Mathematics in engineering: Identifying, enhancing and linking the implicit mathematics curriculum

Abstract

A study is undertaken to lay out in a structured manner the mathematics skills required of undergraduate students in the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology. The key objective of the research is to identify barriers to deep mathematical understanding among engineering undergraduates. Data from engineering course syllabi and interviews with engineering and mathematics faculty are combined to form an implicit mathematics curriculum, which lists the mathematical skills relevant to core engineering classes along with the flow of learning and utilization. Several problematic areas are identified, including the concept of a function, linearization, and vector calculus. Interview results show that many engineering faculty have an inadequate knowledge of mathematics class syllabi, and often do not know where or how the skills they require are taught, while mathematics instructors often have a limited understanding of how mathematical concepts are applied in downstream engineering classes. A number of recommendations are made, including increased communication between mathematics and engineering faculty, development of joint resources for problematic areas, and dissemination of a formal catalogue of mathematical skills and resources to engineering students and faculty.