Math 422/501: Field and Galois Theory

Fall Term 2020
Lior Silberman

General Information

This is a basic course in algebra, covering one of the most beautiful results in mathematics: Galois's theory of solutions to algebraic equations. There is no required textbook, but many textbooks cover the material, several of which are available in PDF form from the publisher for anyone on the UBC network; a lot of the material can also be found in any "abstract algebra" textbook. More details may be found in the syllabus.


  1. Milne, Field and Galois Theory.
  2. Stewart, Galois Theory (2nd Edition).
  3. [Your favorite author], Abstract Algebra

Midterm Exam

Problem Sets

  1. Problem Set 1 (LyX, TeX), due 18/9/2020. Solutions.
  2. Problem Set 2 (Problem 6(d) corrected) (LyX, TeX), due 25/9/2020. Solutions.
  3. Problem Set 3 (LyX, TeX), due 2/10/2020. Solutions.
  4. Optional Problem Set 4 , due 9/10/2020. Solutions.
  5. Problem Set 5 (questions 4(a),6 clarified) (LyX, TeX), due 16/10/2020. Solutions.
  6. Problem Set 6 due 30/10/2020. Solutions.
  7. Problem Set 7 (LyX, TeX), due 6/11/2020 (Problems 7,8 postponed to PS8). Solutions.
  8. Problem Set 8 (LyX, TeX) (problem numbering clarified) due 13/11/2020. Solutions.
  9. Problem Set 9 due 20/11/2020. Solutions.
  10. Problem Set 10 due 27/11/2020. Solutions.

Lecture-by-Lecture information

Section numbers marked § are in the course notes.

Warning: the following information is tentative and subject to change at any time

Week Date Material Reading Scan Notes
1 W 9/9 Introduction   p1, p2, p3  
F 11/9 Solvable and nilpotent groups §1.4 Scan  
2 M 14/9 (continued)   Scan  
W 16/9 Polynomials §2.1 Scan  
F 18/9 PS1   p1, p2, p3, p4, p5, p6, p7, p8, p9, p10  
3 M 21/9 Field extensions §2.2 p1, p2, p3, p4, p5, p6, p7, p8  
W 23/9 (continued) (continued) p1, p2, p3, p4, p5, p6, p7, p8, p9  
F 25/9 PS2   Scan  
4 M 28/9 Recorded Lecture: Ruler and Compass §2.3 Scan Synchronous meeting cancelled
W 30/9 Splitting fields §3.1 Scan  
F 2/10 PS3   Scan  
5 M 5/10 Normal extensions (continued) Scan  
W 7/10 Example of a splitting field (continued) Scan  
F 9/10 PS4   Scan  
6 W 14/10 Separability §3.2 Scan  
F 16/10 PS5   Scan  
7 M 19/10 (continued)   Scan  
W 21/10 Automorphism groups §3.3 Scan  
F 23/10 (continued)   Scan  
8 M 26/10 The Group Action §3.4 Scan  
W 28/10 Galois Theory §3.5 Scan  
F 30/10 PS6   Scan  
9 M 2/11 Examples §3.6 Scan  
W 4/11 (continued)   Scan  
F 6/11 PS7   Scan  
10 M 9/11 Solubility by radicals §3.7 Scan  
F 13/11 PS8   Scan  
11 M 16/11 (continued)   Scan  
W 18/11 Transcendental extensions   Scan  
F 20/11 PS9   Scan  
12 M 23/11 Transcdence Bases   Scan  
W 25/11 Infinite Galois Theory   Scan  
F 27/11 PS10   Scan  
13 M 30/11 (continued)   Scan  
W 2/11 (continued)   Scan  

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Last modified Monday December 07, 2020