I.The Basic Information of the Course(Time New Rome, 12 points, bold font)
Course Number: 202012420006
The EnglishName of theCourse：Abstract Algebra (Elementary)
The ChineseName of theCourse：抽象代数I
In-classHours andAllocationtotal class hours: 48, classroom teaching: 40 classhours, classroom discussion: 8 classhours
Credit(s):3
Semester:1
AppliedDiscipline(Professional Degree Category)：Mathematics
CourseObjectOriented：Sample:Post-graduates,Academic Doctors
EvaluationMode:Closed-book Examination
TeachingMethod:Heuristic Teaching, Blended Teaching
CourseOpening Department:Department of Mathematics
Notes:Filling explanation to applied discipline: the general courses like foreign languages, ideological and political theory course may fill in “AllDisciplines”,Mathematics general course may fill inScience andEngineeringDiscipline, and the other courses fill in “Name ofApplicableDiscipline” according to actual teaching objects, and the number of applicable discipline may be more than one.
II.Prerequisite Course( Time New Rome 12 points bold font)
(Time New Rome 10.5 points, line space fixed value 25 pounds, the front and the end of the paragraph 0 line, the same below)
Advanced Algebra
III. The Objectives and Requirements of the Course(Time New Rome 12 points, total words: about 200 words)
The aim of this course is to introduce the basic concepts of groups, rings and fields to the students. Meanwhile, field extensions and Galois theory will also be important topics in this course. Through studying the course, the students are required to be familiar with the theories of groups, rings and field, and to have a deep understanding on field extensions and Galois theory. They need to be prepared for potential researches in modern algebra.
IV. The Content of the Course(Time New Rome, 12 points, bold font, 1000-2000 words)
Description:Other course should reflect the content and cases of “Courses for Ideological and Political education”, besides the Course for Ideological and Political Education.
Chapter 1 Introduction (6 class hours)
Introduction to concepts such as maps, algebraic operations, homomorphisms, isomorphisms, classifications of sets and equivalence relations
Chapter 2 Group theory (14 class hours)
Introduction to the definitions of groups, group homomorphisms, permutation groups, cyclic groups, subgroups, cosets, normal subgroups and quotient groups;
Introduction to the group action on sets, Sylow theorem and the structure of finitely generated Abelian groups
Chapter 3 Ring and fields (8 class hours)
Introduction to the basic concepts of rings and fields, integral domains, subrings, ring homomorphisms, polynomial rings, ideals, quotient rings and unique factorization domains.
Chapter 4 Galois theory (12 class hours)
Introduction to field extension, split field of polynomials, finite fields and Galois extension theorems.
Courses for Ideological and Political education: Inspire the students with Galois’ patriotism, and his spirit in the harsh process in building up group theory. Reinforce the students’ pride as being Chinese through introducing the ancient achievements in our country.
V. Reference Books, Reference Literatures, and Reference Materials
A. Text Books, Monographs and References
1.冯克勤,李尚志,章璞.近世代数引论.中国科学技术大学出版社, 2009.
2.张禾瑞.近世代数基础.高等教育出版社, 1978.
3. Nathan Jacobson. Basic Algebra I. W. H. Freeman & Company, 1989.
4. Ghazizadeh, Modℓcohomology of some Deligne-Lusztig varieties for GLn(q), arXiv:2006.14119, 2020.
B. Learning Resources (Time New Rome 12 points)
1.http://v.dxsbb.com/ligong/1269/player-0-0.html
Outline Writer (Signature):
Leader in charge of teaching at the College (Signature)：
Date：
中文
