Krull’s Galois theory (including discussions on transcendental extensions) 2. Commutative algebra (integral extension, primary decomposition, noetherian, artinian) 3. Non-commutative algebra (density theorem, Artin-Wedderburn Theorem, Brauer group) 4. Finite group representation (semi-simplicity, character theory, induced representation) 5. (Optional) Homological algebra (Ext and Tor) 六、評分方式(Evaluation): 1. 作業 40% 2. 期中報告 30% 3. 期末報告 30%
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Average Percentage 83.6
Std. Deviation 9.35
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