Interactive Web Applications for Sets, Groups, and Mappings

Last Change: February 28, 2019

Chapter 7: Groups

• Phosphene: A square array of tiles that can be rotated individually or in groups to create striking patterns.
• Subgroups: Explore subgroups of $(\mathbf{Z}_{m} \times \mathbf{Z}_{n}, +)$ that are generated by selected elements.

Chapter 10: Multiplicative Inverses of Residue Classes

• Pirouette: A Spirograph clone for drawing and printing designs coming from multiplication diagrams for cyclic groups.

Chapter 11: Linear Transformations

• Matrix Multiplication: Guided practice multiplying matrices.
• Gaussian Elimination: Practice the row reduction algorithm for solving a system of linear equations.
• Matrix inversion: Practice the row reduction algorithm for calculating the inverse of a square matrix.

Chapter 13: Permutations

• The Fifteen Puzzle: Unscramble numbered tiles in a $4 \times 4$ array utilizing the single empty square.

Chapter 14: Examples of Finite Groups

• $D_{3}$ Explorer and Navigator.
• $D_{4}$ Explorer and Navigator.
• $D_{6}$ Explorer.

Chapter 15: Cosets

• Cosets: Explore cosets in the additive group $(\mathbf{Z}_{m} \times \mathbf{Z}_{n}, +)$.