Enabling Computer Algebra Use in the Undergraduate Abstract Algebra Curriculum

数学科学（21）这个项目正在提高免费和开放的计算机代数系统GAP的可用性，用于本科抽象代数和数论课程以及本科研究项目。近年来，计算机代数系统已被用于本科课程作为一个说明性和实验性的工具。然而，有效使用这种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。该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组感兴趣的教师在他们的机构进行测试。智力成果：该项目正在开发新的方法，以便在本科课程中进行代数结构的具体计算。它提供了一个新的资源，教师谁想要使用计算机代数系统在本科抽象代数课程或本科研究/调查项目。这些新的和增强的组件帮助数学（包括数学教育）、计算机科学和工程专业的学生理解抽象代数中的概念，提供了学习铅笔和纸不可行的例子的方法。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。类似于现在建立的微积分课程中的计算和计算器的使用，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例子。由于该系统已在许多机构用于代数教学，因此这种增强功能拥有大量用户，并最终将增强对参加该课程的大部分学生的抽象代数教学。

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.