"Mathematics, rightly viewed, possesses not only truth, but supreme beauty." --Bertrand Russell

Symmetry, as wide or narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection. --Hermann Weyl

We will not use a tradtional textbook for this class. Rather, we will use a 2009 book called Visual Group Theory (VGT), by Nathan Carter. The renowned mathematician Steven Strogatz at Cornell, calls it

In class, we will play with the Rubik's cube. We will study patterns and symmetry and use free mathematical software such as

- Course Calendar
- Course Syllabus
- Proctor test policies
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- Visual Group Theory, by Nathan Carter. (Required
textbook). Steven Stogatz calls it
*One of the best introductions to group theory -- or to any branch of higher math -- I've ever read*

- What is abstract algebra? (Wikipedia entry)
- A short article on abstract algebra, by Steven Strogatz, written for a general (non-mathematical) audience that appeared in the New York Times.
- Abstract Algebra: Theory and Applications, a free open-source textbook, by Tom Judson.
- Group
Explorer, a free software program to accompany
*Visual Group Theory* - Guidelines for good mathematical writing, by Francis Su. (4 pages)
- Group theory and the Rubik's cube, by Janet Chen (39 pages).
- Gödel, Escher, Bach: An Eternal Golden Braid
is a wonderful, playful, Pulitzer-Prize winning book exploring the
common themes and symmetries underlying mathematics, art, and
music. It was written by Doug Hofstadter, who Nathan Carter cites as an
influence in his writing of
*Visual Group Theory*(both were at Indiana University). - New discovery as of July 2010: Every configuration of the Rubik's Cube Group is at most 20 moves from the solved state.
- Crystal systems of minerals (lots of pictures, and references to group theory!)
- Group Theory and its Application to Chemistry, from LibreTexts, a ChemWiki hosted at UC Davis.
- Tilings in everyday places, by Dror Bar-Natan of the University of Toronto.

- Lecture 1.1: What is a group? [YouTube (16:15) | Slides]
- Lecture 1.2: Cayley graphs. [YouTube (33:27) | Slides]
- Lecture 1.3: Groups in science, art, and mathematics. [YouTube (30:36) | Slides]
- Lecture 1.4: Group presentations. [YouTube (18:12) | Slides]
- Lecture 1.5: Multiplication tables. [YouTube (19:23) | Slides]
- Lecture 1.6: The formal definition of a group. [YouTube (12:48) | Slides]

- Lecture 2.1: Cyclic and abelian groups [YouTube (30:45) | Slides]
- Lecture 2.2: Dihedral groups [YouTube (16:14) | Slides]
- Lecture 2.3: Symmetric and alternating groups [YouTube (29:50) | Slides]
- Lecture 2.4: Cayley's theorem [YouTube (11:00) | Slides]

- Lecture 3.1: Subgroups. [YouTube (13:43) | Slides]
- Lecture 3.2: Cosets. [YouTube (19:11) | Slides]
- Lecture 3.3: Normal subgroups. [YouTube (14:00) | Slides]
- Lecture 3.4: Direct products. [YouTube (23:16) | Slides]
- Lecture 3.5: Quotients. [YouTube (40:38) | Slides]
- Lecture 3.6: Normalizers. [YouTube (22:46) | Slides]
- Lecture 3.7: Conjugacy classes. [YouTube (39:19) | Slides]

- Lecture 4.1: Homomorphisms and isomorphisms. [YouTube (47:18) | Slides]
- Lecture 4.2: Kernels. [YouTube (31:32) | Slides]
- Lecture 4.3: The fundamental homomorphism theorem. [YouTube (32:52) | Slides]
- Lecture 4.4: Finitely generated abelian groups. [YouTube (24:47) | Slides]
- Lecture 4.5: The isomorphism theorems. [YouTube (46:19) | Slides]
- Lecture 4.6: Automorphisms. [YouTube (24:34) | Slides]
- Lecture 4.7: Semidirect products. [YouTube (??:??) | Slides (coming soon)]

- Lecture 5.1: Groups acting on sets. [YouTube (32:35) | Slides]
- Lecture 5.2: The orbit-stabilizer theorem. [YouTube (27:41) | Slides]
- Lecture 5.3: Examples of group actions. [YouTube (44:05) | Slides]
- Lecture 5.4: Fixed points and Cauchy's theorem. [YouTube (14:00) | Slides]
- Lecture 5.5:
*p*-groups. [YouTube (22:13) | Slides] - Lecture 5.6: The Sylow theorems. [YouTube (48:37) | Slides]
- Lecture 5.7: Finite simple groups. [YouTube (36:34) | Slides]

- Lecture 6.1: Fields and their extensions. [YouTube (26:34) | Slides]
- Lecture 6.2: Field automorphisms. [YouTube (35:41) | Slides]
- Lecture 6.3: Polynomials and irreducibility. [YouTube (38:21) | Slides]
- Lecture 6.4: Galois groups. [YouTube (34:13) | Slides]
- Lecture 6.5: Galois group actions and normal field extensions. [YouTube (26:28) | Slides]
- Lecture 6.6: The fundamental theorem of Galois theory. [YouTube (31:29) | Slides]
- Lecture 6.7: Ruler and compass constructions. [YouTube (22:46) | Slides]
- Lecture 6.8: Impossibility proofs. [YouTube (17:12) | Slides]

- Lecture 7.1: Basic ring theory. [YouTube (32:36) | Slides]
- Lecture 7.2: Ideals, quotient rings, and finite fields. [YouTube (34:20) | Slides]
- Lecture 7.3: Ring homomorphisms. [YouTube (45:53) | Slides]
- Lecture 7.4: Divisibility and factorization. [YouTube (39:38) | Slides]
- Lecture 7.5: Euclidean domains and algebraic integers. [YouTube (30:09) | Slides]
- Lecture 7.6: Rings of fractions. [YouTube (??:??) | Slides]
- Lecture 7.7: The Chinese remainder theorem. [YouTube (??:??) | Slides (coming soon)]

To the best of my knowledge, I was the 2nd person to teach an abstract algebra class using

Homework 1: pdf | tex. Due Thursday, May 12, 2016

Homework 2: pdf | tex. Due Friday, May 13, 2016

Homework 3: pdf | tex. Due Monday, May 16, 2016

Homework 4: pdf | tex. Due Wednesday, May 18, 2016

Homework 5: pdf | tex. Due Friday, May 20, 2016

Homework 6: pdf | tex. Due Monday, May 23, 2016

Homework 7: pdf | tex. Due Friday, May 27, 2016

Homework 8: pdf | tex. Due Monday, May 30, 2016

Homework 9: pdf | tex. Due Wednesday, June 1, 2016

Homework 10: pdf | tex. Due Friday, June 3, 2016

Homework 11: pdf | tex. Due Tuesday, June 7, 2016

Homework 12: pdf | tex. Due Friday, June 10, 2016

Homework 13: pdf | tex. Due Monday, June 13, 2016

Homework 14: pdf | tex. Due Thursday, June 16, 2016

• Practice Midterm 2 (Spring 2014)

• Practice Midterm 1 (Fall 2013)

• Practice Midterm 2 (Fall 2013)

• Practice Midterm 1 (Fall 2010)

• Practice Midterm 2 (Fall 2010)