The PascGalois Project: Visualizing Abstract Mathematics#

The PascGalois project has its origin in a simple exercise with Pascal’s triangle. Take each entry in the triangle and replace it with its congruent value mod n, where n is a positive integer larger than 1. By assigning each of the values \(0, 1, \ldots, n - 1\) a distinct color, patterns reminiscent of fractals appear. Our interest in this construction lies in the fact that addition mod n is the group operation of the cyclic group \(\mathbb{Z}_n\) and the patterns seen in the triangles are related to the structure of these groups. By replacing \(\mathbb{Z}_n\) with other finite groups one can use the same fractal-like patterns to visualize the structure of these non-cyclic groups.

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The PascGalois Project was made possible through two grants from the National Science Foundation, DUE-0087644 and DUE-0339477.

For more information or questions about the project please contact us at,

Dr. Mike Bardzell
Department of Mathematical Sciences
Henson School of Science & Technology
Henson Hall, 132C
Salisbury University
Salisbury, Maryland 21801
mjbardzell@salisbury.edu
Dr. Kathleen Shannon
Department of Mathematical Sciences, Retired
Henson School of Science & Technology
Salisbury University
Salisbury, Maryland 21801
kmshannon@salisbury.edu
Dr. Don Spickler
Department of Mathematical Sciences
Henson School of Science & Technology
Henson Hall, 132E
Salisbury University
Salisbury, Maryland 21801
despickler@salisbury.edu

Participants#

Faculty#

Faculty Materials Developers and Authors

  • External Faculty

    • Tyler Evans

    • Michael Fisher

    • Eirini Poimenidou

    • Cynthia Woodburn

    • Nancy Zumoff

Retreat Participants#

2005 Retreat Participants

  • Student Researchers

    • Aaron Churchill

    • Nathan Cochran

    • Ryan Compton

    • Christopher Davis

    • Daniel Erceg

    • Mackenzie Kielman

    • Guangming Lang

    • Bryant Lee

    • Jonathon Miller

    • Jeremy Sherman

    • Julian Trezise

    • Renee Zawistowski

    • Robin Zhao

  • Facilitators

    • Mike Bardzell

    • Tyler Evans

    • Brian Guarraci

    • Nicole Miller

    • Eirini Poimenidou

    • Kathleen Shannon

2006 Retreat Participants

  • Student Researchers

    • Josh Abbott

    • Kyle Anderson

    • Kristy Beam

    • Katelin Childers

    • Julie Coxe

    • Erin Craig

    • Didi Desjardins

    • Ryan Johnson

    • Robin Keng

    • Casey Kuhn

    • Chen Liu

    • Christian Millichap

  • Facilitators

    • Mike Bardzell

    • Aaron Churchill

    • Elena Jeliazkova

    • Jonathon Miller

    • Eirini Poimenidou

    • Kathleen Shannon

    • Don Spickler