Reference book: Harold M. Edwards- Galois Theory
How to solve polynomial equations? We’d like a formula for zeroes/roots in terms of the coefficients a_i. quadratic formulas cubic formulas
[3:40] Galois considered fields extended by rational functions in the variable p, and that enabled him to make the correspondence between permutation groups and fields.
Why No Quintic Formula? - Intuitive Explanation Attempt…
- algebraic structures and complex analysis
- how to describe a normal subgroup
- Vieta’s formulas
update: 04.05.2025
The beginnings of Galois theory
But this massive work is an attempt to curate sequences of problems for secondary students (the stated focus is high school students, but that can be broadly interpreted) that allow them to discover and recreate much of “elementary” mathematics (number theory, polynomials, inequalities, calculus, geometry, combinatorics, game theory, probability) and start edging into the sophisticated world of group theory, Galois theory, etc. ~ Mathematics via Problems - Algebra
- pushing myself to my limits, developing the language as I go