Teaching Abstract Algebra with Maple - Maplesoft

Teaching Abstract Algebra with Maple

Visualize, Explore, and Understand

With Maple, you can engage and enlighten students in your group theory, ring theory, field theory, and other abstract algebra courses

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Focus on the Concepts

Maple has broad support for computations in group theory, ring theory, field theory, and more. With Maple looking after the mechanics of the calculation, students can more easily focus on the concepts.
With Maple, you can:

  • Compute with and visualize permutation groups, finitely presented groups, symbolic groups, and more

    • Construct cyclic, dihedral, Hamiltonian, linear, semi-linear, and many, many other types of groups, as permutation groups or finitely presented groups; and construct many symbolic types of linear and semi-linear groups

    • Compute group properties, including the center, centralizer, normal closures, minimal normal subgroup, etc.

    • Test group properties, such as if a subgroup is normal or a group is directly decomposable

  • Compute with polynomial ideals in commutative polynomial rings over various fields

  • Work with matrices in matrix rings

  • Explore differential rings and Ore rings

  • Compute towers of field extensions

  • And more much!

Read

Teaching Group Theory with the GroupTheory Package

Enlightening Visualizations

Abstract concepts are easier to grasp when you can see them, and Maple provides many helpful visualizations, especially in group theory. These include symmetries of a graph, Cayley graphs, Cayley tables, the lattice of subgroups of a group, and more.

  • Cayley graph the dihedral group of order 3 Cayley graph the dihedral group of order 3
  • Visualization of the subgroup lattice of a group Visualization of the subgroup lattice of a group
  • Cayley table of the Symmetric Group on 3 letters Cayley table of the Symmetric Group on 3 letters
  • Cayley Table of a permutation group Cayley Table of a permutation group

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Powerful Research Tool

Maple supports advanced computations not available in other systems, together with standard mathematical notation, a programming language designed for mathematics, efficient algorithms, and authoring tools to support your research.
Maple provides functionality for working with a wide variety of abstract algebra concepts, including:

  • Polynomial ideals

  • Field extensions

  • Lie Algebras

  • Galois Fields

  • Ore Algebras

  • etc.

  • Magmas

Discover

Overview of the Polynomial Ideals package

Versatile Technical Document Environment

The Maple environment can be for interactive problem solving as well as the development of rich, interactive documents and applications. Maple documents combine live computations and visualizations with explanations, images, videos, parameter sliders and other interactive elements, and more. Common activities performed in the Maple environment include:

  • Demonstrating concepts and working through examples during lectures

  • Exploring “what if” scenarios, including on-the-fly responses to questions during class and independent student explorations

  • Developing lecture notes, assignments, and student resources that can be viewed in Maple, through a web browser, or as PDFs

  • Working through assignments, including written explanations about reasoning and methods

  • Investigating, developing, and presenting results for project-based learning activities

  • Creating custom, interactive applications and algorithms

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Request your personalized demo today, and we’ll arrange for one of our experts to show you what Maple can do for you and your students.

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