>>11476620>The two fields completely split by the time of calculusNo, they don't. If your school is halfway decent, you'll have probability and of course applications of calculus everywhere in asymptotics for fairly mainstream problems.
>Many concepts of higher math in and beyond calculus are translated or ported to CS, but often with large alterations to accommodate the true lack of a practical infinity that higher math assumes is a valid concept.No. They're usually taken in full, but they're discretized sometimes because CS is about finding local steps to make a global solution. The finiteness of the structure isn't as important as it is the finiteness of the steps we take, This is more or less true in math as well - we can reason about infinite objects so long as we give a proof in finite time.
> Where higher math tends to excite the imagination with imaginary and fantastical representationsAgain, I keep telling you CS isn't different. Look at oracle machines, the various more esoteric complexity classes, analytic combinatorics, domain theory, etc. Algebraic topology is taken completely without 'porting' in CS applications. In topological data analysis, we even allow ourselves to consider an infinite R submodule for barcodes...and data analysis is supposed to be practical (and TAD is a practical data analysis tool)
>CS takes the practical approach and has to work within hard defined limits of mechanical engineering and the hardware components that define the limits of the calculations a computer will do.No, it is the study of algorithms and complexity how we can computationally reason in finite time, but this doesn't force our structures nor our research to be about finite objects. To give another example, engineering generally relies heavily on '''infinite mathematics''' but even though we end up making systems with finite sets of behaviors, etc etc, we have found reasonable ways to make sense of what seems like an unreasonable concept.
