GAP teaching materials and routines written by Peter Webb

Teaching materials
On several occasions Peter Webb has taught a graduate level group theory course which includes a 50 minute session each week in the computer lab. The format has been that each member of the class is presented with a list of GAP commands together with minimal commentary, and at the direction of the instructor they work through these commands and observe what happens. At key points there is plenary discussion. The instructor introduces background theory as it is needed. In the later lessons reference is made to certain standard texts.

If you use these teaching materials, please do send a brief note of this to webb@math.umn.edu
Like everyone else, I do have to justify my existence in this world and it helps me to say that my work has been used.

Here are the GAP Lessons which are presented to the students:
1 2 3 4 5 6
In lesson 2 a file Conway is used, and in lesson 6 we use the file lesson6code.
Lesson 6 requires a handout on Stabilizer Theory.

The class has also been required to turn in homework, some of which is specific to GAP. Here are the most recently used homework questions from 2003.

GAP routines
For quite a long time Peter Webb has been developing GAP code to handle representations and cohomology, of groups and more generally of categories.

Nerves of Categories
The code presented here computes the (co)homology of nerves of categories. Regarding a group as a category, we obtain the usual group cohomology, but the routines presented here are not efficient for this. Regarding a poset as a category we get the homology of the order complex. Every simplicial complex may be given up to homeomorphism in this fashion. The user is advised first to read the tutorial before going to the routines.

Tutorial on nerves of categories.
Routines to handle nerves of categories.

If you use these routines, please do send a brief note of this to webb@math.umn.edu
Like everyone else, I do have to justify my existence in this world and it helps me to say that my work has been used!

Routines to handle group representations in positive characteristic
These are general routines, with a philosopy different to that of, for example, the meataxe. Read first the tutorial, then download the file of routines and read it in at the start of your GAP session. Do let me know if you have problems!
Tutorial on representation routines.
Routines to handle group representations.

If you use these routines, please do send a brief note of this to webb@math.umn.edu
Like everyone else, I do have to justify my existence in this world and it helps me to say that my work has been used!

The other GAP routine which Peter Webb has written is an implementation of a fast algorithm to compute minimal resolutions of the trivial module in positive characteristic. At the moment it is still in a process of development.