A Discovery Method for Undergraduate Linear Programming

在这个概念证明项目中，正在开发的材料将成为线性规划本科课程的教科书。本课程的目标读者是职前中学数学教师以及数学专业的学生，并且在教材的开发过程中，美国国家数学教师委员会（NCTM）的标准起着不可或缺的作用。该项目的创新方面包括材料的选择和交付方法，以及相关技术的使用。该项目是：(i)引入一种开发先进证明技能的新方法；（ii）通过在教材叙述中加入练习来吸引读者；（三）包括学生自创的习题，以及学生自检的解决方案；（iv）包括广泛的个人和小组项目，(v)将广泛的本科主题整合到课程中。此外，还编写了一份详尽的教师手册，其中包括课堂活动思想、工作表和样本测验，以方便首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来最顶尖的算法之一，因为它的广泛使用，它在工业和数学上的强大应用，它优雅的简单性，以及它迷人的数学基础，单纯形法是材料的一个突出部分。该项目的目的之一是让很少或从未开设线性规划课程的院系将其作为课程的一部分。除教科书外，研究结果还将通过在AMS、MAA、AMS- mer和其他国家会议上的演讲来传播。

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.