Robert Gardner's Online Modern Algebra: Groups

Online Modern Algebra: Groups
with online videos Dr. Bob's Online University
(Not an actual university)
Robert 'Dr. Bob' Gardner

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 can be streamed from YouTube and should remain permanently available. (The videos previously on ETSU's Panopto host site have been, or may soon be, deleted.)

0. Introduction: Prerequisites and Preliminaries

SECTION	NOTES	SUPPLEMENTS	VIDEOS ON YOUTUBE
0.1-0.6. Logic, Sets and Classes, Functions, Relations and Partitions, Products, Integers	0.1-0.6 Notes	0.1-0.6 Supplement 0.1-0.6 Supplement Print File	-
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 ON YOUTUBE
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 Video, Part 1 (34:43) Section I.1 Video, Part 2(55:35)
I.2. Homomorphisms and Subgroups	I.2 Notes	I.2 Supplement I.2 Supplement Print File	Section I.2 Video, Part 1 (39:01) Section I.2 Video, Part 2 (18:04)
I.3. Cyclic Groups	I.3 Notes	I.3 Supplement I.3 Supplement Print File	Section I.3 Video (54:15)
I.4. Cosets and Counting	I.4 Notes	I.4 Supplement I.4 Supplement Print File	Section I.4 Video, Part 1 (57:05) Section I.4 Video, Part 2(39:11)
I.5. Normality, Quotient Groups, and Homomorphisms	I.5 Notes	I.5 Supplement I.5 Supplement Print File	Section I.5, Video, Part 1 (1:48:35) Section I.5 Video, Part 2 (1:19:59)
I.6. Symmetric, Alternating, and Dihedral Groups	I.6 Notes	I.6 Supplement I.6 Supplement Print File	Section I.6 Video, Part 1 (1:05:31) Section I.6 Video, Part 2 (1:28:35)
I.7. Categories: Products, CoProducts, and Free Objects	I.7 Notes	I.7 Supplement I.7 Supplement Print File	Section I.7 Video, Part 1 (54:28) Section I.7 Video, Part 2 (44:53)
I.8. Direct Products and Direct Sums	I.8 Notes	I.8 Supplement I.8 Supplement Print File	Section I.8 Video, Part 1 (1:10:42) Section I.8 Video, Part 2 (53:13) Section I.8 Video, Part 3 (11:32)
I.9. Free Groups, Free Products, Generators & Relations	I.9 Notes	I.9 Supplement I.9 Supplement Print File	Section I.9 Video, Part 1 (1:21:41)* Section I.9 Video, Part 2 (54:38)

*Online notes have been adjusted in the last part of the proof of Theorem I.9.2 to replace g̅ with g.

II. The Structure of Groups.

SECTION NOTES SUPPLEMENTS VIDEOS ON YOUTUBE
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 Section II.4 Video, Part 1 (50:50)
Section II.4 Video, Part 2 (37:56)
II.5. The Sylow Theorems II.5 Notes II.5 Supplement
II.5 Supplement Print File Section II.5 Video, Part 1 (46:08)
Section II.5 Video, Part 2 (1:00:07)
II.6. Classification of Finite Groups II.6 Notes II.6 Supplement
II.6 Supplement Print File Section II.6 Video, Part 1 (1:04:14)
Section II.6 Video, Part 2 (1:05:31)
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 -

Return to Dr. Bob's webpage

Last updated: March 15, 2024.