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Abstract Algebra

Description
Abstract Algebra deals with groups, rings, fields, and modules. These are abstract structures which appear in many different branches of mathematics, including geometry, number theory, topology, and more. They even appear in scientific topics such as quantum mechanics.
Lessons
Resources
What is Abstract Algebra? (3:22)
Group Definition (11:15)
Group Definition (Quick) (3:11)
Cosets and Lagrange's Theorem (9:19)
Group Multiplication Tables (Cayley Tables) (7:32)
Groups - Motivation for Definition (2:05)
Normal Subgroups and Factor Groups (11:24)
Subgroups (1:42)
Cyclic Groups (5:01)
Group or Not Group? (Integer Edition) (2:42)
Group Homomorphisms (10:04)
Group Homomorphisms (Quick) (4:12)
Isomorphisms for Groups (5:04)
Kernel of Group Homomorphisms (4:53)
Order of an Element (3:01)
Cycle Notation for Permutations (12:37)
Symmetric Groups (5:30)
Dihedral Groups (4:17)
Direct Products of Groups (8:55)
Matrix Groups (4:16)
Simple Groups (8:53)
Symmetry Groups of Triangles (3:56)
Ring Definition (6:51)
Ring Definition (Quick) (3:13)
Ring Examples (7:18)
Units in a Ring (7:14)
Field Definition (8:06)
Field Definition (Quick) (1:54)
Field Examples: Infinite Fields (5:37)
Ideals in Rings (11:57)
Integral Domains (7:34)
Modules (7:43)
Vector Spaces (6:58)
Abstract Algebra Textbook
Abstract Algebra Textbook
Abstract Algebra by Dummit & Foote is a standard textbook used by colleges and universities. It is extremely well written with lots of examples and exercises. It covers all the topics for a solid first course in Abstract Algebra. We use this on occasion as a reference for inspiration or reference. Highly recommended!
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