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Subjects
Mathematics
Algebra
Abstract Algebra

Free Online

Abstract Algebra Courses and Certifications

Explore group theory, ring theory, and polynomial structures through rigorous mathematical proofs and problem-solving. Access comprehensive video tutorials on YouTube from mathematicians like Michael Penn, plus structured courses on Udemy, perfect for mathematics students and those applying algebra to game development.

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Abstract Algebra: Group Theory with the Math Sorcerer
572 ratings at Udemy

Master abstract algebra fundamentals through group theory, from basic operations to advanced concepts like homomorphisms and quotient groups. Develop mathematical maturity through proven theorems and practical problem-solving.
- Udemy
- 10 hours 1 minute
- On-Demand
- Paid Course
Abstract Algebra

Explore fundamental concepts of abstract algebra, including groups, rings, fields, and vector spaces, with a focus on definitions, examples, and key theorems.
- YouTube
- 3 hours 30 minutes
- On-Demand
- 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
- On-Demand
- 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
- On-Demand
- 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
- On-Demand
- 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
- On-Demand
- Free Video
Wrath of Math
Abstract Algebra

Master group theory fundamentals through binary operations, subgroups, homomorphisms, and quotient groups with rigorous proofs and practical examples.
- YouTube
- 6 hours 12 minutes
- On-Demand
- Free Video
Insights into Mathematics
An Introduction to Abstract Algebra - Abstract Algebra Math Foundations
1 review

Explore fundamental algebraic structures like groups, rings, fields, and vector spaces through intuitive examples, providing a bird's-eye view of abstract algebra's foundational concepts.
- YouTube
- 26 minutes
- On-Demand
- Free Video
Insights into Mathematics
Logical Challenges in Abstract Algebra - Math Foundations 214

Explores logical difficulties in abstract algebra, focusing on defining groups and the impact of different definitions on group theory development. Emphasizes critical thinking in mathematical foundations.
- YouTube
- 42 minutes
- On-Demand
- Free Video
Michael Penn
The Number Theory You Need to Learn Abstract Algebra

Explore essential number theory concepts like division algorithm, Euclidean algorithm, and congruence modulo n, laying the foundation for abstract algebra studies.
- YouTube
- 44 minutes
- On-Demand
- Free Video
Michael Penn
Abstract Algebra - Eisenstein's Criterion

Proof and examples of Eisenstein's criterion in abstract algebra, demonstrating its application in determining polynomial irreducibility over rational numbers.
- YouTube
- 23 minutes
- On-Demand
- Free Video
Michael Penn
Abstract Algebra - The Division Algorithm for Polynomials

Explore the division algorithm for polynomials over a field, including its statement and proof, in this concise abstract algebra lesson.
- YouTube
- 21 minutes
- On-Demand
- Free Video
Michael Penn
Abstract Algebra - Polynomial Rings

Explore polynomial rings, their properties, and key theorems, including the proof that R[x] is an integral domain when R is one.
- YouTube
- 21 minutes
- On-Demand
- Free Video
Michael Penn
Abstract Algebra - Ring Homomorphisms

Explore ring homomorphisms in abstract algebra, including definitions, examples, and key properties like multiplicative behavior and kernels.
- YouTube
- 20 minutes
- On-Demand
- Free Video
Michael Penn
Abstract Algebra - Units and Zero Divisors of a Ring

Explore units and zero divisors in Zn and 2x2 real matrices, classifying elements and proving key properties in abstract algebra.
- YouTube
- 23 minutes
- On-Demand
- Free Video

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