Counting. The math I used most often is making sure I don't make a fence post error when creating loops. As my statistical mechanics professor said, counting is the hardest thing to do in math. I suspect you wanted to know which branch of mathematics is most applicible. I'd have to go with discrete math, which includes graph theory, discrete optimization, information theory, game theory, complexity theory, etc. The algorithms course every CS major takes is based on discrete math. It is used when we selected algorithms (e.g. O(n^2) vs O(nlgn)). It is used when we map data sets to structures. It is used when we determine which approach is easiest. It is used when pooling resources. Of course, in most of these cases, we've comfortable enough with the concepts to be able to do it intuitively. Nevertheless, our intuition is based on underlying mathematical proofs. --Mark
It depends on the app. I've been required to do apps that had to solve pairs of partial differential equations, but most numerical apps are just 4-banger arithmetic. Though periodically I play with celestial mechanics problems which involve calculus and trig. On a daily basis, however, it'd be #1, Algebra and #2, Propositional Calculus. I'm talking about code generation here - the reduction, optimization and proofing. The actual end product is, as I've mentioned, usually just basic arithmetic. A well-rounded set of general programming skills should include set theory (useful in maintaining collections and in formulating SQL) and graph theory (trees, linked lists, etc.). Since a lot of these come in canned solutions now, it's perhaps not quite as essential as formerly, but it gives an edge. A first-term calculus course spends a lot of time on functions, which, of course, are one of the key concepts of modern-day programming. On the other hand, I've only flunked one college course in my life: Calc II. It had been over 10 years since high school, and by that time, I'd forgotten about the very existence of trigonometic identities. By the time I'd relearned them, it was too late. I had to take the course over.
"privilege" comes from the Latin words for "private" and "law" (legal) and dates to feudal times. To "claim privilege" meant that you were above the laws that applied to the common people.
I suspect you wanted to know which branch of mathematics is most applicible. I'd have to go with discrete math, which includes graph theory, discrete optimization, information theory, game theory, complexity theory, etc. The algorithms course every CS major takes is based on discrete math. --Mark[/QB]
Bingo! This is what CS is all about. I miss inductive proofs. But, when coding a recursive method, I can "feel" the proof. It is putting the "engineering" in software enginnering. Essentially applying theoretic math to solve real world problems.