MATH3030 - Abstract Algebra - 2024/25
Announcement
- Course outline [Download file]
- No tutorial in the first week. The first tutorial will be held on Sep 12, 2024 (Thu).
- Please submit your homework solutions via Blackboard. In case you haven't been added to the system yet, please email the course teacher.
General Information
Lecturer
-
CHAN Kwok Wai
- Office: LSB 212
- Tel: 3943 7976
- Email:
Teaching Assistant
-
LAM Chin Hang Eddie
- Office: LSB 222B
- Tel: 3943 7963
- Email:
-
MU Zuodong
- Office: LSB 222B
- Tel: 3943 7963
- Email:
Time and Venue
- Lecture: Wed 10:30am - 12:15pm at YIA LT4; Thu 2:30pm - 3:15pm at SC L2
- Tutorial: Thu 3:30pm - 4:15pm at SC L2
Course Description
This is a second course on Abstract Algebra, after MATH2070/2078. In this course, we will discuss more advanced topics in group theory and ring theory which include:
- Normal subgroups; quotient construction in group theory
- Free groups; presentations of groups
- Isomorphism theorems; subgroup series and decomposition of groups
- Group action; Cayley's theorem
- Sylow theorems and their applications
- Prime and maximal ideals
- Factorization in rings
- PIDs and UFDs
We assume as prerequisite a solid understanding of the basic theory of groups and rings, as covered in MATH2070/2078.
Textbooks
- D. Dummit and R. Foote, Abstract Algebra (mainly Chapters 3 - 9), 3rd edition, John Wiley and Sons.
References
- P. Aluffi, Algebra: Chapter 0 (mainly Chapters II - V), Graduate Studies in Mathematics Vol. 104, American Mathematical Society.
- M. Artin, Algebra, 2nd edition, Prentice Hall.
- J. Fraleigh, A First Course in Abstract Algebra, Addison-Wesley, 7th edition
Lecture Notes
- Review of basic group theory
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Review of basic ring theory
- Lecture 6
- Lecture 7
Tutorial Notes
- Tutorial 1
- Tutorial 1 solutions
- Tutorial 2
- Tutorial 2 solutions
- Tutorial 3
- Tutorial 3 solutions
- Tutorial 4 (semidirect product)
- Tutorial 4 solutions
- Tutorial 5
- Tutorial 5 solutions
- Tutorial 6
- Tutorial 6 solutions
- Tutorial 7
- Tutorial 7 solutions
- Tutorial 8
- Tutorial 8 solutions
- Tutorial 9
- Tutorial 9 solutions
- Tutorial 10
- Tutorial 10 solutions
Assignments
- HW 1 (due on Sep 12, 2024)
- HW 2 (due on Sep 26, 2024)
- HW 3 (due on Oct 3, 2024)
- HW 4 (due on Oct 10, 2024)
- HW 5 (due on Oct 17, 2024)
- HW 6 (due on Oct 24, 2024)
- HW 7 (due on Nov 7, 2024)
- HW 8 (due on Nov 21, 2024)
- HW 9 (due on Nov 28, 2024)
- HW 10 (due on Dec 5, 2024) <-- The last homework assignment!
Solutions
- HW 1 solutions
- HW 2 solutions
- HW 3 solutions
- HW 4 solutions
- HW 5 solutions
- HW 6 solutions
- Midterm solutions
- HW 7 solutions
- HW 8 solutions
- HW 9 solutions
Assessment Scheme
| Homework | 10% | |
| Midterm | 30% | |
| Final | 60% |
Honesty in Academic Work
The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:
http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.
Assessment Policy Last updated: November 28, 2024 23:43:37