MATH2078 - Honours Algebraic Structures - 2022/23

Course Year: 
2022/23
Term: 
2

Announcement

  • Course outline [Download file]
  • On Mondays, we will have lectures during 2:30pm - 3:15pm and tutorials during 3:30pm - 4:15pm (in contrast with the timetable announced on CUSIS), starting from Week 1.
  • The tutorial in Week 1 will be replaced by lectures. The first tutorial will be held on Jan 16 (Mon) 3:30pm - 4:15pm.
  • Please submit your homework solutions via Blackboard. In case you haven't been added to the system yet, please email the lecturer.

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:

Time and Venue

  • Lecture: Mon 2:30pm - 3:15pm, LPN LT; Wed 4:30pm - 6:15pm, MMW 702
  • Tutorial: Mon 3:30pm - 4:15pm, LPN LT

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

  • J. A. Gallian, Contemporary Abstract Algebra, CRC Press, 10th edition (Recommended).
  • M. Artin, Algebra, Prentice Hall, 2nd edition.
  • J. Fraleigh, A First Course in Abstract Algebra, Addison-Wesley, 7th edition.
  • P. Aluffi, Algebra: Chapter 0, Graduate Studies in Mathematics Vol. 104, American Mathematical Society.
  • D. Dummit and R. Foote, Abstract Algebra, John Wiley and Sons, 3rd edition.

Lecture Notes


Tutorial Notes


Assignments


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: February 07, 2023 14:11:24