302 S5 Splitting Fields

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This lecture is part of an online course on Galois theory. We define the

Field Theory: Let f(x) = x^4 -16x^2 +4. We find the roots of f(x), calculate the

This video screencast was created with Doceri on an iPad. Doceri is free in the iTunes app store. Learn more at ...

This video screencast was created with Doceri on an iPad. Doceri is free in the iTunes app store. Learn more at ...

The Tower Law contends that finite extensions of finite extensions are finite extensions, and that their degrees multiply.

https://h5bedi.github.io/GaloisTheory/

Field Theory 3,

Two examples of

Field Theory 4, Existence of

So here we define

We show that Q(∛5) is not a normal extension of Q.

Automorphisms are a key tool for understanding field extensions, particularly

This is isomorphism between two

So let us now talk about uniqueness of

... f which Lies Over field F and you have this extension K Over F where K is the

In what sense does the Galois group of a polynomial measure how "stubborn" it is to

Why are quadratic and cubic polynomials all solvable by formulas in radicals? We introduce the notion of a radical extension ...

Splitting field

In this video we introduce the concept of the