MAT 412 Abstract Algebra

Instructor: Nandor Sieben
additional policies

Test 2: Friday 4/8.

The test includes Sections 1.9 - 1.13 (possibly 1.14) of the lecture notes (available on bblearn). You need to know all the definitions, theorems, proofs and examples. I am not going to ask you to write GAP code.
No notes or electronic devices are allowed on the test. Please review the Test Etiquette.

Text book

There is no required text for the course. Lecture notes are going to be available on Bblearn.

Free online books:
Algebra Abstract and Concrete by Frederick M. Goodman
Abstract Algebra: Theory and Applications by Thomas W. Judson
Elementary Abstract Algebra: Examples and Applicationsons by Justin Hill, Chris Thron (eds), Thomas Judson, Dave Witte Morris, Joy Morris, A. J. Hildebrand, Holly Webb, Johnny Watts, David Weathers
You might want to glance at the group actions Wikipedia page to get a flavor of what we are going to start with.

List of free e-books and guides on Abstract Algebra.

Printed text books:
If you want a printed textbook, Dummit and Foote is an option. This is a graduate text that is often used in MAT 511 but it is very readable.
You might already own a copy of Contemporary Abstract Algebra by Gallian from your MAT 411 course. This book is a useful general reference but it is not alligned closely enough to what we are going to do.

Writing mathematics with LyX/LaTeX

I highly recommend that you use the LyX homework template (right click to download) to type your homework solutions. LyX is my main computer tool. I use it to write pretty much everything, research papers, tests, quizzes, class notes, letters. LyX is available in the computer labs. It is freely available to download and install from the LyX web site. The installation script automatically installs LaTeX as well.

Please read the wisdom about mathematical writing

LaTeX is also available in our computer labs. Please use the LaTeX homework template (also in pdf form) if you prefer to use LaTeX. I recommend that you use or to write LaTeX.

Some help for LaTeX:
Latex examples
Latex guide
Tikz (creating figures inside LaTeX)

GAP / Sage

We are going to use the GAP (Groups, Algorithms, Programming) system which is a free computational algebra program and Sage. Some of the homework will ask you to write small programs in GAP. You may want to glance at the GAP tutorials and the reference manual in the documentation section of the main GAP web site. You may also want to look at the Sage documentation or the Sage for Undergraduates book.

GAP is also available at You can test small GAP programs at (change the language to GAP). Don't forget to save your programs in a text file if you go with this option. Sage stops printing output if the amount of output is large. For larger programs you need to include Print commands.

A simple GAP example run.

You may want to install GAP (or Sage) on your computer. It is a standard package on most Linux distributions and so it is very easy to install. It runs on windows as well (a bit less reliable). You may want to give a try to the Windows installer at: Start GGAP after installation.

Project Euler

Please create an account at and solve problems 3,1,5,6,7,10,2,12,20 using GAP.