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Dear GAP Forum:

I have a book "Applied abstract algebra" which has lots of GAP exercises

(some of them "borrowed" from Alexander Hulpke). It is due to the

publishers (Johns Hopkins) this month, so should be available late next spring.

I'm not sure how much of it I'd be allowed to put on the web.

The topics include number theory, rings, fields, groups, and coding

theory, all from a very basic point of view.

All my royalties go directly to charity.

- David Joyner

Charles Wright wrote:

Dear GAP Forum subscribers --

Recent letters to the Forum have asked about the existence of teaching

materials that use GAP. The answers have not been completely

satisfactory, for various reasons. Over the years, some people have been

privately collecting examples, exercises and the like that use GAP for

instruction, but there has been no major effort to collect all of these

components together or to generate more, nor has there been any good way

to recognize the efforts of those who have developed pedagogical materials.I am hopeful that this situation will change soon, especially if you are

willing to help.Right now we are in the process of revising the main GAP web site, and

one of the new pages will be devoted to the instructional use of GAP.

The plan is to try to organize the existing materials and to solicit

more, even those that are not yet perfect. In addition, I hope it will

be possible to expand upon our present refereeing process for

computational GAP packages to designate "accepted" pedagogical packages

of a certified high standard whose authors would get recognition for

their work. I am aware of several people who have a current interest in

such projects and have already made varying degrees of progress, so this

year should be a good one.As I see it, possible reasons for introducing a computational algebra

system into a course include the following. (1) The software can act as

a fancy calculator to let the students accurately run a variety of

experiments that would take prohibitive amounts of hand calculation. (2)

Learning how to communicate with the software can give students a clear

picture of what one would want to know about a group or a ring or a

field--what would be most useful, what less so. For example, just

thinking about how to describe a group as input or to construct it from

other groups already raises questions students may not have thought of

from reading a textbook. (3) Students can see some programming models

and get opportunities to think algorithmically themselves. (4) And

students can begin to ask how the software actually works, which can

lead them to ask good questions about the mathematics as well as about

programming. As a simplest example, students could look at the different

methods Order can select, depending upon the type of group involved.In my view, whenever we build an example or an exercise that asks

students for some kind of interaction with the software, it's essential

that we ask ourselves which of these, or other, goals we are aiming at.

Just the fact that the software CAN do something is not, by itself, a

justification for asking students to use it for that. But if we know why

we're asking the questions, then it's amazing how much the students can learn.You can see, I think, the sorts of things I'd like to be able to make

available to the GAP community and to our students. Let me ask all

interested Forum subscribers to think seriously about instructional

materials that we can put on the GAP site. We can continue to use the

Forum itself as a place for brief questions and answers on the subject,

but it may be best to write directly to me or to Professors Neubueser or

Robertson with detailed questions or suggestions.Charles Wright

Chairman, the GAP Council

wright@math.uoregon.edu

Miles-Receive-Header: reply

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