MATH3040 - Fields and Galois Theory - 2020/21

Course Name: 
Fields and Galois Theory
Teacher: 
Prof. Kwok Wai CHAN
Course Year: 
2020/21
Term: 
2

Announcement

  • Course outline [Download file]
  • Tentative class and HW schedule [Download file]
  • Lectures -- ZOOM Meeting ID: 980 7554 9400, Passcode: 455123
  • Tutorials -- ZOOM Meeting ID: 952 0288 8427, Passcode: 042173
  • There is no tutorial in the first week; the first tutorial will be held on Jan 19.
  • We are going to hold a 24-hour Take Home Midterm Test for MATH3040, during 9 March (6pm) - 10 March (6pm). We will cover materials up to Lecture 5 (or the lecture on Feb 9). The question paper will be posted on Blackboard and sent to you by email at 6pm on 9 March (Tuesday). It is an open-book/open-notes exam, but discussions with anyone are strictly prohibited. Please submit your answers to Blackboard in a SINGLE PDF file. We allow multiple submissions, and your last submission before the deadline (10 March 6pm) will be taken as the final version of your solution. NO submissions after 10 March 6pm will be accepted.
  • We are going to hold the final examination for MATH3040 on 29 April 2021 during 9:30am - 12:00noon. We will post the question paper on Blackboard and send it to your email address at 9:30am on 29 April 2021 (Thursday). Please submit your answers to Blackboard in a SINGLE PDF file, and please reserve sufficient time to do so. It is an open-book/open-notes exam, but discussions with anyone are strictly prohibited. We will allow multiple submissions (but since this could be quite time consuming, please avoid doing so), and your last submission before 29 April 12:00noon will be taken as the final version of your solution. NO submissions after 29 April 12:00noon will be accepted.
  • Online final examination -- Zoom meeting ID: 941 9439 7495, Passcode: 158891. Please enter the Zoom room at 9:15am and prepare your student ID card for identity verification.

General Information

Lecturer

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

Teaching Assistant

  • LAM Chin Hang Eddie
    • Office: LSB G08
    • Tel: 3943 7954
    • Email:
  • NG Ming Ho
    • Office: LSB 228
    • Tel: 3943 7955
    • Email:

Time and Venue

  • Lecture: Mon 4:30pm - 6:15pm & Tue 4:30pm - 5:15pm, online
  • Tutorial: Tue 5:30pm - 6:15pm, online

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.


Textbooks

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

References

  • 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)

Pre-class Notes


Lecture Notes


Class Notes


Assignments


Solutions


Assessment Scheme

Homework 20%
Take-Home Midterm Test 30%
Final Exam 50%

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 26, 2021 15:49:50