Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. The "Proofs of Theorems" files have not been classroom tested and may have some typographical errors; these files were created with the help of William "Ty" Frazier during the fall 2015 semester.
Preliminaries.
 Supplement. Why The Hell Am I In This Class? PDF.
 Section 0. Sets and Relations PDF.
I. Groups and Subgroups.
 Section 1. Introduction and Examples. PDF.
 Section 2. Binary Operations. PDF.
 Section 3. Isomorphic Binary Structures. PDF.

Supplement. Proofs of Theorems in Section I.3. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section I.3. PDF.
 Section 4. Groups. PDF.

Supplement. Proofs of Theorems in Section I.4. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section I.4. PDF.
 Section 5. Subgroups. PDF.

Supplement. Proofs of Theorems in Section I.5. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section I.5. PDF.
 Section 6. Cyclic Groups. PDF

Supplement. Proofs of Theorems in Section I.6. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section I.6. PDF.
 Section 7. Generating Sets and Cayley Digraphs. PDF (This section includes a multiplication table for the Quaternions, Q_{8}.)

Supplement. Proofs of Theorems in Section I.7. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section I.7. PDF.
 Study Guide I. PDF.
II. Permutations, Cosets, and Direct Products.
 Section 8. Groups of Permutations. PDF. (This section includes multiplication tables for the dihedral groups D_{3}≅S_{3} and D_{4}.)

Supplement. Proofs of Theorems in Section II.8. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section II.8. PDF.
 Section 9. Orbits, Cycles, and the Alternating Groups. PDF.

Supplement. Proofs of Theorems in Section II.9. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section II.9. PDF.
 Section 10. Cosets and the Theorem of Lagrange. PDF.

Supplement. Proofs of Theorems in Section II.10. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section II.10. PDF.
 Section 11. Direct Products and Finitely Generated Abelian Groups. PDF.

Supplement. Proofs of Theorems in Section II.11. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section II.11. PDF.
 Supplement. Small Groups. PDF.
 Section 12. Plane Isometries.
 Supplement. Groups: A Geometric Introduction. There is a PowerPoint presentation (prepared in Microsoft PowerPoint 2010) with embedded audio, a transcript in PDF, and a Windows Media Video: PowerPoint, transcript, video. The video is also on YouTube here (last accessed 8/11/2014).
 Study Guide II. PDF.
III. Homomorphisms and Factor Groups.
 Section 13. Homomorphisms. PDF. (This section includes the image which is the logo for the ETSU Abstract Algebra Club.)

Supplement. Proofs of Theorems in Section III.13. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section III.13. PDF.
 Section 14. Factor Groups. PDF.

Supplement. Proofs of Theorems in Section III.14. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section III.14. PDF.
 Section 15. FactorGroup Computations and Simple Groups. PDF.

Supplement. Proofs of Theorems in Section III.15. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section III.15. PDF.
 Supplement. The Alternating Groups A_{n} are Simple for n ≥ 5. PDF. (This supplement includes a multiplication table for A_{4}.)
 Supplement. Finite Simple Groups. PDF.
 Section 16. Group Action on a Set.
 Section 17. Application of GSets to Counting.
 Study Guide III. PDF.
IV. Rings and Fields.
 Section 18. Rings and Fields. PDF.

Supplement. Proofs of Theorems in Section IV.18. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section IV.18. PDF.
 Section 19. Integral Domains. PDF.

Supplement. Proofs of Theorems in Section IV.19. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section IV.19. PDF.
 Section 20. Fermat's and Euler's Theorem. PDF.

Supplement. Proofs of Theorems in Section IV.20. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section IV.20. PDF.
 Section 21. The Field of Quotients of an Integral Domain. PDF.

Supplement. Proofs of Theorems in Section IV.21. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section IV.21. PDF.
 Section 22. Rings of Polynomials. PDF.

Supplement. Proofs of Theorems in Section IV.22. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section IV.22. PDF.
 Section 23. Factorization of Polynomials over a Field. PDF

Supplement. Proofs of Theorems in Section IV.23. PDF (prepared in Beamer).

Supplement. Printout of the Proofs of Theorems in Section IV.23. PDF.
 Section 24. Noncommutative Examples.
 Section 25. Ordered Rings and Fields.
 Study Guide IV. PDF.
Other Notes.
 Supplement. Dr. Bob's Modern Algebra Glossary. PDF.
Return to Bob Gardner's home page