Everything after the times tables and fractions . There was no value to me in any high school or college math course I was made to take.
I’m not sure that modern geometry courses really bear much resemblance to Euclid. There’s a lot less emphasis on construction, and even when they’re proving the same things that Euclid did, the structure of the proofs is usually different than how Euclid did them (for instance, the most common modern proof of the Pythagorean Theorem is based on proportions, which Euclid didn’t even start on until a couple of books after he proved the Pythagorean theorem).
Calculus might look useless for a mostly-discrete field like computer science, but a computer scientist ought to know about things like complexity classes of algorithms, and that requires knowing things like logs and exponentials, and those aren’t seen in any significant detail until calculus. And a heck of a lot of modern computing is linear algebra, so even though you might not use it, a great many of your classmates will.
In CS especially they also spend some time on discrete calculus, sums and differences, generating functions, solving recurrences and other functional equations. Old-school hackers also tend to be familiar with things like Gosper’s algorithm and hypergeometric identities.
The Stewart calculus text is traditional calculus for first year college students, not even remotely modern. But the full version (used by math students, engineers, physicists and the like; there are smaller versions for other specialties) includes a lot of historical problems, short biographies on prominent mathematicians, their proofs and sometimes their notation, sample questions in the text discussing their original problems, and the like. It’s not hundreds of pages, but it is far and away above what most math texts do. It is the reason the book is beloved of academics, and why the author made tens of millions from textbooks, as it is simply much more comprehensive.
I did have two university professors who delighted in teaching things like Buffon’s problem. Most of the math relevant in undergraduate engineering was worked out by, or before, the deluge of (largely) brilliant French or European scientists before the late 1800s. I have a book “Modern Mathematics for the Engineer” published in the 1970s, and we only covered a few of the ideas - mainly in graduate courses part of our honours program.
No argument there. I am not trying to make a case that it shouldn’t be required, just that I never used it. I did not develop applications that were math intensive. Once I had to know how to do linear regression. Once I had to know analytic geometry.