Classroom Resources

PascGalois JE Labs (Web-based Versions using Applets)

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

• Introduction
  • Introduction to the Student
  • Introduction to the Professor
  • Introduction to the PascGalois Applet System
• Core Labs
  • Introduction to the PascGalois JE Applets
  • Pattern Recognition and Pascal's Triangle Modulo n
  • An Introduction to Isomorphism: Groups of Order 4
  • Subgroups and Generators of Z_n
  • Isomorphism
  • Quotient Groups of Z_n
• Supplemental Labs
  • Building A Group with PascGalois Triangles
  • Pattern Recognition Using Dihedral Groups
  • Subgroups and Generators of D_n and S_n
  • Direct Products and Automorphisms
  • Quotient Groups of D_n and S_n
  • 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

PascGalois JE Labs (PDF Versions using the PascGalois JE Application)

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 Z_n
  • Isomorphism
  • Quotient Groups of Z_n
• Supplemental Labs
  • Building A Group with PascGalois Triangles
  • Pattern Recognition Using Dihedral Groups
  • Subgroups and Generators of D_n and S_n
  • Direct Products and Automorphisms
  • Quotient Groups of D_n and S_n
  • 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

Pascal GT Labs

by Mike Bardzell and Kathleen Shannon

• The Complete Lab Manual
• 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
  • Appendix: Brief Introduction to the PascalGT Software

Web-based Versions using Applets

• 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

PDF Versions using the PascGalois JE Application

• 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