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Abstract Algebra
Abstract Algebra
47 lessons across 14 topics
1. Algebraic Structures and Examples
1
Binary Operations
2
Definitions And Examples Of Groups
3
Motivation From Symmetry And Arithmetic
2. Subgroups and Cyclic Groups
4
Cyclic Groups And Classification Basics
5
Generated Subgroups
6
Subgroup Tests
3. Permutation Groups
7
Alternating Groups Overview
8
Cycle Notation
9
Products And Inverses
10
Symmetric Groups
4. Cosets and Lagrange’s Theorem
11
Consequences Of Lagrange’s Theorem
12
Index
13
Left And Right Cosets
14
Orders Of Elements
5. Normal Subgroups and Quotient Groups
15
Canonical Examples
16
Factor Groups
17
Normality
6. Homomorphisms and Isomorphisms
18
First Isomorphism Theorem
19
Isomorphism Ideas
20
Kernels And Images
7. Group Actions or Advanced Group Topics
21
Group Actions
22
Or Review Of Quotient Structures
23
Orbits And Stabilizers
24
Symmetry Applications
8. Midterm 1 and Introduction to Rings
25
Commutative Rings And Unity
26
Midterm 1
27
Ring Definitions And Examples
9. Ring Homomorphisms and Ideals
28
Ideals
29
Quotient Rings
30
Ring Homomorphisms
31
Subrings
10. Integral Domains and Fields
32
Domains And Fields
33
Polynomial Examples
34
Units
35
Zero Divisors
11. Polynomial Rings
36
Division Algorithm
37
Irreducibility
38
Roots And Factorization
12. Euclidean Domains (SLASH) PID (SLASH) UFD Overview
39
Euclidean Algorithms
40
Greatest Common Divisors
41
Unique Factorization, If Included
13. Field Extensions or Additional Topics
42
Constructibility Ideas
43
Finite Fields Overview
44
Or Deeper Group/ring Applications
14. Final Review
45
Key Themes In Final Review
46
Review Of Proof Techniques And Abstract Reasoning
47
Structural Synthesis
