Math 3140 (Fall 2012): Abstract algebra
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
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.
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 Take care: this book was published more than 100 years ago, and some of the terminology may be outdated.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.