PREP - Professional Enhancement Programs of the MAA

Abstract Algebra with GAP

A PREP Workshop

Workshop Program

Click on the links on this page to download workshop materials in pdf format. Materials will appear during the week (we don't want you working too far ahead!)

Lead-in Activities

Approximately six weeks in advance of the on-line workshop, participants will be asked to begin preparing for the workshop by downloading and installing GAP, and completing preliminary testing and a GAP tutorial. On-line connectivity tests with each participant site are also planned and will be scheduled in consultation with each participant.

On-line Program (July 14 - July 18, 2003)

The on-line portion is planned to run for two one and a half hour time blocks, 10:00 am - 11:30 am and 2:30 pm - 4:00 pm Central Daylight Time, each day. Participants are expected to spend time on workshop activities between the on-line sessions.

Approximate Schedule

This schedule is likely to be adjusted to fit the actual pace of the workshop.

Monday July 14, 10 am - 11:30 am

Introduction to the workshop
Section 1 (Permutation Groups) (also download Figures for Section 1)

Rotations of the Cube example (also download Figures for the rotations of the cube)

Monday July 14, 2:30 pm - 4 pm

Complete Section 1
Section 2 (Direct Products) (also download orderFrequency - right click or hold down control or option when you click, so the file downloads instead of opening in your browser)

Appendix with description of how to make and read in functions

Section 3 (A Sylow Theorem) (also download sylows - right click or hold down control or option when you click, so the file downloads instead of opening in your browser)
Section 4 (Proof that A_n is Simple)

Tuesday July 15, 10 am - 11:30 am

Section 5 (Groups Defined using Generators and Relations)

Tuesday July 15, 2:30 pm - 4 pm

In response to a question, Juli's syllabus for our class, and Russell's syllabus for our class
Section 6 (Factor Groups)
Section 7 (Group Homomorphisms) (also download the files autoDn and homoDn - right click or hold down control or option when you click, so the file downloads instead of opening in your browser)

Wednesday July 16, 10 am - 11:30 am

Section 8 (Introduction to Rings) (also download the files nilpotentCount and intror - right click or hold down control or option when you click, so the file downloads instead of opening in your browser)
Section 9 (Ring Homomorphisms)

Wednesday July 16, 2:30 pm - 4 pm

Section 10 (Polynomial Rings)

Thursday July 17, 10 am - 11:30 am

Section 11 (Vector Spaces)
Section 12 (Finite Fields)

Thursday July 17, 2:30 pm - 4 pm

Section 13 (Extension Fields)

Coding Theory example

Friday July 18, 10 am - 11:30 am

Section 14 (Introduction to Galois Theory)

Solution to Exercise 14.11

Friday July 18, 2:30 pm - 4 pm

Section 15 (Another False Conjecture) (also download Figures for Section 15)
Section 16 (Gaussian Integers)
Section 17 (Solvable Groups)
Conclusion

Follow-Up Activities

After the On-Site workshop:

Participants are expected to implement workshop-created GAP activities in their own classrooms
Participants are expected to participate in an on-line discussion list, sharing their experiences using GAP in the classroom
Participants are encouraged to disseminate materials they develop both within the participant group, and also to the wider mathematics community

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This PREP workshop is made possible by the NSF grant DUE: 0089005