Abstract Algebra Courses and Certifications

Abstract Algebra

Introduces abstract algebra through groups, homomorphisms, rings, fields, vector spaces, and modules, emphasizing core algebraic structures and their relationships.

• YouTube
• 3 hours 30 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - The Basics of Rings

Explore fundamental ring theory concepts including types, properties, homomorphisms, ideals, and polynomial rings through comprehensive examples and proofs.

• YouTube
• 4 hours 36 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - The Basics of Groups

Discover fundamental group theory concepts including subgroups, cosets, Lagrange's theorem, isomorphisms, homomorphisms, normal subgroups, and quotient groups through examples.

• YouTube
• 6 hours 31 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - Examples of Groups

Explore dihedral, symmetric, alternating, and quaternion groups through concrete examples and cycle notation in abstract algebra.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - Preliminaries

Master fundamental proof techniques and mathematical structures essential for abstract algebra through direct proofs, contradiction, induction, relations, and functions.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

Insights into Mathematics

An Informal Introduction to Abstract Algebra

An informal review of fields, rings, and vector spaces, ending with subobjects, homomorphisms, and quotient objects as common algebraic constructions.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - Cyclic Groups

Explore cyclic groups in abstract algebra, covering subgroups, general results, and classification theorems through comprehensive mathematical analysis.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - Eisenstein's Criterion

A proof of Eisenstein's criterion for polynomial irreducibility, illustrated with examples.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Abstract Algebra

2 ratings

Explore abstract algebra through groups, homomorphisms, quotient groups, group actions, and conjugacy with worked proofs and examples.

• YouTube
• 10 hours
• Self-Paced
• Free Video

Wrath of Math

Cool Examples of Quotient Groups in Abstract Algebra

Explore fascinating examples of quotient groups in abstract algebra, including finite order elements, commutators, and group centers. Gain insights into factor groups and their properties.

• YouTube
• 15 minutes
• Self-Paced
• Free Video

Kimberly Brehm

Abstract Algebra

1 rating

Explore groups from square symmetries and Cayley tables through dihedral groups, isomorphisms, Cayley’s theorem, and automorphisms.

• YouTube
• 2 hours 30 minutes
• Self-Paced
• Free Video

Algebra 1: Foundations

Builds modern algebra from sets and elementary proof through groups, rings, fields, and linear algebra, culminating in an elementary proof of Jordan form.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

IMSC;  NPTEL

Algebra - I

Graduate-level abstract algebra develops groups, rings, modules, and their classification, culminating in finitely generated abelian groups and Jordan canonical form.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

Introduction to algebraic structures

Introduces algebraic structures through set theory, combinatorics, graph theory, number theory, and elementary group theory.

• Swayam
• Available until Oct 9, 2026
• Free Online Course

NPTEL;  IIT Kanpur

Modern Algebra

Explore how algebra abstracts geometric objects and numbers, revealing fundamental properties and enabling applications beyond direct methods.

• YouTube
• 14 hours
• Self-Paced
• Free Video