A Discovery Method for Undergraduate Linear Programming

Arizona State University, Scottsdale AZ

Investigators

Abstract

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.