MTB Quant Library
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Abstract Algebra
Abstract Algebra
Groups, rings, fields, and the structural foundations of modern algebra.
22
chapters
Beginner
01
Algebraic Structures & Axioms
Medium
→
02
Groups — Definition and Examples
Medium
→
03
Subgroups & Cyclic Groups
Medium
→
Intermediate
04
Cosets & Lagrange's Theorem
Hard
→
05
Normal Subgroups & Quotient Groups
Hard
→
06
Group Homomorphisms & Isomorphism Theorems
Hard
→
07
Direct Products & Direct Sums
Medium
→
08
Group Actions
Hard
→
11
Rings — Definition and Examples
Medium
→
12
Ideals & Quotient Rings
Hard
→
13
Ring Homomorphisms
Medium
→
14
Polynomial Rings
Hard
→
15
Euclidean Domains & Principal Ideal Domains
Hard
→
16
Chinese Remainder Theorem
Hard
→
Advanced
09
Sylow Theorems
Rigorous
→
10
Free Groups & Presentations
Hard
→
17
Fields — Definition and Basic Properties
Medium
→
18
Field Extensions
Rigorous
→
19
Splitting Fields & Algebraic Closures
Rigorous
→
20
Galois Theory — Fundamentals
Rigorous
→
21
Galois Theory — Solvability by Radicals
Rigorous
→
22
Modules over Rings & Structure Theorems
Rigorous
→
