A Proposed Exercise to Reinforce Abstract Thinking for Upper-Division Computer and Electrical Engineering Students: Modeling a High-Speed Inverter Using Cognitive Representations and Abstract Algebra

摘要

In mathematics, physics, and engineering, abstract concepts are an indispensable foundation for the study and comprehension of concrete models. As concepts within these fields become increasingly detached from physical entities and more associated with mental events, thinking shifts from analytical to conceptual-abstract. Fundamental topics taken from the abstract algebra (aka: modern algebra) are unquestionably abstract. Historically, fundamental concepts taught from the abstract algebra are detached from physical reality with one exception: Boolean operations. Even so, many abstract algebra texts present Boolean operations from a purely mathematical operator perspective that is detached from physical entities. Some texts on the abstract algebra introduce logic gate circuits, but treat them as perceptual symbols. For majors of pure or applied mathematics, detachments from physical entities is not relevant. For students of Computer and Electrical Engineering (CpE/EE), mental associations of Boolean operations are essential, and one might argue that studying pure Boolean axioms are unnecessary mental abstractions. But by its nature, the CpE/EE field tends to be more mentally abstract than the other engineering disciplines. The depth of the mathematical abstractions that we teach to upper-division CpE/EE majors is certainly up for questioning.