The trouble with being self-taught is few manage to teach themselves calculus let alone advanced calculus, and one can have yawning gaps in knowledge and be completely unaware of their existence.
The trouble with being self-taught is few manage to teach themselves calculus let alone advanced calculus, and one can have yawning gaps in knowledge and be completely unaware of their existence.
I can't even fathom why knowing anything at all about calculus is going to be useful when automating things, writing APIs, or doing anything that nearly every business wants their "tech" people to do.
Some things you can't do without math: curve fitting, statistics, implementing Shazam, 3D graphics, write a game engine, do data flow analysis, implement a neural net, non-trivial use of floating point, write a lunar lander game, etc.
I remember two pages of math in a college economic textbook. Reading it, I realized they were doing differentiation by going around the horn. Instead of requiring calculus for the class, they taught it.
Except they never mentioned the words "calculus", "differentiation", or "integration". I suppose they figured those words would dissuade people from the class :-/
The amusing thing is the poor schlubs taking the class would never realize that they'd learned calculus!
FWIW Teaching things yourself is much easier now, i.e. you can get pretty much any textbook for free (nudge nudge wink wink). It's a truly great time to be fascinated by things
But if I'd never gone to college, I would not know that FA existed, or if I did, I wouldn't know what it was good for. I'd probably invent some sort of ad-hoc ineffective algorithm for it. I've certainly seen a lot of ad-hoc kludge algorithms from smart people who simply didn't know there were excellent mathematical methods to solve it.
For example, I know one who was trying to reduce the noise in an electronic circuit. He randomly tried adding resistors and capacitors of various values. Until eventually a coworker looked at it, calculated the right values in a few minutes, and eliminated the noise.
I've seen this sort of thing again and again, in diverse fields.
But if I did need them, I know enough to know just were to look to refresh my memory :-)
Math is the fundamental building block for doing so many interesting things with programs, so to me every interesting programming job requires boatloads of maths. Sure you can do forms and crud and authorization checks and messaging apps and large distributed systems etc without maths, but that doesn't sound terribly exciting to me.
Like I enjoy the fact I know calc but I’m not about to oversell it’s usefulness for most programming. Math is not the fundamental building block of software imho, logic is.