A Discovery Method for Undergraduate Linear Programming

在这个概念验证项目中，正在开发材料，以成为线性规划本科课程的教科书。 该课程的目的是为职前中学数学教师以及数学专业的学生，和国家数学教师理事会（NCTM）的标准发挥了不可分割的作用，在材料的发展。 该项目的创新方面包括材料和交付方法的选择，以及相关技术的使用。 该项目是：（i）引入发展高级证明技能的新方法;（ii）通过在教科书材料的叙述中加入练习来吸引读者;（iii）包括学生自我生成的练习，以及学生自我检查的解决方案;（iv）包括广泛的个人和小组项目，以及（v）将广泛的本科主题融入课程。 此外，正在编写一本全面的教师手册，其中载有课堂活动的想法、练习和测验样本，以方便初次使用和不熟悉线性规划的教师使用。 单纯形法被广泛认为是过去几十年中最重要的算法之一，因为它的广泛使用，它在工业和数学中的强大应用，它的优雅简洁，以及它迷人的数学基础，单纯形法是材料的一个突出部分。该项目的一个目的是为那些很少或从未开设过线性规划课程的部门提供课程。 除教科书外，还将通过在AMS、MAA、AMS-MER和其他国家会议上的介绍来传播成果。

In this proof of concept project, materials are being developed to become a textbook for an undergraduate course in linear programming. The course is intended for pre-service secondary mathematics teachers as well as mathematics majors, and standards of the National Council of Teachers of Mathematics (NCTM) play an integral role in the development of the materials. Innovative aspects of the project include both choice of materials and method of delivery, with the employment of relevant technology. The project is: (i) introducing a new method of developing advanced proof skills; (ii) engaging the readers by including exercises in the narrative of the textbook materials; (iii) including exercises that students self-generate, with solutions that students self-check; (iv) including a wide range of individual and group projects, and (v) integrating a wide range of undergraduate topics into the course. In addition, a thorough instructors' manual with classroom activity ideas, worksheets, and sample quizzes to facilitate first-time use and use by teachers not familiar with linear programming is being written. Widely recognized as one of the top algorithms of the last several decades for its widespread use, its powerful applications to industry and to mathematics, its elegant simplicity, and its fascinating mathematical underpinnings, the Simplex method is a prominent part of the materials.One intent of the project is for departments that have rarely or never offered a course in linear programming to make it part of their curriculum. In addition to the textbook, results will be disseminated through presentations at AMS, MAA, AMS-MER, and other national conferences.