## 核心能力 Competence

Ability to handle continuity phenomena and approximations.

Ability to operate with symbols and digits.

Ability to visualize space, shape, and images.

Ability of using computer to do mathematics.

Ability to apply stochastic mathematics.

Ability to handle large amount of data.

Ability to do mathematics relating to discrete models.

Ability to do independent studies of mathematics.

Abilities to use computer as a tool.

## 課程概述 Course Description

Algebra (1) and (2) is a natural continuation of Linear Algebra, but the material is much more proof-driven and abstract. During the year, the structures groups, rings, and fields will be introduced, and the method of studying them will be developed, and applications to other areas will be seen. The general objective of this course is to continue providing students with a deeper understanding and working knowledge of mathematics, strengthening the analytic skills, increasing the ability to communicate mathematics symbolically and orally, making students comfortable with reading and understanding mathematics on their own, and continuing to develop the appreciation for abstract mathematics.

## 課程學習目標 Course Objectives

• Groups, subgroups, quotient groups, homomorphisms
• Actions of groups
• Rings, ideals, quotients rings, homomorphisms
• Polynomial rings, domains
• ## 課程進度 Progress Description

進度說明 Progress Description
1Groups,
2Subgroups,homomorphisms
3Cyclic groups
4Permutation groups
5Cosets; Quotient groups
6Cosets; Quotient groups, Lagrange's theorem,
7Isomorphism theorems, transpositions, alternating groups;
8Group actions, conjugation, automorphisms
9 Group actions, conjugation, automorphisms
10Midterm Exam
11Direct products
12Rings, examples
13ideals, Quotient rings
14Euclidean domains, Principal ideal domains
15Unique factorization domains
16Polynomial rings
17Review
18Final Exam
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? 否
Is this course recognized as a Community engagement and Service learning course? Which community will be engaged? No