Training Abstract Algebra

Abstract Algebra

Linear & Abstract Algebra
Advanced 245 minutes 7 lessons
Master the algebraic structures underlying mathematics: groups, rings, fields, Galois theory, and representation theory — the language of symmetry and structure.

Learning Objectives

  • Classify groups using Lagrange's theorem and Sylow theory
  • Apply isomorphism theorems to groups and rings
  • Work with polynomial rings and field extensions
  • Understand the Galois correspondence and solvability by radicals
  • Compute character tables for group representations
  • Apply the structure theorem for modules over PIDs

Lessons

1
Groups: Definitions & Examples
35 min
2
Homomorphisms, Kernels & Quotient Groups
35 min
3
Rings, Ideals & Polynomial Rings
35 min
4
Fields & Field Extensions
35 min
5
Galois Theory
35 min
6
Group Actions & Sylow Theory
35 min
7
Modules & Representation Theory
35 min

Quick Practice

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Key Concept Flashcards

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