"Introduction to Modern Algebra Class Notes" Webpage

Introduction to Modern Algebra Class Notes
A First Course In Abstract Algebra, 7th Edition, John B. Fraleigh Fraleigh's First Course in Abstract Algebra book, 7th edition

Fraleigh's First Course in Abstract Algebra book, 7th edition

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? Whay Am I Here notes
Section 0. Sets and Relations Section 0.0 notes

I. Groups and Subgroups.

Section 1. Introduction and Examples. Section I.1 notes
Section 2. Binary Operations. Section I.2 notes
Section 3. Isomorphic Binary Structures. Section 1.3 notes

Supplement. Proofs of Theorems in Section I.3. Proofs of Theorems in Section I.3
Supplement. Printout of the Proofs of Theorems in Section I.3. Print out of the Proofs of Theorems in Section I.3

Section 4. Groups. Section I.4 notes

Supplement. Proofs of Theorems in Section I.4. Proofs of Theorems in Section I.4
Supplement. Printout of the Proofs of Theorems in Section I.4. Print out of the Proofs of Theorems in Section I.4

Section 5. Subgroups. Section I.5 notes

Supplement. Proofs of Theorems in Section I.5. Proofs of Theorems in Section I.5
Supplement. Printout of the Proofs of Theorems in Section I.5. Print out of the Proofs of Theorems in Section I.5

Section 6. Cyclic Groups. Section I.6 notes

Supplement. Proofs of Theorems in Section I.6. Proofs of Theorems in Section I.6
Supplement. Printout of the Proofs of Theorems in Section I.6. Print out of the Proofs of Theorems in Section I.6

Section 7. Generating Sets and Cayley Digraphs. Section I.7 notes (This section includes a multiplication table for the Quaternions, Q₈.)

Supplement. Proofs of Theorems in Section I.7. Proofs of Theorems in Section I.7
Supplement. Printout of the Proofs of Theorems in Section I.7. Print out of the Proofs of Theorems in Section I.7

Study Guide I

II. Permutations, Cosets, and Direct Products.

Section 8. Groups of Permutations. Section II.8 notes (This section includes multiplication tables for the dihedral groups D₃≅S₃ and D₄.)

Supplement. Proofs of Theorems in Section II.8. Proofs of Theorems in Section II.8
Supplement. Printout of the Proofs of Theorems in Section II.8. Print out of the Proofs of Theorems in Section II.8

Section 9. Orbits, Cycles, and the Alternating Groups. Section II.9 notes

Supplement. Proofs of Theorems in Section II.9. Proofs of Theorems in Section II.9
Supplement. Printout of the Proofs of Theorems in Section II.9. Print out of the Proofs of Theorems in Section II.9

Section 10. Cosets and the Theorem of Lagrange. Section II.10 notes

Supplement. Proofs of Theorems in Section II.10. Proofs of Theorems in Section II.10
Supplement. Printout of the Proofs of Theorems in Section II.10. Print out of the Proofs of Theorems in Section II.10

Section 11. Direct Products and Finitely Generated Abelian Groups. Section II.11 notes

Supplement. Proofs of Theorems in Section II.11. Proofs of Theorems in Section II.11
Supplement. Printout of the Proofs of Theorems in Section II.11. Print out of the Proofs of Theorems in Section II.11

Supplement. Small Groups. Small Groups notes
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: "Groups: A Geometric Introduction" PowerPoint version and "Groups: A Geometric Introduction" transcript. The video is also on YouTube "Groups: A Geometric Introduction" YouTube video (last accessed 8/11/2014).
Study Guide II

III. Homomorphisms and Factor Groups.

Section 13. Homomorphisms. Section III.13 notes (This section includes the image which is the logo for the ETSU Abstract Algebra Club.)

Supplement. Proofs of Theorems in Section III.13. Proofs of Theorems in Section III.13
Supplement. Printout of the Proofs of Theorems in Section III.13. Print out of the Proofs of Theorems in Section III.13

Section 14. Factor Groups. Section III.14 notes

Supplement. Proofs of Theorems in Section III.14. Proofs of Theorems in Section III.14
Supplement. Printout of the Proofs of Theorems in Section III.14. Print out of the Proofs of Theorems in Section III.14

Section 15. Factor-Group Computations and Simple Groups. Section III.15 notes

Supplement. Proofs of Theorems in Section III.15. Proofs of Theorems in Section III.15
Supplement. Printout of the Proofs of Theorems in Section III.15. Print out of the Proofs of Theorems in Section III.15

Supplement. The Alternating Groups A_n are Simple for n ≥ 5. Alternating Groups notes (This supplement includes a multiplication table for A₄.)
Supplement. Finite Simple Groups. Finite Simple Groups notes
Section 16. Group Action on a Set.
Section 17. Application of G-Sets to Counting.
Study Guide III

IV. Rings and Fields.

Section 18. Rings and Fields. Section IV.18 notes

Supplement. Proofs of Theorems in Section IV.18. Proofs of Theorems in Section IV.18
Supplement. Printout of the Proofs of Theorems in Section IV.18. Print out of the Proofs of Theorems in Section IV.18

Section 19. Integral Domains. Section IV.19 notes

Supplement. Proofs of Theorems in Section IV.19. Proofs of Theorems in Section IV.19
Supplement. Printout of the Proofs of Theorems in Section IV.19. Print out of the Proofs of Theorems in Section IV.19

Section 20. Fermat's and Euler's Theorem. Section IV.20 notes

Supplement. Proofs of Theorems in Section IV.20. Proofs of Theorems in Section IV.20
Supplement. Printout of the Proofs of Theorems in Section IV.20. Print out of the Proofs of Theorems in Section IV.20

Section 21. The Field of Quotients of an Integral Domain. Section IV.21 notes

Supplement. Proofs of Theorems in Section IV.21. Proofs of Theorems in Section IV.21
Supplement. Printout of the Proofs of Theorems in Section IV.21. Print out of the Proofs of Theorems in Section IV.21

Section 22. Rings of Polynomials. Section IV.22 notes

Supplement. Proofs of Theorems in Section IV.22. Proofs of Theorems in Section IV.22
Supplement. Printout of the Proofs of Theorems in Section IV.22. Print out of the Proofs of Theorems in Section IV.22

Section 23. Factorization of Polynomials over a Field. Section IV.23 notes

Supplement. Proofs of Theorems in Section IV.23. Proofs of Theorems in Section IV.23
Supplement. Printout of the Proofs of Theorems in Section IV.23. Print out of the Proofs of Theorems in Section IV.23

Section 24. Noncommutative Examples.
Section 25. Ordered Rings and Fields.
Study Guide IV

Other Notes.

Supplement. Dr. Bob's Modern Algebra Glossary. Modern Algebra Glossary

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