PREP - Professional Enhancement Programs of the MAA

Exploring Abstract Algebra Using Computer Software

A PREP Workshop

Workshop Program

Click on the links on this page to download workshop materials in pdf format.

Lead-in Activities

Approximately six weeks in advance of the on-line workshop, participants were 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 were scheduled and conducted in consultation with each participant.

On-line Program (June 28 - July 2, 2004)

The on-line portion ran 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 were expected to spend time on workshop activities between the on-line sessions.

Schedule

Monday June 28, 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 June 28, 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)

Tuesday June 29, 10 am - 11:30 am

Section 4 (Proof that A_n is Simple)
Section 5 (Groups Defined using Generators and Relations)

Tuesday June 29, 2:30 pm - 4 pm

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)
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)

Wednesday June 30, 10 am - 11:30 am

Complete Section 8
Section 9 (Ring Homomorphisms) (also download the files and ringHoms and ringHoms2 - right click or hold down control or option when you click, so the file downloads instead of opening in your browser)
Section 10 (Polynomial Rings)

Wednesday June 30, 2:30 pm - 4 pm

Complete Section 10
Section 11 (Vector Spaces)
Section 12 (Finite Fields)

Thursday July 1, 10 am - 11:30 am

Complete Section 12
Section 13 (Extension Fields)

Thursday July 1, 2:30 pm - 4 pm

Complete Section 13

Coding Theory example

Section 14 (Introduction to Galois Theory)

Friday July 2, 10 am - 11:30 am

Complete Section 14

Solutions for Problem 14.11

Section 15 (Another False Conjecture) (also download Figures for Section 15)

Friday July 2, 2:30 pm - 4 pm

Section 16 (Gaussian Integers)
Section 17 (Solvable Groups)
Section 18 (Orbits and Stabilizers)
Conclusion

Follow-Up Activities

After the On-Line 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: 0341481