How math intensive is computer science?

College Majors Engineering Majors
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<p>I've always been under the impression that computer science dealt with a lot of math. However, I was talking to my Calculus BC (AP equivalent of Calculus 2) teacher who told me that her husband had done the computer science track at the college that I want to go to (only a few years ago), and that he only took 4 math classes throughout his undergraduate career: Calculus 1 & 2, Linear Algebra, and a Statistics class. How right is she?</p>

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<p>It depends on your school’s CS curriculum. Some schools lessen the math requirements. Other schools require more. I know at my school CS majors take math through Calc 3, as well as other math course such as Discrete Math. Although I’m not a CS major, but I think if you look into computer security systems there is a lot of math involved.</p>

<p>I know one thing, the better you are at math the easier CS is. Lots of programming requires a solid mathematical foundation.</p>

<p>Also, the further you go in CS the harder the math gets…like anything else in a quantitative major.</p>

<p>Many people who can’t do the math for a CS degree often opt for a slightly less math intensive degree like MIS.</p>

3

<p>Calculus is worthless for the most part if you’re doing computer science (basic derivation/integration is good though).</p>

<p>Discrete math and graph theory are both good things to have. Linear algebra for some applications. You only need to know continuous math if you’re going into applied math.</p>

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<p>Trout, strange that you say Calculus is worthless in CS, when I have to take Numerical Calculus through my school’s CS department next semester.</p>

<p>I actually know very little about the applications of Calculus to CS, so the class will be somewhat interesting. You might be right, it could be worthless to CS.</p>

5

<p>Unless you are working on mathematically intensive projects, you won’t run in to much math in the real world. However, schools love to force it down your throats, some more than others.</p>

6

<p>Some schools are now dropping Differential Equations from the CS program. Even fewer have also dropped Calculus III from the program although I would think vectors and the coordinate system would be needed for areas like computer graphics.</p>

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Why is this?</p>

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<p>Computer security can also include mathematical areas like cryptology/error-correcting codes in which you would need a background in number theory and rings. The subject of rings can be included in an abstract algebra course.</p>

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<p>Calculus has very few applications to CS, but computers have applications in solving calculus problems, which is what you’ll study. You won’t be solving problems exactly, but looking at algorithms that converge to the right answer, and proving bounds on convergence. </p>

<p>I can’t think of any branches in CS research besides scientific computing that use calculus outside of basic diff/integ. Most of the theory out there works in combinatorics, probability, statistics, linear programming, abstract algebra.</p>

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<p>Calc 1-3 and prob & statitistics are the only math courses required at my school.</p>

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<p>Computer Graphics uses a fair amount of Calc/Linear Algebra.</p>

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<p>o_O really? I though most of CG related mathematics revolves around optimization problems and those can be expressed more succinctly via Linear Algebra</p>

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<p>The problem seems to stem from how you define a “math” class, or more generally, exactly where the dividing line between math and computer science is, especially at the theoretical level. Computer science as a distinct academic discipline was largely developed by mathematicians such as Alan Turing and Alonzo Church and computer science courses on computability theory, complexity theory, and algorithm analysis are arguably math courses. </p>

<p>Indeed, at MIT, those courses on those topics are math courses, being cross-listed by both departments and hence being populated by students from both departments. For example, the MIT EECS course 6.840J on the theory of computation *is exactly the same course * as the mathematics course 18.404J: same prof, same time/location, same lectures, same assignments, same exams, same everything. Moreover, the homework assignments and exams require relatively little programming as such, but rather require the solving of theorems via proofs, which what most upper-division mathematics courses require. </p>

<p>Indeed, attempting to actually program many of the concepts taught in computation theory would be useless, because most such programs would cause your system to run until the end of time without ever completing/halting, and that’s the whole point of the class - that many programs will never complete even if given infinite resources. In other words, no matter how much our computer hardware resources improve, there will always be a class of programs that will never run to completion. But you obviously can’t show that by just writing programs to see if they take infinite time to complete, as the program might not require infinite time, but just many centuries after which none of us will be around to watch it complete. The only way to show that a program will never complete is through a proof, which effectively means you have to become a mathematician.</p>

14

<p>Undergraduate computer science doesn’t really use much math, unless you’re talking about graphical models and all that. When people say that computer science is “mathy,” they’re more-so talking about the logical thinking the major requires. However, to develop that logical thinking, most colleges require a lot of math classes. My college, for example, requires up to multivariable calculus, differential equations, linear algebra, discrete math, and one probability class.</p>

<p>With that said, things like graph theory will come in to play. If someone is bad at math, I probably wouldn’t recommend computer science to them just because I doubt it would be their strength.</p>

15

<p>Piggybacking on what Sakky said, the following courses usually fall into the cross-listed category Math/Computer Science courses:</p>

<ul>
<li>Combinatorics (sometimes part of a Discrete Structures course)</li>
<li>Graph Theory (sometimes part of a Discrete Structures course)</li>
<li>Computational Complexity (as Sakky mentioned above)</li>
<li>Cryptology</li>
<li>Analysis of Algorithms</li>
<li>Computational Mathematics (Numerical Analysis, Numerical Solutions of ODE/PDE,Numerical Linear Algebra,etc)</li>
</ul>

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<p>@sakky
that’s what i was thinking</p>

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<p>I’m sure you can find computer science programs at different universities that require few math courses (4 cited by the OP’s neighbor) versus those that require essentially a math minor (14 or more).</p>

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<p>UCR requires a lot of math for CS.
-First year calculus ( calc 1 and 2 )
-Multivariable Calculus ( some of Calc 3 )
-Linear Algebra
-Differential Equations
-Lower div and upper div Discrete Math
-Upper div statistics
-Optimization</p>

<p><a href=“http://student.engr.ucr.edu/majors/CS%202010.pdf[/url]”>http://student.engr.ucr.edu/majors/CS%202010.pdf&lt;/a&gt;&lt;/p&gt;

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<p>As a double major in Math& CS in a class of predominantly CS majors,am pretty sure one can survive CS without math,but he will be doing rote learning.If a teacher does not cover a section ,your mind goes blank,but if you view it as a math problem you start wondering if there is any point going to class.Math makes CS look obvious</p>

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<p>CS program math requirements vary quite a bit. Some are in the engineering school and have engineering school-level math degree requirements. Some are specialized math majors and require mostly math courses (and less science).</p>

<p>And some are at less rigorous schools that only require a semester of ‘business calculus’. You can even find schools awarding ‘computer science’ degrees that don’t require any calculus. These degrees are worth a whole lot less than those at better schools.</p>

<p>The math reqs for the school you (OP) mentioned match those of an accredited CS program that spans the gap between engineering-based and math-based majors at good schools. I would assume that the degree you mention requires more science than a math major version.</p>

<p>Take a look at some accredited programs via this link -</p>

<p>[Accredited</a> Programs Search](<a href=“http://www.abet.org/AccredProgramSearch/AccreditationSearch.aspx]Accredited”>http://www.abet.org/AccredProgramSearch/AccreditationSearch.aspx)</p>

<p>and check this thread:</p>

<p><a href=“http://talk.collegeconfidential.com/engineering-majors/1040906-does-abet-accreditation-cs-matters-lot.html[/url]”>http://talk.collegeconfidential.com/engineering-majors/1040906-does-abet-accreditation-cs-matters-lot.html&lt;/a&gt;&lt;/p&gt;