抽象代数课程 Abstract Algebra [CC字幕]
https://www.youtube.com/watch?v=pTZrTN-jJ9M&list=PLL0ATV5XYF8DTGAPKRPtYa4E8rOLcw88y&index=1
转载自YouTube上Matthew Salomone的在线课程，是我找了半天才找到的画质清晰+声音清楚+电子板书+CC字幕+帅气小哥的组合。现全119P已更新完成，内容涵盖群、环、域、Galois理论。需要英文字幕的，请按CC字幕按钮。
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视频选集
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301.1 What is Abstract Algebra The Tangle Dance
09:34
301.1 Rational Tangles and the Inverse of T
06:10
301.1b Symmetries of Polygons
11:08
301.1c Polygon Symmetry Wrapup
17:09
301.1d Proofs and Logical Forms
06:48
301.2 Definition of a Group
07:12
301.2B Basic Properties of Groups
12:20
301.3A Finite Groups and Order(s)
13:37
301.3B Cyclic Groups and Subgroups
16:28
301.3C Subgroup Tests
10:02
301.3C1 Important Facts about Order
14:59
301.3D Abelian Groups, Center of a Group
22:08
301.3E Centralizer of an Element of a Group
11:41
301.3F Bonus Center, Centralizer, and Graph Theory
16:50
301.4A Cyclic Groups Introduction
09:12
301.4B Examples of Cyclic Groups
09:57
301.4C Properties of Cyclic Groups
10:24
301.4D Counting Elements of Order d in a Cyclic Group
15:14
301.4D Subgroups of Cyclic Groups, Part I
12:58
301.4E Subgroup Lattice for Cyclic Groups
12:35
301.5A Permutation Groups Intro and Goals
02:53
301.5B Motivating Permutations Anagrams and Symmetries
06:24
301.5C Definition and Stack Notation for Permutations
07:50
301.5D Cycle Notation for Permutations
10:03
301.5E1 Simplifying a Product of Permutations
12:26
301.5E2 Find the Inverse of a Permutation using Cycles
07:25
301.5G Transpositions and the Alternating Group
11:16
301.5H Extra Conjugacy Classes of Permutations
06:24
301.5I Cayley's Theorem for Finite Groups
10:43
301.6A Isomorphisms Introduction and Goals
07:24
301.6B Definition of Isomorphism
16:04
301.6C Examples of Isomorphisms
13:00
301.6D Element Properties of Isomorphisms
15:52
301.6E (Sub)Group Level Properties of Isomorphisms
08:18
301.6F Left and Right Actions; Inner Automorphisms
17:02
301.6G Automorphism Group of G
09:38
301.7A Cosets and Lagrange's Theorem Introduction
07:57
301.7B Cosets Construction and Motivation
15:30
301.7C When are Cosets of H also Subgroups
09:35
301.7D Lagrange's Theorem Proof
16:13
301.7E Converse of Lagrange's Theorem is False
08:04
301.7F Some Consequences of Lagrange's Theorem
08:56
301.7G Extra Counting an Internal Direct Product
11:49
301.7H Extra All Groups of Prime and Double-Prime Order
17:52
301.8A Direct Products of Groups Goals
06:46
301.8B Defining, Motivating, and Modeling Direct Products
13:08
301.8C Direct Products of Cyclic Groups
11:32
301.8D Classifying the Multiplicative Groups U(n)
09:50
301.8E Extra Short Exact Sequences
07:15
301.8F Extra Three Short Exact Sequence Constructions
05:16
301.8G Extra External Direct Product & Short Exact Sequence
06:37
301.8H Extra Two Different Product Constructions
16:25
301.8I Extra Semi-Direct Products of Groups
11:42
301.9A Normal Subgroups and Factor Groups Goals
08:11
301.9B Normal Subgroups Motivation and Definition
20:04
301.9C Extra Normal Subgroups and Conjugacy Classes
08:07
301.9D Factor Groups or Quotient Groups
11:53
301.9E Some Properties of Factor Groups
16:00
301.9F Internal Direct Product of Groups
12:08
301.9G Cauchy's Theorem for Abelian Groups
16:08
301.9G Extra Short Exact Sequences and Factor Groups
11:17
301.9H Extra Groups of Prime-Square Order
13:25
301.10A Homomorphisms of Groups Goals
11:23
301.10B Extra Echoes of Linear Algebra Rank-Nullity Theorem
12:48
301.10C Group Homomorphism Definition and Example
09:40
301.10D Properties of Homomorphisms, Image, Kernel
13:37
301.10E Homomorphism Properties Orders and Subgroups
19:40
301.10F Kernels are Normal Subgroups are Kernels
10:32
301.10G Extra First Isomorphism Theorem - Linear Algebra
09:39
301.10H Applying the First Isomorphism Theorem
11:28
301.10I First Isomorphism Theorem - Proof
06:54
301.10J Using the First Isomorphism Theorem
12:09
301.11A Fundamental Theorem of Finite Abelian Groups - Goals
07:03
301.11B Primes Don't Talk Theorem for Abelian Groups
16:46
301.11C Prime Powers Partition Theorem for Abelian Groups
13:31
301.11D The Fundamental Theorem of Finite Abelian Groups
10:30
301.11E Lagrange's Theorem Abelian Converse
10:56
Exploring Abstract Algebra II_ Contents
04:37
302.7A Polynomials
10:45
302.7B Polynomials - A Change in Strategy
10:23
302.7C La Ideé du Galois
12:08
302.7D What is a Galois Group
14:51
302.8A Rings and First Examples
12:57
302.8B Quaternions and Classifying Rings
10:43
302.8C Ideals
14:53
302.9A Quadratic Extension Rings and their Norm
13:56
302.9B Irreducibility and the Norm
10:24
302.S1 Three Paths to Irreducibility
16:02
302.10A Fields, Multiplication, and Fractions
12:04
302.10B Fields as Quotients of Rings
16:20
302.10C Constructing Finite Fields
15:41
302.S2a Field Extensions and Polynomial Roots
10:11
302.S2b Simple Extensions
13:20
302.S2c Two Isomorphic Simple Extensions
07:06
302.II.3A Intro to Constructible Numbers
12:35
302.II.3B Constructible Numbers and Fields
16:44
302.II.3C Two Constructibility Proofs
07:29
302.S3a Motivation for Minimal Polynomials
08:02
302.S3b Finding Minimal Polynomials
09:24
302.S3c Minimal Polynomials Existence and Uniqueness
12:00
302.S4 Normal Extensions
09:25
302.S5 Splitting Fields
18:08
302.S5y The Tower Law
09:41
302.S6a Motivation for Cyclotomic Fields
13:52
302.S6b Cyclotomic Extensions and Automorphisms
17:07
302.S7a Symmetries to Motivate Field Automorphisms
09:08
302.S7b Field Automorphisms and Galois Groups
13:31
302.S7c Two Galois Group Examples
14:11
302.S8A Why Automorphisms Like Normal Extensions
06:54
302.S8B Conjugate Roots Theorem
07:05
302.S8C Automorphisms of Normal Extensions
15:31
302.S9A Galois Groups and Stubborn Polynomials
13:49
302.S9B The Galois Correspondence
18:03
302.S10A Quadratic and Cubic Formulas and Fields
11:16
302.S10B Radical Extensions & Solvable Groups
12:56
302.S12A Quintic Impossible 1 - Solvability in Degrees 2, 3, 4
11:00
302.S12B Quintic Impossible 2 - An Insolvable Quintic
17:00
302.S13A Fundamental Theorem of Algebra -- Statements
08:17
302.S13B Fundamental Theorem of Algebra -- Proof
14:51
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