Abstract
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.
Highlights
In traditional computer and electrical engineering curricula, juniors must complete a course sequence in microelectronic devices and circuits
One of the successions of topics covered in this sequence is digital circuits, which includes a meticulous study of the dynamic switching characteristics of a basic metal-oxide semiconductor field-effect transistor (MOSFET) inverter
Students have to spend several weeks learning about the comprehensive physical structure and current-voltage characteristics of these devices, followed by how MOSFETs are biased to operate as linear amplifiers
Summary
In traditional computer and electrical engineering curricula, juniors must complete a course sequence in microelectronic devices and circuits (often referred to as microelectronics or electronic circuits). One of the successions of topics covered in this sequence is digital circuits, which includes a meticulous study of the dynamic switching characteristics of a basic metal-oxide semiconductor field-effect transistor (MOSFET) inverter Prior to this juncture, students have to spend several weeks learning about the comprehensive physical structure and current-voltage characteristics of these devices, followed by how MOSFETs are biased to operate as linear amplifiers. If the CpE/EE student chooses to pursue more advanced courses in the areas of digital electronic circuits or digital logic operations, they have a variety of advanced-undergraduate courses to choose from [11]-[17] These courses are structured to teach 1) the analysis and design of CMOS integrated circuits; 2) architectures and implementations of data converters; 3) energy-efficient VLSI design; 4) the development of hardware for embedded microcontroller systems. The author sees the benefit of such a unified exposure at a level that is appropriate for junior CpE/EE’s
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