# Abstract Algebra

**Course:** Math 332, Spring 2009

**Time & Place:** TR 2:30–3:50 pm in RKC 102

**Instructor:** Jim Belk (belk@bard.edu)

**Office Hours:** Wednesday, 2–4 pm and 7–9 pm in the Albee lounge.

## Announcements

#### Monday Office Hours

I will be having office hours this Monday afternoon from 1:00 pm to 3:00 pm. These will be held in the **physics lab**.
#### Quiz Practice Problems (with solutions)

Here are some practice problems for the quiz:
- Quiz 3 Practice Problems (PDF, TeX)

and here are the solutions:
#### Quiz Tuesday

The final quiz will be this Tuesday in class. It will cover the following topics:
- • Quotient groups and homomorphisms
- • The classification of finite abelian groups
- • Rings and subrings
- • Ideals, quotient rings, and ring homomorphisms

The quiz will include at least two proofs. Practice problems for the quiz will be posted soon!
#### No Class Today

There is no class today (Thursday, May 13).
#### Homework 8

The eighth homework assignment is due this Thursday, May 13. Here is the assignment:
#### Homework 7

The seventh homework assignment was due last Thursday, May 6. Here is the assignment:
#### Takehome Midterm

The takehome midterm was due on Friday, April 30:
#### Quiz 2 Solutions

Here are the solutions to the second quiz:
#### Study Guides

I have written up some study guides for the material covered by the quiz. The study guides outline all of the important ideas and theorems that we have covered, and indicate which problems are related to which ideas:
- Study Guide: Isomorphisms and Automorphisms (PDF, TeX)
- Study Guide: Direct Products (PDF, TeX)
- Study Guide: Cosets and Lagrange's Theorem (PDF, TeX)

#### Quiz 2 Practice Problms

Here are the practice problems from the second quiz:

- Quiz 2 Practice Problems (PDF, TeX)

Please work on the practice problems this week, and also come talk to me about your midterm grade if you haven't yet.
#### Homework Solutions

Here are complete solutions for the first six homework assignments
- Homework 1 Solutions (PDF, TeX)
- Homework 2 Solutions (PDF, TeX)
- Homework 3 Solutions (PDF, TeX)
- Homework 4 Solutions (PDF, TeX)
- Homework 5 Solutions (PDF, TeX)
- Homework 6 Solutions (PDF, TeX)

#### Homework 6

The sixth homework was due on Thursday, March 18. Here is the assignment:
#### Homework 5

The fifth homework was due on Thursday, March 11. Here is the assignment:
#### Homework 2 Solutions

Here are the solutions to the second homework assignment:
- Homework 2 Solutions (PDF, TeX)

#### Videos

Here are couple of YouTube videos that you might enjoy:
#### Homework 4

The fourth homework was due on Thursday, March 4. Here is the assignment:
Because the assignment contains pictures, I have included a ZIP file with both the TeX source
and the EPS pictures.
#### Reading

Please read section 6 of the text (on isomorphisms and automorphisms) as soon as possible.
#### GAP

GAP (**G**roups, **C**omputations, and **A**lgorithms) is a free computer algebra system
which is designed for solving problems in computational group theory. You can download GAP at the
following link:
You should feel free to use GAP on any of the homework assignments. There is lots of online
documentation to help you get started:
#### Quiz 1 Results

The first quiz was held on Tuesday, February 23, and covered cyclic groups and permutations. Here are the solutions:
The median on the quiz was a 33. Here are the approximate grade ranges:
- 33 – 40: A
- 26 – 32: B
- 19 – 25: C

#### Practice Problems

Here are the practice problems on cyclic groups and permutation groups that we used for the first quiz:
- Cyclic Group Problems (PDF, TeX)
- Permutation Problems (PDF, TeX)

#### Quaternion Article

For your enjoyment, here is a link to an award-winning article from Mathematics Magazine:
#### Homework 3

The third homework is due on Thursday, February 18th. Because you need to study for the quiz, I have made this assignment a little easier than the last two:
#### Homework 1 Solutions

I have written up solutions to the first homework assignment:
- Homework 1 Solutions (PDF, TeX)

#### Homework 2

The second homework is due on Thursday, February 11th. To help you learn LaTeX, I am providing
the assignment in both PDF and TeX format:
#### Sample Homework Solutions

Here is a sample homework assignment and solutions in LaTeX that you can use as a guide to writing your own homework solutions:
Note that the sample solutions are intended only as an example. You do not need to use the same style or format in your own solutions.
#### Homework 1

The first homework assignment is now online. To help you get started with LaTeX, I am providing
the assignment in both PDF and TeX format:
This assignment is due on Thursday, February 4th. To turn in your assignment, please e-mail
me a PDF of your solutions.
#### Welcome!

Welcome to math 332! The first-day handout is available online:
#### LaTeX

You are required to write homework solutions in LaTeX. Here are some links to get you started:
If you want to download LaTeX to your own computer, Ethan recommends TeXShop for Mac users, and proTeXt for PC users:
I use a PC with proTeXT, and the WinEdt editor.
#### Textbook

The textbook is *Contemporary Abstract Algebra*, by Joseph Gallian. This book is currently in its 7th edition, which has a list price
of $178, and is currently selling for $135 at Amazon.com. If you are unwilling to pay this amount, it would be fine to get a used copy of an old edition. Here are some links to get you started:
It is also possible to purchase access to the 7th edition as an e-book. This costs $89 dollars and will give you complete access for 6 months. You can do this from the publisher's page:
## Feedback

How is the class going? Are there any changes you want me to make? Let me know by using the following feedback form!