Set Theory and Proofs for Engineering Education

Abstract

Through evaluations of learning objectives on several Engineering courses, the majority of students at some point will struggle with demonstration of proof of a principle in their homework assignments, quizzes, and exams. An early introduction of "Set Theory and Proofs" to engineering students can enrich their intuition and ability to solve comprehensive problems. As illustrated in this paper, set theory can be recognized by students as a simple and unnecessary topic. However, the understanding of principles in set theory and its derived concepts are essential to engineering students so they can improve their problem-solving skills when approaching a more complex problem using mathematics. Set Theory is a vast field of study which includes: Operations and algebra with sets, power sets, product sets, relations, functions, quantifiers, family of sets, index sets, just to name a few [1]. At The University of Texas at Tyler, the authors experienced set theory embedded in the learning objectives of Manufacturing Systems (MENG 5318) course offered by the Mechanical Engineering Department to its graduate students. In Fall 2016 and 2017, most of the students in the class failed to apply some of the principles in set theory. Overall, set theory is an important topic to engineering students where an understanding of the principal will ensure the success in completing advanced level courses.