基本素養 Basic Literacy
無核心能力 Competence
□ 掌握連續與逼進的能力
Ability to handle continuity phenomena and approximations.
■ 處理數字及符號運算的能力
Ability to operate with symbols and digits.
■ 透視形像與空間的能力
Ability to visualize space, shape, and images.
□ 利用計算機處理數學的能力
Ability of using computer to do mathematics.
□ 應用隨機理論的能力
Ability to apply stochastic mathematics.
□ 處理大量數據的能力
Ability to handle large amount of data.
■ 處理離散型數學的能力
Ability to do mathematics relating to discrete models.
□ 獨立研究的能力
Ability to do independent studies of mathematics.
□ 使用計算機的能力
Abilities to use computer as a tool.
課程概述 Course Description
多項式根，伽羅瓦群，域擴展。Roots of polynomials, Galois groups, field extensions.
課程學習目標 Course Objectives
課程進度 Course Outline
| 週次 Week | 進度說明 Progress Description |
|---|---|
| 1 | Polynomials |
| 2 | Irreducibility criteria |
| 3 | Field extensions |
| 4 | Algebraic extensions |
| 5 | Straightedge and compass constructions; Splitting fields |
| 6 | University holidays (no classes) |
| 7 | Algebraic closures; Separable extensions |
| 8 | Cyclotomic polynomials |
| 9 | Midterm Examination |
| 10 | Galois extensions; Galois groups |
| 11 | Fundamental theorem of Galois theory; Finite fields |
| 12 | Composite extensions; Simple extensions |
| 13 | Cyclotomic extensions and abelian extensions |
| 14 | Galois groups of polynomials |
| 15 | Radical extensions |
| 16 | Insolvability of the general quintic |
| 17 | Transcendental extensions |
| 18 | Final examination |
以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.
有關課程其他調查 Other Surveys of Courses
1.本課程是否規劃業界教師參與教學或演講? 否Is there any industry specialist invited in this course? How many times? No
2.本課程是否規劃含校外實習(並非參訪)? 否
Are there any internships involved in the course? How many hours? No
3.本課程是否可歸認為學術倫理課程? 否
Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics? No
4.本課程是否屬進入社區實踐課程?
Is this course recognized as a Community engagement and Service learning course? Which community will be engaged?