MATH3040 - Fields and Galois Theory - 2018/19

Course Year: 


  • Course outline [Download file]
  • Tentative class and HW schedule [Download file]
  • There is no tutorial in the first week; the first tutorial will be held on Jan 17.
  • Some words from TA: Every week, a few problems are uploaded one to two days prior to the tutorial class (usually on Thu). Please have a look if you want to attend.
  • HW 1 (due date: Jan 25) has been posted.
  • HW 2 (due date: Feb 1) has been posted.
  • HW 3 (due date: Feb 15) has been posted.
  • Lectures and Tutorials on Feb 18 (Mon) and Feb 21 (Thu) will be cancelled.
  • The Midterm will be held on Feb 28 (Thu) in class starting at 4:30pm in LSB C2. We will cover up to Lecture 5 (or §29, 30, 33, 48 & 49 in the textbook).
  • HW 4 (due date: Mar 1) has been posted.
  • HW 5 (due date: Mar 15) has been posted.
  • HW 6 (due date: Mar 29) has been posted.
  • HW 7 (due date: Apr 8) has been posted.
  • HW 7: a hint is added to the present pdf
  • HW 8 (due date: Apr 12) has been posted.
  • HW 9 (due date: Apr 19) has been posted.
  • HW 10 (due date: Apr 26) has been posted.

General Information


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

Teaching Assistant

  • CHOW Chi Hong
    • Office: AB1 505
    • Tel: 3943 4298
    • Email:

Time and Venue

  • Lecture: Mon 4:30pm - 6:15pm at AB1 G03; Thu 4:30pm - 5:15pm at LSB C2
  • Tutorial: Thu 5:30pm - 6:15pm at LSB C2

Course Description

This course is an introduction to the theory of field extensions and Galois theory. It is one of the continuations of MATH3030 (the other being MATH4080).

Topics include: field extensions, algebraic extensions, algebraic closures, geometric constructions, finite fields, splitting fields, separable and inseparable extensions, Galois extensions, Galois correspondences, cyclotomic extensions, solvability by radicals, etc.

Students are expected to have knowledge in MATH2040, MATH2070 and MATH3030, or equivalent.


  • J. Fraleigh, A First Course in Abstract Algebra, 7th edition, Addison-Wesley.


  • M. Artin, Algebra, 2nd edition, Prentice Hall.
  • D. Dummit and R. Foote, Abstract Algebra, 3rd edition, John Wiley and Sons.
  • J. Milne, Fields and Galois Theory (freely available online here)

Pre-class Notes

Lecture Notes

Class Notes

Tutorial Notes



Assessment Scheme

Homework 10%
Midterm (Feb 28) 40%
Final (Apr 29) 50%

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:

and thereby help avoid any practice that would not be acceptable.

Assessment Policy

Last updated: April 22, 2019 14:08:14