Well, I will. But the basic point is what you need is to learn how to learn if you are going to be a highly successful computer professional. Courses in logic, reason, analysis, education and so forth are far more useful than learning calculus. I can code up Simpson’s rule or the trap rule pretty quickly, so the two semesters I spent being taught other methods to do what those algorithms do was just a very expensive waste of time.
You can’t work on brand new technology and ideas if you are relying on being trained to do it first. You have to be able to teach yourself anything you need.
But this is what Calculus is. It takes you systematically from some basic first principles, clarifying simple intuitive ideas like what a limit is, via deductive reasoning and analysis, through and past some theory (such as theorems that tell you where to look for optima for functions) into the applications. It encapsulates this entire approach to reasoning, from concept formulation to deep applications, in one course, at a level that anyone with facility in algebra can comprehend and master. It is pretty much the only subject in mathematics whose span is so great with so little investment in time and effort.
I’m a mathematical logician by primary training and research interest, but I would never advocate replacing Calculus by a course in logic.
You must have had far better teachers than I! I’ve seen more than one brilliant computer geek leave college without a degree because of math requirements. Math is a field where the reaper harvests; over 70% of my first college math course failed outright, and nobody at all got an A.
I’m primarily a computer scientist and I surely would! Perhaps that says more about our personalities than our professions, though. I detest mathematics as drudgery, but I can program huge code blocks cheerfully, which doesn’t really make sense objectively.
I’m pretty much self-taught on Calculus, but I teach it regularly and try hard to communicate the above. Students are often too early in their intellectual career to appreciate the message, however. Also, since we serve a wide variety of students with the same Calc class, there is much more material in the syllabus than a major in any one field would need, which can obfuscate the main theme of the class.
mathematics as drudgery
Any mathematician will tell you that the main point of mathematics is the ability to do difficult things with as little effort as possible, ie the opposite of drudgery.
MIT has open courseware, which basically means they make materials from some of their courses available online.* Not the same as coursework itself, but still pretty useful. Also try MOOCs such as Coursera, but YMMV.
something something Aaron Swartz
How about Runge-Kutta?[quote=“enso, post:126, topic:93137”]
The last math instructor I had in undergrad literally droned in a monotone. It was hypnotic.
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So he was boring. That doesn’t mean math is drudgery, it means that guy was boring. At worst, it means you find math boring, but that still doesn’t make it drudgery.
You know the cyclic speed up - slow down effect you get when you redrill the hole on a vinyl record off-centre? I had a mathematics lecturer who spoke like that. It was massively disorienting, as the pacing of his speech had no connection to the beginning or end of sentences or concepts.
I had another one who would deactivate his hearing aid at the start of each lecture so he wouldn’t have to answer questions.
I wasn’t saying math is boring. I may be pointing out that the quality of math instruction, even at universities, often leaves a lot to be desired and may contribute to the view of math as “drudgery” above.
Where I went to uni: I - differentiation, II - integration, III - vector algebra, IV - difficult equations. Who needs it? Why, every possible flavor of enginerd! That’s who!
I would say that you could make a case that the quality of instruction in higher education is… lacking. In general (and not specific to any particular subject area).
The compulsory mathematics for first-year B.Sci. at my uni was two semesters of calculus, one of statistics and one of linear algebra.
The linear algebra lecturer was good; the others were universally appalling. As well as the issues mentioned above, there was extra fun such as:
The “tutorials” consisted of fifty students spread across two non-adjacent rooms while one tutor uselessly runs between them.
Constant typos in the lecture notes and practice assignments, so that you never knew if your “incorrect” answer was actually wrong.
Lecture notes put online in a format derived from a geometrical modelling program, so that every image was newly constructed from basic mathematical principles on the fly every time it was viewed. What this meant was that, if you tried to print it without first converting it to a normal jpeg or whatever, it would lock up the printer for an hour while the tiny onboard CPU tried to do hardcore geometry. This made you very popular at the communal library printers.
In those calculus classes, I can’t have made more than 30%. But I still passed, as the entire class performed so poorly that there was a huge boost from grade normalisation. Throughout the rest of my academic career (psych and philosophy B.Sci, neuroscience PhD) I maintained an average around 90%.
What little calculus I learnt fell out of my head seconds after the last class. Fortunately, I never had any need for it again; the mathematics in neuroscience is pretty much all statistics and practical algebra. On the rare occassions when heavier math is required, it’s usually computed automatically by a HPLC machine or somesuch.
The problem with “mathematics for everybody!” is that doing so makes it into a prerequisite for a scientific career. If you’re going to do that, then you’d damn well better make sure that it’s taught competently, or you risk excluding a vast swathe of the population.
Mathematics is a language. Some people are naturally quick at picking up languages; others can do so only with great effort. But just because someone isn’t a born linguist doesn’t mean that they can’t be a worthwhile scientist.
Shitty mathematics lecturers came very close to stopping my scientific career dead before I’d had a chance to publish a single paper.
My only thought here is that the format must have been postscript (or PCL?). I can’t think of anything else that a printer would even bother trying to execute. Of course, even if the application were to output postscript, there’s no reason it couldn’t do so in a way that wouldn’t require re-running the calculations in order to print it.
Given the lecturer, it may have been some weird homebrew thing. Going into the printer settings and ordering it to “print as image” got around the problem.
The lecture note thing wasn’t a serious impediment once you figured out how to bypass it, but I bring it up as an example of just how much they didn’t give a shit about the experience of their students.
The overall vibe was that teaching basic calculus was a trivial chore that was beneath their talents, and they were determined to do it with as little effort as possible. Those typo-filled practice assignments were displayed on ye olde overhead projector plastic sheets, and they’d been in use since at least the 1980s.
Notably, the one good lecturer (linear algebra) was the only “new” academic; he was in his late twenties. The others had been in place for decades.
