# Math 3140 (Fall 2012): Abstract algebra

## Course Information

## Assignments

Assignment 1 [tex] [solutions]. Note that Exercise 2 has been moved to Assignment 2 and Exercise 12 12 has been moved to Assignment 3!

Assignment 2 [tex] [solutions]

Assignment 3 [tex] [solutions]. Note that Exercise 27 has moved to Assignment 4

Assignment 4 [tex] [solutions]

Assignment 7 [tex] [solutions]

Suggested paper topics [tex] [bib]

## Readings

Lecture notes are available for some topics. Last update: September 23.

Week 1: Groups (Fraleigh, §4), permutations (Fraleigh, §8)

Week 2: Symmetric groups (Fraleigh, §8, 9), subgroups (Fraleigh, §5)

Week 3: Symmetric groups (Fraleigh, §8, 9), subgroups (Fraleigh, §5), homomorphisms (Fraleigh, §13)

Week 4: Cayley's theorem (Fraleigh, §8), alternating groups (Fraleigh, §9), cyclic groups (Fraleigh, §6)

Week 5: Cyclic groups (§6)

Week 6: Midterm exam

Week 7: Products (§11), group actions (§16, §17)

Week 8: Midterm exam

## Other materials

Handout 3 (corrected and split into several handouts)

Here is an extra problem, related to the definition of the sign of a permutation, and to topics that will be important near the end of the class.

Review problems for the first exam. Solutions will not be posted.

## References

There are many resources about group theory available online. Here is a very partial list:

- Groups and symmetry [amazon] [google], by Mark A. Armstrong is an excellent reference.
- Your classmate, Jacob Sheppard, found this nice reference about symmetry groups.
- A classic book about group theory by William Burnside is available free in its entirety from Google Books. Take care: this book was published more than 100 years ago, and some of the terminology may be outdated. It may also be more abstract than Fraleigh's text in some ways.