Calculus probably isn't the best example, because you really don't need it. Real engineers need it, but if software engineers got a different sequence in discrete math I think they'd be better prepared for the job market. I ended up doing a math concentration so I got both Calc 1-3 and some nice discrete courses like number theory, combinatorics, and abstract algebra that were super useful, and in my opinion we could definitely stand to replace memorizing integration techniques with studying some of those topics.
This really is not true. Using a little calculus to derive a closed form solution to a problem can reduce computational burden. A team where I work just had to do exactly this for a geographic distance optimization problem. At first glance it seemed like you needed dynamic programming and it was expensive, but drawing it out and modeking it with equations, we actually set up a Lagrange multiplier formula for the problem and found it had an exact solution. This was not a team of mathematicians or anything, just database engineers working on a specialized in-house search optimization problem.
If you do work in statistics, then calculus matters quite a bit, especially for transformations of variables and deriving the formulas for the probability distributions you’re working with. In Bayesian methods, even if you use autodifferentiation tools to automatically sample from your model, you still often need to do a bit of calculus here or there.
Likewise, if you ever find that you need to implement your own model training algorithms, you’ll probably need to calculate gradients (for example, the gradient of custom log-likelihood functions) analytically before writing them as software functions.
Calculus is pretty pervasive in professional software engineering. You don’t need to be an expert, but should have working knowledge and ability to dig into references and work through it.
Yeah the statistics and machine learning applications are a bit hard to get away from. But I would still replace the calculus sequence with discrete math, assuming the number of math credits had to stay the same. At my school (University of Maryland, College Park) most CS majors just took calculus 1-3, statistics, and one basic discrete math course from the computer science department. The size of calculus seems massive (3/5 of the total math load) compared to the benefit. That precious time could be spent digging deep into linear algebra or combinatorics or graph theory etc, and that's useful for all developers who write algorithms, not just in specific applications' niches.
Why do you think they are mutually exclusive? Generating functions, geometric series, difference equations, integrals over discrete probability distributions, elliptic curve cryptography, general linear programming and optimization, eigenvalue analysis in graph theory, stochastic optimization, all these things involve calculus to solve discrete algorithmic questions.
In fact I’d argue it makes calculus more important than what is typically understood as “discrete math” because in order to have the mathematical maturity to really understand the meaning of major discrete math results and theorems, it requires understanding calculus first.
If you “just” study discrete math mistakenly believing “that’s where the value is” then you’d end up with a shallow understanding of discrete math, lacking ability to extract value from it except in some narrow sense from rote discrete math application-specific coursework.
