Is programming a subset of math? [closed]

It's math in the sense that it requires abstract thought about algorithms etc.
It's engineering when it involves planning schedules, deliverables, testing.
It's art when you have no idea how it's going to eventually turn out.

Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.

--E. W. Dijkstra

Overall, remember that mathematics is a formal codification of logic, which is also what we do in software.

The list of topics in your question is loaded with mathematical problems. We are able to do programming on a fairly high level of abstraction, so the raw mathematics may not be staring you in the face. For example, you mentioned DFAs.. you can use a regular expression in your programs without knowing any math, but you'll find more of a need for mathematics when you want to design a good regular expression engine.

I think you've hit on an interesting point. Programming is an art and a science. There are a lot of "tools of the trade", and you don't necessarily sit down and do a lot of high-level mathematics in order to simply write a program. In fact, when you're programming, you many not really being doing much mathematics or computer science.

It's when we start to solve difficult problems in computer science that mathematics shows up. The deeper you go, the more it will flesh itself out.. often in lower levels of abstraction.

There are also some realms of programming that you don't necessarily have to work in, but they involve more math. For example, while you can certainly learn a language and write some apps without any formal mathematics, you won't get very far in algorithm analysis without some applied math.

Doesn't mention programming, but idea is still relevant.

OK, I was a math and CS major in college. I would say that if the set A is Math and the set B is CS, then A intersects B. It's not a subset.

It's no doubt that many of the fathers and mothers of computer science were Mathematicians like Turing and Dykstra. Most of the founders of the internet were either Phd's in Math, Physics, or Engineering. Most of the core concepts of computer science come from math, but the act of programming isn't really math. Math helps us in our daily lives, but the two aren't the same.

But there is no doubt that the original reasoning behind the computer was to well, compute things. We have come a long way from there in such a short time.