MATH3030 - Abstract Algebra - 2022/23

Announcement

• Course outline [Download file]
• No tutorial in the first week. The first tutorial will be held on Sep 14, 2022 (Wed).
• The lecture and tutorial on Wed will be swapped. So the new schedule is lecture from 2:30pm - 3:15pm and tutorial from 3:30pm - 4:15pm on Wed.
• Please submit your homework solutions via Blackboard. In case you haven't been added to the system yet, please email the lecturer.
• Tentative teaching schedule (subject to changes) [Download file]
• The midterm of MATH3030, which will cover materials up to Lecture 3 and HW5, will be held on Oct 26, 2022 (Wed) from 2:30pm - 4:00pm in SC LG23.

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General Information

Lecturer

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

Teaching Assistant

• LIN Zichao
  • Office: AB1 407B
  • Tel: 3943 3720
  • Email:
• SHEN Jianhao
  • Office: AB1 505
  • Tel: 3943 4298
  • Email:

Time and Venue

• Lecture: Mon 2:30pm - 4:15pm, SC LG23; Wed 2:30pm - 3:15pm, SC LG23
• Tutorial: Wed 3:30pm - 4:15pm, SC LG23

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

- 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 Math 2070/2078.

Textbooks

• D. Dummit and R. Foote, Abstract Algebra, 3rd edition, John Wiley and Sons.

References

• P. Aluffi, Algebra: Chapter 0, Graduate Studies in Mathematics V.104, American Mathematical Society.
• M. Artin, Algebra, 2nd edition, Prentice Hall.
• J. Fraleigh, A First Course in Abstract Algebra, 7th edition, Addison-Wesley.

Lecture Notes

• Review of basic group theory (supplemented with a bit of category 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
• Tutorials 1-10
• Tutorials 1-10 with answer

Assignments

• HW 1 (due on Sep 15, 2022)
• HW 2 (due on Sep 29, 2022)
• HW 3 (due on Oct 6, 2022)
• HW 4 (due on Oct 13, 2022)
• HW 5 (due on Oct 23, 2022). Note that this HW is due on Sunday, instead of Thursday! No need to hand in Q3 in HW5 because it's the same as Q7 in HW4.
• HW 6 (due on Nov 10, 2022)
• HW 7 (due on Nov 17, 2022)
• HW 8 (due on Nov 24, 2022)
• HW 9 (due on Dec 1, 2022)
• HW 10 (due on Dec 8, 2022)

Solutions

• HW1 answer
• HW2 answer
• HW3 answer
• HW4 answer
• HW5 answer
• Midterm answer
• HW6 answer
• HW7 answer
• HW8 answer
• HW9 answer

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 30, 2022 11:55:08