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Abstract Algebra

via YouTube

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Details

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Provider

YouTube
Pricing

Free Video
Languages

English
Effort

3 hours 30 minutes
Sessions

Self-Paced
Level

Intermediate

Found in

This course introduces the foundations of abstract algebra, beginning with groups and progressing through homomorphisms, quotient structures, rings, fields, vector spaces, and modules. It also examines symmetry groups, matrix groups, direct products, and related examples.

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 Lagrange’s 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).