Mathematics for Computer Science (2017) [pdf]

A few tools that I use for solving optimization problems in practice are:

- MiniZinc, https://www.minizinc.org/ a constrain set programming language that can also optimize an objective

- Picat, http://picat-lang.org/ a general purpose language that specializes in logic and optimization

In the US, at least, computer engineering != programming. Computer engineering is more commonly (when you look at the courses) electrical engineering with a digital logic focus with some additional programming courses (often the first 2-4 CS courses). Programming falls squarely within computer science.

Just for perspective, math (and some compsci) students (and practitioners) would consider everything in the linked book to be "trivial math". That's because this book is a compilation of surface level sampling from various branches of math.

Mathematicians' version of your lamentation would probably look something like "I studied all the ins and outs of measure theory/functional analysis and category theory/algebraic geometry for four years and all I do today is teach engineering students calculus and freshman math majors - elementary real analysis. That's deeply sad". :)

As a web dev I needed to know some trig to visualize a star shaped diagram. Not that advanced, I know.

In HFT firms you need to know some calculus as some of your data are going to be mathematical objects that are squarely in the field of calculus.

Game devs need to know about matrices and quaternions. Mostly on how to use it, no proofs necessary.

There are some fields and exploit chains where knowing some math to advanced math is necessary for hacking. For example checkout Triton and PIN from Intel and SMT solvers. I needed to instrument a binary program in class and use Triton to make an SMT equation, solve it and crack a password that way.

Data scientists need to know statistics but you could argue they aren’t software devs but I bet some of them are both while having data scientist as a title.

When performing speed optimization experiments, it is necessary in some cases to know statistics as you’re really finetuning things. Simply hitting run for a few times and observing a 5x to 10x speedup doesn’t fall into this category, as the speedup is obviously visible. I am talking about stuff that you can’t distinguish that easily.

In general life, I would say strong knowledge about statistics is helpful. It helped me accurately assess the covid threat where I live. It also taught me to take every small chance out there. If I take enough chances then the likelihood of me hitting one of them becomes very very likely. I played poker as a teenager and have used statistical/chance-based thinking ever since and it helped me to experience more certainty in uncertain situations. I have played enough hands to know what a 1% chance of losing feels like (it feels like paying a fee to win the other 99 times, on average. Except if you’re not paying attention. Then it feels like you shouldn’t have lost and you’re probably going on tilt.).

That’s what I know so far.

I was going to assume that I did -- until I actually looked at the PDFs Table of Contents. I was hoping they'd cover more linear algebra techniques and get into data-driven mathematical modeling, but nada. I feel like if you are developing a course like this today techniques like SVD, PCA, DMD etc. would be included.

Companies doing clinical trials of new medical devices or drugs require at least statistics to generate the evidence required to satisfy regulators. Calculus may be necessary to identify flow rates, etc.

I always find the fascination of programming courses with mathematics to be interesting. In my mind, it is pretty clear that programming is a technique, that can be applied in any field. There is of course the field of programming programming languages, which does tend to require mathematical knowledge. Statistics is also an extremely broadly applicable mathematical tool, used today in almost any field.

But in general, knowledge of biology or sociology is about as likely to be useful in your programming career as knowledge of mathematics is - domain-specific knowledge of the domain you are programming for is the real key. If you're programming a biology or sociology tool, those will be more useful than maths. If you're programming a mathematical tool, of course maths is extremely important. If you're programming a library of base algorithms, algorithm knowledge is important.

It often seems to me that I haven't learned much lately, and then I see something which makes me think "I would not have even have understood what this is about two years ago." What people need to do well and grow in their vocation and avocations is to understand the field, and understanding is not just a matter of knowing a collection of immediately-relevant facts. Learning (more than just knowing) this math and other concepts is the sort of thing that leads to understanding; for one thing, it provides an explanation and justification for the pragmatic facts and links them as a cohesive whole.

In my company the development of anything mathematical is the domain of DS or DA; Engineering deals with operations / integration / scale but rarely looks inside.