MATH 440 • SPRING 2027

Galois Theory

Solution formulas, one per row. Solve x² + ax + b = 0: x = (−a ± √(a² − 4b)) / 2.
Solve x³ + ax² + bx + c = 0: Cardano's formula, a sum of two cube roots of nested square roots, filling two lines.
Solve x⁴ + ax³ + bx² + cx + d = 0: Ferrari's formula, in small print with several auxiliary quantities.
Solve x⁵ + ax⁴ + bx³ + cx² + dx + e = 0: an empty box containing only question marks.

In 1831, Évariste Galois discovered why the question marks cannot be filled in.

In MATH 440 – Galois Theory you will learn:

how the structure of fields can be understood through groups
the complete structure and classification of finite fields
why a regular 17-gon can be drawn with ruler and compass, but a 7-gon cannot
how to compute Galois groups and what they tell you about equations

Lectures: MWF 10:30–11:20
First class: Wednesday, January 6, 2027
Prerequisites: MATH 340; MATH 341 recommended
Instructor: Nils Bruin • nbruin@sfu.ca
SC K 10507 • (778) 782 3794
Text: David A. Cox, Galois Theory, 2nd ed., Wiley 2012