What math courses should be taught to undergrad electrical engineers: a 40 years update

Question

I was browsing IEEE xplore the other day and found this gem called "What Mathematics Courses Should an Electrical Engineer Take? A Report on the National Study of Mathematics Requirements for Scientists and Engineers" by G.H. Miller. dated 1970. I believe this paper is most likely aimed at undergrad electrical engineers.

In this paper he collected a survey from two groups: awards group and abstracts group. Awards group is a list of electrical engineers who won nationally or internationally recognized awards. Abstracts group were people who published profusely.

The goal was to determine just which courses should ELECTRICAL engineers take during undergrad. Note again this was from the 70s.

The conclusion of the paper is as follows:

Highly recommended: calculus sequence, vectors, elementary DE, intermediate ODE, advanced calculus, elementary complex variables, matrix theory, elementary probability

Moderately recommended: tensor analysis, advanced ODE, advanced PDE, calculus of variations, complex variables and machine computation, numerical analysis and integral transform

and this quote:

There was little use for newer courses in modern mathematics such as group theory, lie lgebras, multilinear algebra, mathematical logic, game theory, and geometric algebra. Therefore, these courses shoud be given low priority.

This quote raises obvious questions. Group theory is the foundation of signal processing. Lie algebra is used widely in quantum mechanics which is important for semiconductor physics. Mathematical logic is core of modern programming and control theory. Geometric algebra has many application in both signal processing and control theory. So it appears highly likely that the paper is out of date.

Three questions I have in mind hope some one can help me with (in no particular order)

1. Are recent or more modern sources for undergrad electrical engineer to decide on which math courses to take?

2. As the work force becomes more segmented, it is highly likely that a working electrical engineer will never use much of the math taught in school. (how much math is needed in quality assurance anyhow?)

So this is more aimed towards research engineers. Are there any research electrical engineers who might wish to dispute some of the claims in the paper?

3. What courses outside of the high and moderate recommendations should an electrical engineer student consider and why?

Answer 1

In my experience teaching undergraduate engineering students, key topics include at least some calculus, linear algebra and differential equations. Exactly how much depends on the field/subfield of engineering. A sampling of other topics includes:

• Boolean algebra (digital electronics)
• Graph theory and algorithms (networks)
• Probability and statistics (reliability engineering, quality assurance and communications)

The main thing I miss from a modern perspective in Miller's lists is discrete mathematics, which has increased in importance with the rise of computers in the last few decades. On a more specialized note, I would add discrete/computational geometry for its applications in areas such as robotics and sensor networks.

Research engineers may need to draw on a much wider and deeper array of knowledge. An example would be Michael Robinson at American University (http://www.drmichaelrobinson.net/), whose research includes signal processing, dynamics and applied topology. See, for instance, his recent book Topological Signal Processing, which draws on ideas from sheaf theory, category theory and computational topology. Note that this book is published in Springer's Mathematical Engineering series, which in the words of the publisher

...presents new or heretofore little-known methods to support engineers in finding suitable answers to their questions, presenting those methods in such manner as to make them ideally comprehensible and applicable in practice.

An undergraduate interested in pursuing such an area would conceivably be advised to take courses in topology and abstract algebra as preparation, both of which remain unorthodox choices for most engineers to the best of my knowledge.

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Edit: The 2014-2015 ABET (Accreditation Board for Engineering and Technology) accreditation criteria can be found at http://www.abet.org/uploadedFiles/Accreditation/Accreditation_Step_by_Step/Accreditation_Documents/Current/2014_-_2015/E001%2014-15%20EAC%20Criteria%203-13-14(2).pdf.

(Thanks Michael E2 for the link.)

In particular, on page 11:

These program criteria apply to engineering programs that include “electrical,” “electronic,” “computer,” “communications,” or similar modifiers in their titles.

1. Curriculum

The structure of the curriculum must provide both breadth and depth across the range of engineering topics implied by the title of the program.

The curriculum must include probability and statistics, including applications appropriate to the program name; mathematics through differential and integral calculus; sciences (defined as biological, chemical, or physical science); and engineering topics (including computing science) necessary to analyze and design complex electrical and electronic devices, software, and systems containing hardware and software components.

The curriculum for programs containing the modifier “electrical” in the title must include advanced mathematics, such as differential equations, linear algebra, complex variables, and discrete mathematics.

The curriculum for programs containing the modifier “computer” in the title must include discrete mathematics.

Answer 2

I believe Discrete Mathematics, Logic, and Calculus to Electrical Engineers.

How much has to be studied in Calculus, and how the curriculum is to be arranged, however, is a tough question.

The current educational system in my country teaches Electrical Engineers the following: Year 1: Linear Algebra, Matrix Theory, Differentiation and Integration, Logic

Note that at least this much is necessary to understand circuits, programming, and the physics curriculum (which includes basic forms of the Maxwell Equations)

Year 2: Partial Differentiation, Differential Equations, Discrete Mathematics, Probability and Statistics

Note that this curriculum is set to help them understand topics they study in Modern Physics, programming, and electronics.

After the 2nd year, undergraduates start to specialize to the extent that it is no longer possible to provide one universal curriculum which all electric engineers must know. Engineers working on electronics will need to know different mathematical concepts than those working in communication, for example.

Answer 3

Life requires prioritization. You are emphasizing some very intricate backgrounds (group theory to quantum to semiconductor physics to EE). And implicitly ignoring the huge amount of times that students will need basic calculus or ODEs in derivations or homework problems. More of C is less of A. The list is prioritized, your remarks are essentially "why not more C" so don't even show the benefit of comparison. Of stating what you would lower on the list if you raise something.

I actually get a little bit the impression you know a lot about math but not that much about EE. I'm not an EE, but took two solid semesters of junior level EE as part of engineering requirement and also had training in it at nuke school. And even worked in a firm that had ME and EEs.

Furthermore, I have a pretty solid quantum background for a chemist and did a Ph.D. in solid state that involved a lot of semiconductor physics (but light and experimental for a physicist, but still way more at least exposure than the average cat). And I never had my learning hurt by the lack of theoretical group theory for quantum (it was more diffyq based). Heck, even if you do look at quantum theory in terms of group theory, the average physicist would just use the parts of group theory he needed.

And the idea that a BS EE needs that level of quantum theory? Noooo. (There are only so many hours in the day and EEs already bust ass. They have to learn about a gazillion things from op amps to squirrel cage induction motors and Y-D transformers.)