Mathematics in Electrical Engineering Practice

Engineering is known for its heavy use of maths and true to form, university engineering courses tend to be maths-heavy. But in my experience, one that is shared by many other practicing engineers, the amount of maths an engineer actually uses in industry is merely a fraction of what is taught. So let’s look at the mathematics that I’ve used so far in my professional work: ....

• Elementary arithmetic and arithmetic functions, e.g. basic operations, fractions, percentages, etc
• Elementary algebra, e.g use of variables, basic expressions (linear, polynomial, radical, exponential and logarithmic), systems of linear equations
• Basic calculus, e.g. understanding differentiation and integration as it applies to physical phenomena
• Complex analysis, e.g. functions of complex variables, basic algebra for complex quantities, complex exponentials
• Basic statistics and probability, e.g. probability distributions, descriptive statistics, basic statistical inference
• Euclidean geometry, e.g. vector algebra, trigonometry

To summarise, there are three things an electrical engineering practitioner really needs: 1) some level of numeracy (i.e. comfort with numbers), 2) the ability to manipulate algebraic equations, and 3) some spatial ability to visualise points, lines and shapes on 2 or 3-dimensional spaces.

Now I was lucky enough not to be corrupted at school to despise maths and actually find it interesting. But knowledge of more advanced maths isn’t necessarily more useful to engineers than just knowing the above. For example, here’s a list of maths topics that I learnt at university, but have never used at work:

• More advanced calculus, e.g. contour integration, surface integrals, Fourier transforms, convolutions, etc
• Optimisation techniques, e.g. lagrangian multipliers, envelope theorems, etc
• More advanced statistical inference, e.g. assessing estimators, finding confidence intervals, etc
• Linear algebra, e.g. matrix algebra, vector spaces, eigenvector decomposition, etc
• Differential equations

Most of these topics are loosely categorised under the umbrella of “engineering mathematics”, but you’d probably never use them unless you were in academia doing research. Rather than calculating complicated vector integrals of electromagnetic fields, electrical engineers tend to rely on rules of thumb, empirical formulae or tables. Even the technical standards are filled with empirical or approximate relationships; someone in academia has already done the hard work and distilled it into a form that a practicing engineer can use quickly.

This isn’t to say that learning the more advanced facets of maths is useless – of course there are cognitive benefits from pushing your mind to learn and understand increasingly abstract mathematical concepts. But it does touch on the broader discussion of the benefits of “learning maths for maths sake” and whether “more maths is always better”, especially when interest is distinctly lacking. In a Washington Post article from Oct 2010, mathematics professor G.V. Ramanathan opines about the level of maths competency needed in everyday life by the broader community, and he concludes that it’s not much. But with the potential indirect benefits from learning maths (e.g. improved logical and abstract reasoning), what is the appropriate level of maths education for engineers and more broadly, the general public?

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