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課程名稱 |
高等線性代數 一
Advanced Linear Algebra (Ⅰ) |
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開課學期 |
107-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
康明昌 |
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課號 |
MATH5087 |
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課程識別碼 |
221 U8310 |
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班次 |
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學分 |
3.0 |
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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) |
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上課地點 |
天數305 |
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備註 |
總人數上限：40人 |
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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 |
The principal axis theorem, Jordan normal forms, simultaneous triangularization of commuting square matrices, tensor products and exterior products, projective spaces and projective geometry (the synthetic method and the analytic method), some elementary notion in representation theory and homological algebra |
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課程目標 |
This is a course of some advanced topics of linear algebra. It starts from some basic theorems in linear algebra and leads to an introduction of the representation and cohomology theory.
At the beginning we will review the standard theorems of linear algebra : We emphasize the approach of vector spaces and linear transformations instead of vectors and matrices.
Then we move to some topics of the classical projective plane: Pappus Theorem, Desargue Theorem, some problems in enumerative geometry.
Finally we will discuss the “glorified” linear algebra, i.e., the basic notion of modules, group representations, cohomology, and derived functors. |
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課程要求 |
Linear Algebra (a 2-semester required course) and Algebra (at least one semester) |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
Katznelson, A (terse) introduction of linear algebra.
Hartshorne, Foundation of projective geometry.
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評量方式
(僅供參考) |
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