Abstract Algebra II (Spring 2017) by James Cook

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source: James Cook      2017年1月16日

solution to cubic, 1-16-17 52:03 I intend to post videos of my Lectures from Math 422 in the Spring 2017 Semester at Liberty University. This is a continuation of Abstract Algebra I. We begin with a tour of classical Galois Theory guided by Rotman's introductory text on the topic. Then, I'll likely spend a week on Differential Galois Theory. At that point we have some classroom interaction (aka Test 1). Then, we'll transition to working through select parts of Dummit and Foote's Chapters 10, 11, 12 and 18.
splitting fields, mostly review on extension fields, 1-18-17 48:50
Galois group introduced, 1-20-17 53:08
Theorem 55, 56, elementary Galois group examples, 1-23-17 53:45
tower of Babel, roots of unity begins, 1-25-17 53:12
roots of unity section, 1-27-17 54:04
Galois reboot, 1-31-17 48:24
characters and fixed field theorems, 2-1-17 50:46
Fundamental Theorem of Galois Theory, 2-3-17 48:26
splitting field x8-2, finite field overview, composite fields, 2-6-17 51:02
splitting field for general polynomial, 2-13-17 52:14
Insolvability of the Quintic etc. 2-17-17 53:58
Galois group example D4 part 1, 2-20-17 52:50
Galois group example D4 part 1, the conjugation trick, 2-20-17 52:19
from differential fields to elementary functions, 2-22-17 58:26
sketch of Differential Galois Theory, Takehome Test 1, 2-24-17 49:52
introduction to modules, 3-1-17 50:14
on modules and algebra basics, 3-3-17 52:55
module homomorphism basics, 3-6-17 51:44
direct sum of submodule theorem, 3-6-17 10:01
free module construction, extending scalars, 3-8-17 52:40
more on tensor and module homomorphisms, 3-10-17 52:39
tensor product of modules, 3-20-17 55:29
tensor product is associative, multilinear maps, 3-22-17 54:55
short exact sequence idea, tensor product on vectors, 3-24-17 56:25
on complexification and tensor algebra, 3-27-17 53:32
existence theorems of module over PID, 4-3-17 (no sound) 51:07
fundamental theorem of finitely generated Abelian groups example, 4-5-17 53:17
Smith Normal Form for Abelian Groups, 4-7-17 52:54
correction to Lecture on 4-7-17 0:57
smith normal form, start of rational canonical forms, 4-10-17 47:39
rational canonical form, 4-12-17 25:09
rational and Jordan form of matrix, 4-14-17 55:42
discussion of Jordan form, 4-19-17 40:31
representations of groups and algebras, basic ideas, 4-21-17 53:09
3 hyperbolic number fun, finite group reps, 4-24-17 49:23
a bit of representation theory, 4-26-17 53:42
proof of Mashke's Theorem, a word on Wedderburn, 4-28-17 48:07
how to use Smith Normal form to get rational form, 5-1-17 55:04
Final Exam Bonus Dance 0:23