"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 Syllabus
- 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.
- 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* - 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, a ChemWiki hosted at UC Davis.
- Tilings in everyday places, by Dror Bar-Natan of the University of Toronto.

Chapter 1: What is a group?

Chapter 2: Cayley graphs

Chapter 3: Groups in science, art, and mathematics

Chapter 4: Algebra and group presentations

Chapter 5: Five families of groups

Chapter 6: Subgroups

Chapter 7: Products and quotients

Chapter 8: Homomorphisms

Chapter 9: Group actions

Chapter 10: The Sylow theorems

Chapter 11: Galois theory

Chapter 12: Ruler and compass constructions

Chapter 13: Basic ring theory

Chapter 14: Divisibility and factorization

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

Homework 1: pdf | tex. Due Friday, January 17, 2014

Homework 2: pdf | tex. Due Friday, January 24, 2014

Homework 3: pdf | tex. Due Friday, January 31, 2014

Homework 4: pdf | tex. Due Friday, February 7, 2014

Homework 5: pdf | tex. Due Friday, February 14, 2014

Homework 6: pdf | tex. Due Monday, February 24, 2014

Homework 7: pdf | tex. Due Monday, March 3, 2014

Homework 8: pdf | tex. Due Friday, March 7, 2014

Homework 9: pdf | tex. Due Friday, March 14, 2014

Homework 10: pdf | tex. Due Friday, March 28, 2014

Homework 11: pdf | tex. Due Friday, April 4, 2014

Homework 12: pdf | tex. Due Monday, April 14, 2014

Homework 13: pdf | tex. Due Monday, April 21, 2014

Homework 14: pdf | tex. Due Friday, April 25, 2014

• Midterm 2

• Practice Midterm 1 (Fall 2013)

• Practice Midterm 2 (Fall 2013)

• Practice Midterm 1 (Fall 2010)

• Practice Midterm 2 (Fall 2010)