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Galois Theory of

Galois Theory of Finite Fields: Some Applications (Algebra 3: Lecture 22 Video 2)

Isomorphisms between Finite

Isomorphisms between Finite Fields (Algebra 3: Lecture 22 Video 4)

Counting Irreducible Polynomials

Counting Irreducible Polynomials of Given Degree (Algebra 3: Lecture 22 Video 3)

Examples of the

Examples of the Galois Correspondence (Algebra 3: Lecture 21 Video 2)

Linear Independence of

Linear Independence of Characters (Algebra 3: Lecture 21 Video 3)

Fundamental Theorem of

Fundamental Theorem of Galois Theory: Intersections and Composites (Algebra 3: Lecture 21 Video 1)

A Sketch of

A Sketch of the Proof of Theorem 9 (Algebra 3: Lecture 21 Video 4)

The Fundamental Theorem

The Fundamental Theorem of Galois Theory I (Algebra 3: Lecture 20 Video 1)

Properties of the

Properties of the Galois Correspondence (Algebra 3: Lecture 20 Video 2)

The Fundamental Theorem

The Fundamental Theorem of Galois Theory: When is E/F Galois? (Algebra 3: Lecture 20 Video 3)

K/F is Galois

K/F is Galois Implies an Irreducible with a Root in K Splits in K[x] (Algebra 3: Lecture 19 Video 2)

Fixed Field and

Fixed Field and Galois Extensions (Algebra 3: Lecture 19 Video 1)

K/F is Galois

K/F is Galois iff K is the Splitting Field of a Separable Polynomial (Algebra 3: Lecture 19 Video 4)

The Definition of

The Definition of a Normal Extension (Algebra 3: Lecture 19 Video 3)

Examples of Galois

Examples of Galois Extensions (Algebra 3: Lecture 18 Video 1)

Examples of Galois

Examples of Galois Extensions: The Splitting Field of x^3-2 (Algebra 3: Lecture 18 Video 2)

Examples of Galois

Examples of Galois Extensions: The Splitting Field of x^4-2 (Algebra 3: Lecture 18 Video 3)

The Definition of

The Definition of a Galois Extension (Algebra 3: Lecture 17 Video 2)

If L/K is

If L/K is Finite then Aut(L/K) is Finite (Algebra 3: Lecture 17 Video 1)

Automorphisms of Fields

Automorphisms of Fields (Algebra 3: Lecture 16 Video 1)

An Example of

An Example of a Galois Group (Algebra 3: Lecture 17 Video 3)

An Element of

An Element of Aut(L/K) Permutes the Roots of f(x) (Algebra 3: Lecture 16 Video 3)

Examples where [L:K]

Examples where [L:K] is Greater than 1 but Aut(L/K) is Trivial (Algebra 3: Lecture 16 Video 2)

Existence and Uniqueness

Existence and Uniqueness of Finite Fields (Algebra 3: Lecture 15 Video 1)