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課程名稱 |
代數幾何導論
INTRODUCTION TO ALGEBRAIC GEOMETRY |
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開課學期 |
96-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
蔡宜洵 |
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課號 |
MATH5101 |
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課程識別碼 |
221 U4580 |
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班次 |
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學分 |
3 |
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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 |
星期三3,4,@(10:20~) |
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上課地點 |
舊數103 |
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備註 |
總人數上限：30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 content centers around the following.
The precise content and material depends on the speed of the lectures.
1. Basic notions
2. Selected topic (I): Interaction between Analysis and Algebra, p-adic analysis as an analogue of real number system in Calculus, with applications to integral solutions of polynomial equations.
3. Selected topic (II): Interaction between geometry and number fields, analogy between number fields and function fields, Riemann-Roch in function fields
4. Selcted topic (III): Interaction between KdV equations and algebraic curves, algebraic geometry provides solutions to some non-linear PDE equations.
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課程目標 |
This course is meant for students who haven't had any knowledge about algebraic geometry (nor Riemann surfaces). It would like to provide some interesting aspects in algebraic geometry, which is of geometric origin and of applications to other branches of mathematics such as algebra, number theory or even PDE problems.
This course assumes no background in algebraic geometry. A standard course in algebraic geometry might include the introduction of sheaf theory and cohomology theory. However, this course takes an alternative, and avoids the use of them. Its purpose is to provide a motivation for students to have some appreciation of the richness of this subject, within a relative short period of time.
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課程要求 |
建議先修：Introductory algebras such as group, ring and fields,advanced calculus
評量：
A final written examination will be given.
other:
Some useful reference books will be given in the first meeting day of the course.
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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 |
None. But for content i), one may see the book |
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評量方式
(僅供參考) |
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