MATH3030 - Abstract Algebra - 2025/26

Announcement

• Course Outline [Download file]
• No tutorial in the first week. The first tutorial will be held on Sep 11, 2025 (Thu).
• Tentative teaching schedule (newly updated on Oct 27, 2025; subject to further changes) [Download file]
• Please submit your homework solutions via Blackboard. In case you haven't been added to the system yet, please email the lecturer.
• The lecture on Sep 24, 2025 will be replaced by a recorded lecture. A link to the recording has been sent to your email.
• Reminder: Midterm will be held in class on Oct 23, 2025 (Thursday). It will cover materials up to Lecture 3 or HW 5.

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General Information

Lecturer

• CHAN Kwok Wai
  • Office: LSB 212
  • Tel: 3943 7976
  • Email:

Teaching Assistant

• YE Zhenyu
  • Office: AB1 505
  • Tel: 3943 4298
  • Email:
• ZHENG Xukun
  • Office: LSB 232
  • Tel: 3943 5294
  • 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

• TA 1
• TA 2-3
• TA 4
• TA 5
• TA 6
• TA 7
• TA 7 Solution
• TA 8

Assignments

• HW 1 (due on Sep 11, 2025)
• HW 2 (due on Sep 25, 2025); updated version postedon Sep 23, with a question in the optional part modified
• HW 3 (due on Oct 2, 2025)
• HW 4 (due on Oct 16, 2025)
• HW 5 (due on Oct 20, 2025 <-- Monday!); updated version postedon Oct 16, with some typos corrected.
• HW 6 (due on Oct 30, 2025)
• HW 7 (due on Nov 13, 2025)
• HW 8 (due on Nov 20, 2025)
• HW 9 (due on Nov 27, 2025)

Quizzes and Exams

• Midterm solution

Solutions

• HW_Solution1
• HW_Solution2
• HW_Solution3
• HW_Solution4
• HW_Solution5
• HW_Solution6

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.

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Assessment Policy

Last updated: November 13, 2025 14:46:55