MATH 500 - Spring 2020 - Lee DeVille - UIUC

MATH 500 - Spring 2020 - Lee DeVille - UIUC

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Lecture 43, Part 3 of 3 1 of 30

duration 10 minutes 11 seconds

Lecture 43, Part 3 of 3

Lecture 43, Part 3 of 3

Lecture 43, Part 3 of 3

Lecture 43, Part 3 of 3

Solvability Theorem

From Lee DeVille

13 plays 0
Lecture 43, Part 2 of 3 2 of 30

duration 5 minutes 40 seconds

Lecture 43, Part 2 of 3

Lecture 43, Part 2 of 3

Lecture 43, Part 2 of 3

Lecture 43, Part 2 of 3

Solvability in terms of radicals

From Lee DeVille

5 plays 0
Lecture 43, Part 1 of 3 3 of 30

duration 11 minutes 12 seconds

Lecture 43, Part 1 of 3

Lecture 43, Part 1 of 3

Lecture 43, Part 1 of 3

Lecture 43, Part 1 of 3

Cyclic Extensions

From Lee DeVille

11 plays 0
Lecture 42, Part 3 of 3 4 of 30

duration 11 minutes 11 seconds

Lecture 42, Part 3 of 3

Lecture 42, Part 3 of 3

Lecture 42, Part 3 of 3

Lecture 42, Part 3 of 3

Examples

From Lee DeVille

4 plays 0
Lecture 42, Part 2 of 3 5 of 30

duration 5 minutes 48 seconds

Lecture 42, Part 2 of 3

Lecture 42, Part 2 of 3

Lecture 42, Part 2 of 3

Lecture 42, Part 2 of 3

Square roots and the Alternating Group

From Lee DeVille

6 plays 0
Lecture 42, Part 1 of 3 6 of 30

duration 9 minutes 5 seconds

Lecture 42, Part 1 of 3

Lecture 42, Part 1 of 3

Lecture 42, Part 1 of 3

Lecture 42, Part 1 of 3

Galois groups and S_n

From Lee DeVille

7 plays 0
Lecture 41, Part 6 of 6 7 of 30

duration 14 minutes 14 seconds

Lecture 41, Part 6 of 6

Lecture 41, Part 6 of 6

Lecture 41, Part 6 of 6

Lecture 41, Part 6 of 6

Examples

From Lee DeVille

5 plays 0
Lecture 41, Part 5 of 6 8 of 30

duration 3 minutes 14 seconds

Lecture 41, Part 5 of 6

Lecture 41, Part 5 of 6

Lecture 41, Part 5 of 6

Lecture 41, Part 5 of 6

Review of the Fundamental Theorem

From Lee DeVille

7 plays 0
Lecture 41, Part 4 of 6 9 of 30

duration 19 minutes 21 seconds

Lecture 41, Part 4 of 6

Lecture 41, Part 4 of 6

Lecture 41, Part 4 of 6

Lecture 41, Part 4 of 6

Implications of subgroup theorem

From Lee DeVille

8 plays 0
Lecture 41, Part 3 of 6 10 of 30

duration 18 minutes 28 seconds

Lecture 41, Part 3 of 6

Lecture 41, Part 3 of 6

Lecture 41, Part 3 of 6

Lecture 41, Part 3 of 6

Theorem about subgroups of Aut

From Lee DeVille

5 plays 0
Lecture 41, Part 2 of 6 11 of 30

duration 8 minutes 12 seconds

Lecture 41, Part 2 of 6

Lecture 41, Part 2 of 6

Lecture 41, Part 2 of 6

Lecture 41, Part 2 of 6

Characters of a Group

From Lee DeVille

7 plays 0
Lecture 41, Part 1 of 6 12 of 30

duration 10 minutes 14 seconds

Lecture 41, Part 1 of 6

Lecture 41, Part 1 of 6

Lecture 41, Part 1 of 6

Lecture 41, Part 1 of 6

Statement of the Fundamental Theorem of Galois Theory

From Lee DeVille

9 plays 0
Lecture 40, Part 2 of 2 13 of 30

duration 20 minutes 13 seconds

Lecture 40, Part 2 of 2

Lecture 40, Part 2 of 2

Lecture 40, Part 2 of 2

Lecture 40, Part 2 of 2

Galois extensions

From Lee DeVille

9 plays 0
Lecture 40, Part 1 of 2 14 of 30

duration 19 minutes 31 seconds

Lecture 40, Part 1 of 2

Lecture 40, Part 1 of 2

Lecture 40, Part 1 of 2

Lecture 40, Part 1 of 2

Automorphism groups and fixed fields

From Lee DeVille

11 plays 0
Lecture 39, Part 3 of 3 15 of 30

duration 11 minutes 6 seconds

Lecture 39, Part 3 of 3

Lecture 39, Part 3 of 3

Lecture 39, Part 3 of 3

Lecture 39, Part 3 of 3

Cyclotomic Extensions

From Lee DeVille

8 plays 0
Lecture 39, Part 2 of 3 16 of 30

duration 12 minutes 55 seconds

Lecture 39, Part 2 of 3

Lecture 39, Part 2 of 3

Lecture 39, Part 2 of 3

Lecture 39, Part 2 of 3

Separability in characteristic p

From Lee DeVille

8 plays 0
Lecture 39, Part 1 of 3 17 of 30

duration 13 minutes 51 seconds

Lecture 39, Part 1 of 3

Lecture 39, Part 1 of 3

Lecture 39, Part 1 of 3

Lecture 39, Part 1 of 3

Separability

From Lee DeVille

11 plays 0
Lecture 38, Part 4 of 4 18 of 30

duration 8 minutes 23 seconds

Lecture 38, Part 4 of 4

Lecture 38, Part 4 of 4

Lecture 38, Part 4 of 4

Lecture 38, Part 4 of 4

Algebraic Closures

From Lee DeVille

10 plays 0
Lecture 38, Part 3 of 4 19 of 30

duration 6 minutes 47 seconds

Lecture 38, Part 3 of 4

Lecture 38, Part 3 of 4

Lecture 38, Part 3 of 4

Lecture 38, Part 3 of 4

Uniqueness of Splitting Fields

From Lee DeVille

6 plays 0
Lecture 38, Part 2 of 4 20 of 30

duration 12 minutes 6 seconds

Lecture 38, Part 2 of 4

Lecture 38, Part 2 of 4

Lecture 38, Part 2 of 4

Lecture 38, Part 2 of 4

A bunch of examples

From Lee DeVille

8 plays 0
Lecture 38, Part 1 of 4 21 of 30

duration 6 minutes 33 seconds

Lecture 38, Part 1 of 4

Lecture 38, Part 1 of 4

Lecture 38, Part 1 of 4

Lecture 38, Part 1 of 4

Existence of Splitting Fields

From Lee DeVille

8 plays 0
Lecture 36, Part 4 of 4 22 of 30

duration 9 minutes 14 seconds

Lecture 36, Part 4 of 4

Lecture 36, Part 4 of 4

Lecture 36, Part 4 of 4

Lecture 36, Part 4 of 4

Composite fields

From Lee DeVille

8 plays 0
Lecture 36, Part 3 of 4 23 of 30

duration 10 minutes 53 seconds

Lecture 36, Part 3 of 4

Lecture 36, Part 3 of 4

Lecture 36, Part 3 of 4

Lecture 36, Part 3 of 4

Finitely-generated extensions

From Lee DeVille

6 plays 0
Lecture 36, Part 2 of 4 24 of 30

duration 7 minutes 44 seconds

Lecture 36, Part 2 of 4

Lecture 36, Part 2 of 4

Lecture 36, Part 2 of 4

Lecture 36, Part 2 of 4

Chains of field extensions

From Lee DeVille

9 plays 0
Lecture 36, Part 1 of 4 25 of 30

duration 16 minutes 18 seconds

Lecture 36, Part 1 of 4

Lecture 36, Part 1 of 4

Lecture 36, Part 1 of 4

Lecture 36, Part 1 of 4

Algebraic numbers

From Lee DeVille

13 plays 0
Lecture 35, Part 4 of 4 26 of 30

duration 5 minutes 32 seconds

Lecture 35, Part 4 of 4

Lecture 35, Part 4 of 4

Lecture 35, Part 4 of 4

Lecture 35, Part 4 of 4

Simple extensions

From Lee DeVille

11 plays 0
Lecture 35, Part 3 of 4 27 of 30

duration 5 minutes 7 seconds

Lecture 35, Part 3 of 4

Lecture 35, Part 3 of 4

Lecture 35, Part 3 of 4

Lecture 35, Part 3 of 4

Examples

From Lee DeVille

11 plays 0
Lecture 35, Part 2 of 4 28 of 30

duration 7 minutes 45 seconds

Lecture 35, Part 2 of 4

Lecture 35, Part 2 of 4

Lecture 35, Part 2 of 4

Lecture 35, Part 2 of 4

Field extensions

From Lee DeVille

12 plays 0
Lecture 35, Part 1 of 4 29 of 30

duration 7 minutes 23 seconds

Lecture 35, Part 1 of 4

Lecture 35, Part 1 of 4

Lecture 35, Part 1 of 4

Lecture 35, Part 1 of 4

Prime fields

From Lee DeVille

19 plays 0
Lecture 34, Part 4 of 4 30 of 30

duration 15 minutes 39 seconds

Lecture 34, Part 4 of 4

Lecture 34, Part 4 of 4

Lecture 34, Part 4 of 4

Lecture 34, Part 4 of 4

Jordan canonical form

From Lee DeVille

10 plays 0

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