Group Theory Topics

THIS SECTION OF THE DOCUMENTATION IS INCOMPLETE.

A future release of Group Explorer will have this page filled in.

This page is a fairly large project in and of itself, and I want to take time to do it well. At the same time, there was no sense delaying the release of GE just for this page. Furthermore, I welcome suggestions from users of what they would like to see on this page; therefore it made sense to get GE2.0 out without this page first.

The purpose of this page is given below.

A little textbook

I want to put on this page a miniature group theory textbook. It will be miniature in the sense that it will only cover material appearing in the first chapter or two of a typical group theory textbook. Also, it will not have any definitions (but rather simply hyperlinks to the group theory terminology page), nor will it feel the need to act as if it is the reader's only source of information on group theory.

Why would I do such a thing? Because this group theory textbook would be different than standard ones in that it would be heavily (in fact mostly) visual. Not only would there be many illustrations, but just as in other portions of the Group Explorer documentation, the hyperlinks are active--they can open group info windows, create lattices of subgroups, show you highlighted cycle graphs, etc. So it would be an interactive textbook.

It will contain assignments, and the reader can do the assignments right within Group Explorer. Instructors could assign their students homework from this page. If it grows long enough, this page will become many pages.

Further details

Now here are a few specifics that will be useful for me as I return to this page and want to write it, and which can be guidance to anyone who wishes to contribute content for consideration for inclusion here.

The page should be very "lightweight" compared to a normal textbook, in the sense that it will neither treat topics exhaustively nor with deep and surpassing pedagogy. Remember that the goal is to stress visuals, with plenty of links to example sheets and visualizers for the user to explore and enhance on their own.
On the other hand, this page should be more in-depth than the simple information that shows up in each group info window. In fact, as this page matures I will link to it from simpler documentation, like the group info windows, the group theory terminology page, and the Group Explorer terminology page.
This page will be sectioned like a normal textbook for at least the following reasons.
- An intelligent reader should be able to start at the beginning and read through, even if they have never had group theory before, and understand most of the content. They may need to refer to external resources (a real textbook, for example) occasionally when a topic is too large for this page.
- Students who are studying a topic should be able to come to this page and immediately find that topic in the table of contents for this page, and jump to it, to supplement their ordinary textbook and classroom experience, whether their instructor directed them to do so or not.
Some portions of this page may simply link to other pages in the Group Explorer documentation. For instance, I will not write another introduction to multiplication tables or Cayley diagrams when such things already exist (here, here, here, and here).

Contributions

If you have suggestions for information that fits the above criteria, please email it to me. Read the "About Group Explorer" window for up-to-date contact information (Help | About GE 2 on Windows, or GroupExplorer | About GE 2 on Mac OS). Examples of things you might want to send include

particularly beautifully confiured visualizers,
clear and informative sheets,
insightful exposition on visualizing group theory in any way,
and anything else that seems like it might be good as per the goals described above.