一、課程說明(Course Desc<x>ription) 
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<br>本課程目的是介紹研究所程度的代數方法及應用。 
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<br>所需的預備知識是線性代數以及大學程度的代數。 
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<br>課程的進度會比較迅速。希望修課的學生能注意。 
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<br>二、指定用書(Text Books) 
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<br>N. Jacobson : Basic Algebra I, Freeman and Company 
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<br>三、參考書籍(References) 
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<br>1. S. Lang : Algebra (Third Edition), GTM 211, Springer-Verlag 1993
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<br>2. T. W. Hungerford : Algebra, GTM 73, Springer-Verlag 1974 
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<br>3. M. F. Atiyah & I. G. Macdonald：Introduction to commutative algebra, CRC Press 1994.
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<br>4. N. Jacobson：Basic Algebra II, Freeman and Company 
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<br>5. P. A. Grillet：Abstract Algebra, GTM 242, Springer 2007
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<br>四、教學方式(Teaching Method) 
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<br>Lectures, discussions, also problem session 
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<br>五、教學進度(Syllabus)
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<br>1. Group Theory (Group Action, Jordan-Holder Theorem)
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<br>2. Ring Theory (Chinese Remainder Theorem, PID & UFD, Polynomial Rings)
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<br>3. Module Theory (Modules over PID, Hom & Tensor Product)
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<br>4. Field Theory (Finite Extension, Splitting Field, Finite Galois Theory, Finite Field)
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<br>六、成績考核(Evaluation) 
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<br>1. 期中考 30% 
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<br>2. 期末考 30% 
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<br>3. 作業成績 40%