302.S5: Splitting Fields
A splitting field for a polynomial is the smallest field that contains all its roots (and therefore over which the polynomial splits). In the Goldilocks story of algebraic extensions, it's "just right."
▶︎
302.S5y: The Tower Law
▶︎
302.S6a: Motivation for Cyclotomic Fields
▶︎
Galois theory: Splitting fields
▶︎
The Insolvability of the Quintic
▶︎
How Newton Calculated Pi in a Single Afternoon
▶︎
302.S4: Normal Extensions
▶︎
302.7C: La Ideé du Galois
▶︎
302.S2a: Field Extensions and Polynomial Roots
▶︎
Richard Feynman Explains Why GENIUS RAMANUJAN Got Math Answers In His Dreams
▶︎
302.S2b: Simple Extensions
▶︎
302.S3a: Motivation for Minimal Polynomials
▶︎
The Anti Trampoline Effect
▶︎
The Test That Terence Tao Aced at Age 7
▶︎
We're 99.9% sure this pattern is true, but no one can prove it
▶︎
Galois Theory Explained Simply
▶︎
Only 2 Primes Have This Property. We Don't Know Why.
▶︎
302.S3c: Minimal Polynomials Existence and Uniqueness
▶︎
Find a Splitting Field of x^3-1 over ℚ
▶︎