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if i'm right about this, then why didn't the academics just say so without all that ridiculous math?
Because that's what academics do, given that it's all they know. I've solved a few really complex problems that the academicians were totally unable to. In one case, I took a multi-spectral image analysis that took minutes to run on a single video frame, realized all they were doing was an absurdly complicated lookup algorithm, and turned it into a real time mapping, all within the vertical refresh period of the video stream.
I never took CS, because i never went to college, but i do remember reading that academics typically treat math as purely "functional" and stateless, and leave things like lookup tables to practice rather than theory.
I hate to defend them, but this might be such a case. I initially ran into a similar issue implementing finite state machines from something theoretical.
But yeah I don't necessarily trust them either. Real world experience will kill pure theory, but having both is really the key to writing great code, I think, at least when it's complicated. Being able to subject your code to a rigorous mathematical treatment seems to have its advantages in terms of behavior diagramming and testing.
When I was growin' up, I was the smartest kid I knew. Maybe that was just because I didn't know that many kids. All I know is now I feel the opposite.
A mathematician dealing with an algorithmic problem will be as suited as a software developer dealing with a mathematical problem. Horses for courses. It's like the old story where the old guy meets a neurosurgeon and asks him to take a look at his sore back.
When I was taking CS, the mandated math courses were second year calculus and linear algebra. I haven't used either since. A complete waste of time in my opinion, unless you're a numerical analysis weenie or something.
What I found truly useful, and have used many times since, were combinatorics and graph theory. And abstract algebra to some degree.