MATH3030 - Abstract Algebra - 2023/24
Announcement
- Course outline [Download file]
- No tutorial in the first week. The first tutorial will be held on Sep 14, 2023 (Thu).
- Please submit your homework solutions via Blackboard. In case you haven't been added to the system yet, please email the lecturer.
- Reminder: The midterm, which will cover materials up to Lecture 4 and HW6, will be held in class on Nov 1, 2023 (Wed).
- The lecture and tutorial on Nov 2, 2023 (Thu) will be replaced by recorded videos; links have been sent to your CUHK emails. The physical lectures will be resumed on Nov 8, 2023 (Wed).
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:
-
SHEN Jianhao
- Office: AB1 505
- Tel: 3943 4298
- Email:
Time and Venue
- Lecture: Wed 10:30am - 12:15pm at YIA LT4; Thu 2:30pm - 3:15pm at LSB LT3
- Tutorial: Thu 3:30pm - 4:15pm at LSB LT3
Course Description
This is a second course on Abstract Algebra. In this course, we will discuss more advanced topics in group theory and ring theory which include:
- Normal subgroups; quotient groups
- Free groups; presentations of groups
- Isomorphism theorems; subgroup series
- 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, 3rd edition, John Wiley and Sons.
References
- P. Aluffi, Algebra: Chapter 0, 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
- Studying guide for group theory
- 22-23 Tutorials 1-10
- 22-23 Tutorials 1-10 with answer
- Tutorial 2
- Tutorial 2 solutions
- Tutorial 3
- Tutorial 3 solutions
- Tutorial 4 (semidirect products)
- Tutorial 4 solutions
- Tutorial 5
- Tutorial 5 solutions
- Tutorial 6
- Tutorial 6 solutions
- Tutorial 7
- Tutorial 7 solutions
- Tutorial 8 with solution
- Tutorial 9
- Tutorial 9 solutions
- Tutorial 10-11
- Tutorial 10-11 solutions
Assignments
- HW 1 (due on Sep 14, 2023)
- HW 2 (due on Sep 28, 2023)
- HW 3 (due on Oct 5, 2023)
- HW 4 (due on Oct 12, 2023)
- HW 5 (due on Oct 19, 2023)
- HW 6 (due on Oct 26, 2023)
- HW 7 (due on Nov 9, 2023)
- HW 8 (due on Nov 23, 2023)
- HW 9 (due on Nov 30, 2023)
- HW 10 (due on Dec 4, 2023; this is MONDAY, not Thursday!)
Solutions
- HW1 Solution
- HW2 Solution
- HW3 Solution
- HW4 Solution (ver 231023)
- HW5 Solution (ver 231023)
- Midterm Solution
- HW 6 Solution
- HW 7 Solution
- HW 8 Solution
- HW 9 Solution
- HW 10 Solution
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: December 02, 2023 20:26:13