基本素養 Basic Literacy無
課程概述 Course Description代數學(一)及(二)延續了線性代數課程，但是其題材更為抽象，也有更多證明的訓練。在此一課程中，會介紹群、環、體等結構，發展研究其結構的方法，並且將其應用在不同的領域中。此一課程會持續地帶領學生深入了解數學，也增強學生在以數學符號及口頭來溝通數學，讓學生能優游自在地閱讀、了解數學，進一步培養對抽象數學的鑑賞能力。
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
課程進度 Course Outline
|週次 Week||進度說明 Progress Description|
|1||Set Theory, Mappings, Integers|
|2||Mathematical Inductions, Complex Numbers|
|3||Definition and Examples of Groups|
|4||Subgroups and Lagrange's Theorem|
|5||Homomorphisms and Normal Subgroups|
|6||Homomorphisms and Normal Subgroups|
|8||The Isomorphism Theorems|
|12||Finite Abelian Groups|
|13||Conjugacy and Sylow's Theorem|
|14||Conjugacy and Sylow's Theorem|
有關課程其他調查 Other Surveys of Courses1.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
Are there any internships involved in the course? How many hours? No
Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics?
Is this course recognized as a Community engagement and Service learning course? Which community will be engaged?