Classroom Resources & Articles

Classroom Resources

Abstract Algebra: PascGalois JE Labs

by Mike Bardzell, Jennifer Bergner, Kathleen Shannon, Don Spickler and Tyler Evans

Introduction

• Introduction to the Student

• Introduction to the Professor

• PascGalois JE User’s Manual

Core Labs

• Introduction to PascGalois JE

• Pattern Recognition and Pascal’s Triangle Modulo n

• An Introduction to Isomorphism: Groups of Order 4

• Subgroups and Generators of Zn

• Isomorphism

• Quotient Groups of Zn

Supplemental Labs

• Building A Group with PascGalois Triangles

• Pattern Recognition Using Dihedral Groups

• Subgroups and Generators of Dn and Sn

• Direct Products and Automorphisms

• Quotient Groups of Dn and Sn

• Subnormal Series

• Self-Similarity and the Klein-4 Group

• Rings and Fields

• Discovering a Binomial Identity

• Exploiting Symmetry in Pascal’s Triangle Modulo a Prime by Tyler Evans

Abstract Algebra: Pascal GT Labs

by Mike Bardzell and Kathleen Shannon

The Complete Lab Manual

• The Complete Lab Manual

• Brief Introduction to the PascalGT Software

Individual Labs and Handouts

• Introduction to the Student

• PascGalois Project 1: Pattern recognition and Pascal’s Triangle Modulo n

• PascGalois Project 2: Pattern Recognition Using Dihedral Groups

• PascGalois Project 3: Building A Group with PascGalois Triangles

• PascGalois Project 4: Direct Products and Automorphisms

• PascGalois Project 5: Quotient Groups 1

• PascGalois Project 6: Quotient Groups 2

PascGalois Enhancement Projects

• Self-Similarity and the Klein-4 Group

• Rings and Fields

• Two Dimensional Automata

Mathematics for Elementary Education

by Cynthia Woodburn and Nancy Zumoff

• Developing Pascal’s Triangle

• Coloring Multiples

• Modular Addition

• Color a Z2 Triangle

• Color a Z3 Triangle

• Color Your Own Triangle mod n

• Color Your Own Triangle - General Group

• Coloring Pascal Triangles Contest

• Searching for Patterns - Identity Elements

• Searching for Patterns - More with Identity Elements

• Pascal Petals

• Magic Power of 11

• More Uses of Pascal’s Triangle - Combinations

• Notorious Numbers

Number Theory

by Mike Bardzell, Michael Fisher and Kurt Ludwick

• Unimodality of the Binomial Coefficients by Michael Fisher

• Cryptology by Michael Fisher

• Fermat’s Little Theorem by Michael Fisher

• Fibonacci Primes by Michael Fisher

• How many binomial coefficients are even? by Michael Fisher

• Primitive Roots by Michael Fisher

• Discovering a Binomial Identity by Mike Bardzell

• The Lucas Correspondence Theorem by Kurt Ludwick

Articles

• Searching for Patterns in Pascal’s Triangle With a Twist by Kathleen M. Shannon and Michael J. Bardzell with Applets by Andrew Nagel.

• Discovering Binomial Identities with PascGaloisJE by Tyler Evans.

• The PascGalois Project: Computer Visualizations, Henson Seminar, Michael J. Bardzell and Kathleen M. Shannon.

• Fractal Dimensions in the PascGalois Triangle, Loyola University, Michael J. Bardzell and Kathleen M. Shannon.

• Using Computer Graphics to Investigate Group Structure, Towson University, Michael J. Bardzell and Kathleen M. Shannon.

• Support for the paper: The PascGalois Triangle: A Tool For Visualizing Abstract Algebra, which is part of an MAA Notes publication: Innovations in Teaching Abstract Algebra, Allen C. Hibbard and Ellen F. Maycock, Editors. Authored by Michael J. Bardzell and Kathleen M. Shannon.

• PascGalois Triangles & Hexagons and other Group-related Cellular Automata, by Kathleen M. Shannon and Michael J. Bardzell.