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