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Abstract Algebra

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Syllabus

What is Abstract Algebra? (Modern Algebra).
Group Definition (expanded) - Abstract Algebra.
Abstract Algebra: The definition of a Group.
Abstract Algebra: Motivation for the definition of a group.
Abstract Algebra: The definition of a Subgroup.
Group Multiplication Tables | Cayley Tables (Abstract Algebra).
Cosets and Lagranges Theorem - The Size of Subgroups (Abstract Algebra).
Normal Subgroups and Quotient Groups (aka Factor Groups) - Abstract Algebra.
Cyclic Groups (Abstract Algebra).
Abstract Algebra: Group or Not Group? (Integer edition).
Group Homomorphisms - Abstract Algebra.
Homomorphisms (Abstract Algebra).
Isomorphisms (Abstract Algebra).
The Kernel of a Group Homomorphism Abstract Algebra.
The Order of an Element (Abstract Algebra).
Symmetric Groups (Abstract Algebra).
Cycle Notation of Permutations - Abstract Algebra.
Dihedral Group (Abstract Algebra).
Symmetry Groups of Triangles (Abstract Algebra).
Matrix Groups (Abstract Algebra).
Direct Products of Groups (Abstract Algebra).
Simple Groups - Abstract Algebra.
Abstract Algebra: The definition of a Ring.
Ring Definition (expanded) - Abstract Algebra.
Ring Examples (Abstract Algebra).
Units in a Ring (Abstract Algebra).
Integral Domains (Abstract Algebra).
Ideals in Ring Theory (Abstract Algebra).
Field Definition (expanded) - Abstract Algebra.
Abstract Algebra: The definition of a Field.
Field Examples - Infinite Fields (Abstract Algebra).
What is a Vector Space? (Abstract Algebra).
What is a Module? (Abstract Algebra).

Taught by

Socratica

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