Math 405: Abstract Algebra

Announcements

Here is where I'll be posting timely information about the class.

• Office hours: T 3:30-4:30, WR 9:30-11:00 AM.
• Our second exam is on April 11. It covers § 2.6-7, 3.1, 3.3-6, 5.1-4.
• Here's the information on the project you will be doing this semester.
• Our first exam was on 2/21 during class. It covered sections 1.1-1.10 and 2.1-2.5 (material from 2.6-2.7 may be incorporated into an extra credit problem... if there is one).
• Homework is due at the beginning of class on the assigned date.
• I frequently make use of standard proofreading marks when grading.

Resources

Texts:

We'll be using Algebra: Abstract and Concrete by F. M. Goodman, which is freely available (but be a mensch and donate to one of the causes he recommends). We'll also be using the freely available Abstract Algebra with GAP by Rainbolt and Gallian.

Latex:

We'll be using LaTeX throughout this course. My colleague, David Maxwell, has prepared some excellent installation instructions, which I have modified for use in this course. If you are using a Mac, you should download these, and if you are using a PC, you should download these. Let me know if you notice any errors in the instructions, and I'll update them. If you are running a Linux distribution, you are on your own (but probably don't need any help anyway). You may also find this list of LaTeX math symbols helpful. Detexify is a useful tool for discovering the command that goes with a symbol.

GAP:

GAP is a research grade computing system for doing computations involving the kinds of objects that show up in abstract algebra, but don't be intimidated by that! We'll be using it regularly to explore the topics that come up in this class, and to help us develop intuition. You'll want to install it on your computer to be able to do the homework and some of the group work we'll be doing in class (so if you can, bring your computer to class!). There is an installer available for Windows systems, a nice self-contained app developed by Russ Woodroofe for Macs (nice guy, I met him in Slovenia), and if you are running a unix variant, you can get all the information you need to do the install at the same website as the Windows people.

You can also use GAP in your web browser on most devices by following these steps:

• create an account at CoCalc.com, and sign in.
• create a project with whatever name you want.
• within the project, from the "create" menu item select "Terminal".
• within the terminal window that opens, type "gap" and hit the enter key.

Homework Formatting Instructions

• When preparing your homework in LaTeX, you must use this template. If you compile the template sample file in LaTeX you should get this. If you run into trouble, let me know.
• Your name, class name, and assignment due date should appear at the top of the first page of your assignment. Your assignment must be stapled together in the top lefthand corner and your paper must be devoid of those nasty scritchy bits from having been ripped out of a spiral bound notebook.
• You must include a complete problem statement with each exercise.
• You must write in complete sentences, with appropriate grammar, etc..
• Your language should be appropriately formal, e.g., the use of specialized symbols such as the inverted capital A in place of the words "for all" should generally be avoided. Look to your textbook for a model of when the use of such symbols or abbreviations is appropriate.
• Counterexamples should be specific, not generic, i.e., π+(-π) is a counterexample to the claim that the sum of two irrational numbers is always irrational. Using a generic irrational x∈ℝ\ℚ isn't good form.
• You should proofread the template to avoid making mistakes.
• You should ALWAYS justify your answer.

Failure to follow these instructions will result in deductions from your grade.

Interpreting Graded Problem Scores

I want to give you some idea of how to interpret your performance on each graded exercise. Generally, each graded problem will be assessed on a 5 point scale: 5=entirely or nearly correct, 4=nearly correct but solution is poorly presented or contains a notable error, 3=mostly correct but a significant mathematical error, 2=significant progress in the right direction but multiple errors, 1=a genuine attempt at the problem, 0=little or no real attempt at the problem.

Homework Assignments by Due Date

Be sure to follow the instructions above for the formatting of written assignments. Assignments with study guides will be available to download below.

Corrections to assignments due dates will be written in red. You may need to be logged into your UA account to view the assignment list below properly.