This is slightly off topic, but if you are interested in having undergraduates use technology to explore finite groups, you should check out Nathan Carter's Group Explorer, which is free and can be found here:
http://groupexplorer.sourceforge.net/ Group Explorer approaches group theory from a visual perspective. I use it quite frequently when teaching abstract algebra and my students enjoy playing with it. You can do a lot more than it appears on the surface (do some exploring with sheets). The ability to "chunk" subgroups visually in Cayley diagrams or Cayley tables is just one of the many cool features. Dana On Mar 8, 2010, at 6:57 PM, Mike OS wrote: > I have some funding from my university to develop > materials in SAGE for use in my classes. I've hired > two sharp students, one with a good deal of programming experience, > to work on the project. I have two inter-related goals > 1. Help to make SAGE more accessible to students: > Develop tutorials, materials for use in class, and > assignments/explorations. > > 2. Contribute to SAGE development. > > This post concerns the educational issues. A post to sage-devel has > some > observations and questions about item 2. Our focus right now is on > group theory. > > For both items we are anxious to have some guidance and > collaboration to make our effort broadly useful. > > We have started a tutorial, once it's a bit more polished I'll post a > link. > (We've looked at others on the web, and are borrowing ideas, thank > you.) > > Here is my wish list for using SAGE in courses, I'm interested in > hearing comments: > > A. I'd like elements of A= AbelianGroup( [2,3,4]) to be shown as 3- > tuples. > Currently GAP notation is used, so (1,2,1) is f0*f1^2*f2. > I'd like to write A(1,2,3) to coerce a 3-tuple into A. > > B. There is some functionality lacking in SAGE, that it would be very > nice to have > This gets to the development issues, and the relationship with > GAP, so I'll > just mention a few things. > - Some types of groups are absent or difficult to use in SAGE: > Finitely Presented Groups, > Unit Group of a Ring (e.g. U_n and F_p[x]/f(x) ). I'm not sure > how to make a direct product. > - Matrix groups don't have subgroups implemented. > - I like to introduce homomorphisms early and use homomorphsism > between different > types of groups. This appears to be difficult. > > C. I would like a "student mode" that would be less intimidating to > the user: > -Reduce the number of functions that appear on tab completion. > For a permutation > group there are 122 completions. Perhaps 20-40 are within the > vocabulary of an > undergrad. > -Simplify error messages. > > -- > You received this message because you are subscribed to the Google Groups > "sage-edu" group. > To post to this group, send email to sage-...@googlegroups.com. > To unsubscribe from this group, send email to > sage-edu+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sage-edu?hl=en. > -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-...@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
