Ben-Gurion University of the Negev

Department of Mathematics


Course number: 201-17041; Spring Semester 2016

Galois image


Instructor: Ido Efrat Time and place: Monday 12-14, Building 90, Room 242
Wednesday 13-15, Building 58, Room 101

Prerequisite: Algebraic Structures


Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7

Some practice problems

Course Plan:

  1. Fields
  2. Decomposition of polynomials
  3. Field extensions
  4. Constructions using a ruler and a compass
  5. Algebraicaly closed fields
  6. Splitting fields
  7. Galois extensions
  8. Cyclic extensions
  9. Solvability of polynomials by radicals
  10. Finite fields
  11. Roots of unity
  12. The fundamental theorem of algebra (if time allows)

Exams and Grading:

There will be a final exam. The course' grade will be the final exam's grade.

Recommanded books

  1. D. Cox, Galois Theory, Wiley Interscience, 2004
  2. J.-P. Escofier, Galois Theory, Springer, 2001
  3. D.J.H. Garling, A Course in Galois Theory, Cambridge University Press
  4. N. Jacobson, Basic Algebra, Freeman 1974
  5. S. Lang, Algebra, Addison-Weseley, 1965
  6. M. Artin, Algebra, Prentice-Hall, 1991
  7. J.S. Milne, Fields and Galois Theory, On-line lecture notes, with exercises.
  8. J. Swallow, Exploratory Galois Theory, Cambridge University Press 2004

Some Links:

The life and times of Evariste Galois
The 17-gon
Biographies of Cardano and Tartaglia
Tartaglia vs. Cardano