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.
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:
Tikz (creating figures inside LaTeX)
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.