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Science & Engineering - When working with nearly any other scientific discipline requires calculus: Aerospace, Astrology, Biology, Chemistry, or Engineering. When two problems are not equally hard, complex, or time consuming, the harder one cannot be solved using just the easier one's solutions (without those solutions being processed by an algorithm that closes the difference in complexity in the total algorithm). Reference request: Examples of research on a set with interesting properties which turned out to be the empty set. "Mathematical" computer science is discrete mathematics, automata theory, computability, computational complexity, algorithms, data structures and so on. Thus while each educational program will have its own unique requirements, students can typically expect to take a plethora of math courses throughout their undergraduate career. They too may question how thinly your time and resources were distributed, and question whether you learned one or both the subjects well. Mathematics is a very abstract field in many ways, and jumping into a math major is like embarking on a journey through very challenging terrain in an abstract universe. see eg a recent paper A fully automatic problem solver with human-style output of Fields medalist Gowers who collaborated with a computer scientist. To understand why your sensible linear system is behaving in nonlinear ways, you either need the tools of calculus or you need to re-invent them for your problem space.
I don't see any differential calculus there; I see the word "derivative", but I don't see anything resembling traditional differential calculus. Has there been a naval battle where a boarding attempt backfired? Mathematicians have a different conception of what "math" is (it certainly isn't "long word problems"). TCS distinctions are erased since e.g. Why do these angles look weird in my logo? Automation - Similar to robotics, automation can require quantifying a lot of human behavior. Finally -- you will need Calculus in order to, well, interact with people from other Exact Sciences and Engineering. A simple case is if you determine an algorithm's time complexity to be too great to actually implement, that is still a contribution to computer science. What is the definition of Computer Science, and what is the Science within Computer Science? The time complexity of an algorithm is an invariant measure of it that gives you a feel for how hard a problem is. I also have worked for a small time in business based software engineering. Should I try computer science? Depending on where we put the hole. Examples of “Unrelated” Mathematics Playing a Fundamental Role in TCS? Every job posting that I've been looking at always entails "Computer Science degree, or related degree such as engineering, mathematics, biology, etc." Or the theory behind building a computer which is part of eletrical engineering. I think of Computer Science as Mathematics with a whole bunch of Application and O/S development mixed in. Engineering is "find a good enough way of doing foo in practice" (for some fuzzy definition of "good enough"). An excellent introduction to his view of programming and computer science is: This was the foundational book for me - really the only CS book for first year university. Incidentally, it wasn't until the last year or two of learning about measure theory and some of its applications that I realized what made proofs about bounds, densities, or distributions mathematics and not just statistics. Depending on your university, the requirements for computer science may also be different. Boolean algebra- a subject in discrete math is applied in creating control functions when programming. At other schools where the programs are less intense, you may not encounter this attitude. It seems I interpreted your comment as meaning the complete opposite of what you had in mind. Teacher asking my 5 year old daughter to take a boy student to toilet, All applications cannot open unless Internet is off, Spooky computer game from late 90s/2000 where you fight skeleton pirates at the end, Best approach to safely bump up version of classes, Melville's chain of thought in the "great democratic God" passage in "Moby-Dick". "From this point of view, mathematics is degenerate special case of theoretical computer science" -- or another way, theoretical computer science is mathematics. Maybe Probability and/or Statistics as well depending on your program and what electives you take. Just stay on target and keep your options open for now. It only takes a minute to sign up. What does "worm of yellow convicts" mean? You will be dividing your time between two majors which are very tough on their own. I don't know if this is the exact reasoning, but if you think about it if propositions can be converted to existential, simultaneously holding properties, then in aggregate they describe a kind of object whose definition is the thing which simultaneously holds those properties, so that to prove those propositions true is to prove the type is occupied by some actual thing. As a math major / CS minor, I was taught CS by people in "Dijkstra's school", which I would consider more rigorously grounded in mathematics than Knuth's.
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