Enabling Computer Algebra Use in the Undergraduate Abstract Algebra Curriculum

数学科学（21）本项目旨在提高免费开放的计算机代数系统GAP的可用性，使其用于本科抽象代数和数论课程以及本科研究项目。近年来，计算机代数系统作为一种说明性和实验性的工具已被用于本科课程。然而，有效使用这些系统的一个障碍是缺乏针对本科教学环境的功能和文档，以及对许多潜在用户来说过于复杂的安装过程和用户界面。这个项目提供了新的功能，简化了安装和使用。这种新材料正在由一群感兴趣的教师在他们的机构进行测试。该项目的结果正在因特网上公布。智力优势：该项目正在开发在代数结构中进行具体计算的新方法，在本科课程的背景下。它为希望在本科抽象代数课程或本科研究/调查项目中使用计算机代数系统的教师提供了一种新的资源。这些新的和增强的组件帮助主修数学（包括数学教育）、计算机科学和工程的学生理解抽象代数的概念，提供了学习用铅笔和纸无法实现的例子的方法。更广泛的影响：安装和用户界面的改进使系统GAP的任何用户受益，包括本科生和研究生以及大型研究社区。类似于现在微积分课程中计算和计算器的使用，一个具有用户友好界面的代数计算系统的可用性使抽象代数课程的教师能够展示不能简单地通过手工计算完成的示例。由于该系统已经在许多机构的代数教学中使用，这种增强有大量的用户，并最终将提高抽象代数的教学，使很大一部分参加该课程的学生受益。

Mathematical Sciences (21)This project is enhancing the usability of the free and open computer algebra system GAP for use in undergraduate abstract algebra and number theory courses as well as for undergraduate research projects. In recent years, computer algebra systems have been used in the undergraduate curriculum as both an illustrative and experimental tool. One obstacle to the effective use of such systems, however, is a lack of functionality and documentation aimed at the undergraduate teaching environment, as well as an installation process and user interface that is too complicated for many potential users. This project is providing new functionality and simplifying installation and use. This new material is being tested by a group of interested faculty at their institutions. Results of the project are being made available on the Internet.Intellectual Merit: The project is developing new methods to perform concrete calculations in algebraic structures in the context of an undergraduate course. It provides a new resource for teachers who want to use a computer algebra system in the undergraduate abstract algebra curriculum or for undergraduate research/investigation projects. These new and enhanced components aid students majoring in mathematics (including mathematical education), computer science and engineering in the understanding of concepts from abstract algebra by providing the means to study examples that would not be feasible with pencil and paper.Broader Impact: Improvements to installation and user interface benefit any user of the system GAP, including undergraduate and graduate students and the large research community. Analogous to the now established use of computation and calculators in calculus courses, the availability of a system for algebraic calculations with a user-friendly interface enables teachers of abstract algebra courses to show examples that cannot simply be done by hand calculation. As the system is already in use for teaching algebra at many institutions, this enhancement has a substantial group of users and will ultimately enhance the teaching of abstract algebra to a substantial part of the student population who take the course.