Robert Gardner's Online Modern Algebra: Groups

Online Modern Algebra: Groups (a work in progress)
with videos and transcript on the Zoom server Dr. Bob's Online University
(Not an actual university)

This website includes links to class notes and supplements (in PDF) used in the teaching of East Tennessee State University's Modern Algebra 1 (MATH 5410). Links are also available for video presentations of the notes. The videos have been used as of the teaching of online Modern Algebra 1, starting in spring 2021. The material is largely based on Thomas W. Hungerford's Algebra, Springer (1974):

Robert "Dr. Bob" Gardner can be reached by e-mail at: gardnerr@etsu.edu. His office is in Gilbreath Hall, Room 308F on the ETSU campus.

The following notes and supplements are all in PDF. The videos are stream from Zoom and include a synchronized transcript. However, ETSU does not have control of the Zoom site and these videos may be taken down as some point. For versions of these videos in mp4 housed on ETSU's Panopto Host, see "Online Modern Algebra: Groups, with videos on ETSU's Panopto Host" webpage.

0. Introduction: Prerequisites and Preliminaries

SECTION	NOTES	SUPPLEMENTS	VIDEOS
0.1-0.6. Logic, Sets and Classes, Functions, Relations and Partitions, Products, Integers	0.1-0.6 Notes	-	-
0.7. The Axiom of Choice, Order, and Zorn's Lemma	0.7 Notes	-	-
0.8. Cardinal Numbers	0.8 Notes	-	-

I. Groups.

SECTION	NOTES	SUPPLEMENTS	VIDEOS
Chapter I. Introduction	I. Notes	-	Chapter 1 Video (5:29)
I.1. Semigroups, Monoids, and Groups	I.1 Notes	I.1 Supplement I.1 Supplement Print File	Section I.1, Part 1 Video (34:43) Section I.1, Part 2 Video (55:35)
I.2. Homomorphisms and Subgroups	I.2 Notes	I.2 Supplement I.2 Supplement Print File	-
I.3. Cyclic Groups	I.3 Notes	I.3 Supplement I.3 Supplement Print File	-
I.4. Cosets and Counting	I.4 Notes	I.4 Supplement I.4 Supplement Print File	-
I.5. Normality, Quotient Groups, and Homomorphisms	I.5 Notes	I.5 Supplement I.5 Supplement Print File	-
I.6. Symmetric, Alternating, and Dihedral Groups	I.6 Notes	I.6 Supplement I.6 Supplement Print File	-
I.7. Categories: Products, CoProducts, and Free Objects	I.7 Notes	I.7 Supplement I.7 Supplement Print File	-
I.8. Direct Products and Direct Sums	I.8 Notes	I.8 Supplement I.8 Supplement Print File	-
I.9. Free Groups, Free Products, Generators & Relations	I.9 Notes	I.9 Supplement I.9 Supplement Print File	-

II. The Structure of Groups.

SECTION	NOTES	SUPPLEMENTS	VIDEOS
II.1. Free Abelian Groups	II.1 Notes	II.1 Supplement II.1 Supplement Print File	-
II.2. Finitely Generated Abelian Groups	II.2 Notes	II.2 Supplement II.2 Supplement Print File	-
II.3. The Krull-Schmidt Theorem	II.3 Notes	II.3 Supplement II.3 Supplement Print File	-
II.4. The Action of a Group on a Set	II.4 Notes	II.4 Supplement II.4 Supplement Print File	-
II.5. The Sylow Theorems	II.5 Notes	II.5 Supplement II.5 Supplement Print File	-
II.6. Classification of Finite Groups	II.6 Notes	II.6 Supplement II.6 Supplement Print File	-
Supplement. Direct and Semidirect Products	Direct and Semidirect Products Notes	Direct and Semidirect Products Supplement Direct and Semidirect Products Supplement Print File	-
II.7. Nilpotent and Solvable Groups	II.7 Notes	II.7 Supplement II.7 Supplement Print File	-
II.8. Normal and Subnormal Series	II.8 Notes	II.8 Supplement II.8 Supplement Print File	-

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Last updated: December 11, 2020.