MATH2078 - Honours Algebraic Structures - 2021/22

Course Name: 
Honours Algebraic Structures
Teacher: 
Prof. Kwok Wai CHAN
Course Year: 
2021/22
Term: 
2

Announcement

  • Course outline [Download file]
  • On Tuesdays, we will have lectures during 1:30pm - 3:15pm and tutorials will be moved to 5:30pm - 6:15pm on Wednesdays (in contrast with the timetable announced on CUSIS), starting from Week 1.
  • Please submit your homework solutions via Blackboard. In case you haven't been added to the system yet, please email the lecturer.
  • Tue Lectures -- ZOOM Meeting ID: 935 4004 2003, Passcode: 726718.
  • Wed Lectures & Tutorials -- ZOOM Meeting ID: 937 0265 2980, Passcode: 646009.
  • The midterm of MATH2078, which will cover the group theory part (roughly Week 1 - 6), will be held on Mar 16, 2022 (Wed) from 4:15pm - 6:30pm. It will be done in an online mode - we will post the question paper on Blackboard at 4:15pm on Mar 16 and you need to submit your solutions in one single PDF file to Blackboard at or before 6:30pm on Mar 16 (the same day). Please join the zoom session as usual and stay online during the midterm.
  • The centralized Final Examination will be held online via ZOOM on May 3, 2022 (Tuesday) during 5:30pm - 8:30pm. The ZOOM link details and guidelines of the examination have been sent to you by email. The question paper will be posted on Blackboard at 5:30pm on May 3, 2022. You need to submit your solutions in one single pdf file via Blackboard at or before 8:30pm on May 3, 2022 (the same day).

General Information

Lecturer

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

Teaching Assistant

  • CHEUNG Chin Ho
    • Office: AB1 505
    • Tel: 3943 4298
    • Email:

Time and Venue

  • Lecture: Tue 1:30pm - 3:15pm at ERB 803; Wed 4:30pm - 5:15pm at SC L3
  • Tutorial: Wed 5:30pm - 6:15pm at SC L3

Course Description

This course is an introduction to modern abstract algebra and the algebraic way of thinking in advanced mathematics. The course focuses on basic algebraic concepts which arise in various areas of advanced mathematics, and emphasizes on the underlying algebraic structures which are common to various concrete mathematical examples.

Topics include:

Group Theory - examples of groups including permutation and dihedral groups, subgroups, the Theorem of Lagrange, group homomorphisms, normal subgroups and quotient groups.

Ring Theory - examples of rings including the ring of integers and polynomial rings, integral domains, fields, ring homomorphisms, ideals and quotient rings.

Field Theory - examples of field extensions and finite fields.


Textbooks

  • Lecture notes available at the course webpage.

References

  • D. Dummit and R. Foote, Abstract Algebra, John Wiley and Sons, 3rd edition.
  • P. Aluffi, Algebra: Chapter 0, Graduate Studies in Mathematics Vol. 104, American Mathematical Society.
  • M. Artin, Algebra, Prentice Hall, 2nd edition.
  • J. Fraleigh, A First Course in Abstract Algebra, Addison-Wesley, 7th edition.

Lecture Notes


Tutorial Notes


Assignments


Solutions


Assessment Scheme

Homework 10%
Midterm 30%
Final 60%

Useful Links


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: April 29, 2022 16:34:52