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MAT 412 Abstract Algebra

Instructor:
Nandor Sieben

schedule

additional policies

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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.

Grades

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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.

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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
https://cloud.sagemath.com or
https://www.overleaf.com to write LaTeX.

Some help for LaTeX:

Latex examples

Latex guide

Detexify

Tikz (creating figures inside LaTeX)

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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
https://cloud.sagemath.com.
You can test small GAP programs at
https://sagecell.sagemath.org/ (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:
http://www.math.colostate.edu/~hulpke/binaries/GAP4412Setup.exe
Start GGAP after installation.

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Project Euler

Please create an account at
https://projecteuler.net/archives
and solve problems 3,1,5,6,7,10,2,12,20 using GAP.