The amount of mathematics in CS...

[Saiak]

hi everyone!!! Im a high school student, still looking for the right path...

My question is: Is there a lot of advanced math in CS???And, is it possible to enroll into Masters in math after graduation???


Any kind of feedback would be great, as long as it's appropriate.

[jbking]

First, what you are calling "advanced Mathematics"? There can be some Mathematics in Computer Science depending on what area you are examining:

1) Computational Complexity - Big O notation isn't what I'd call advanced but may be that way to some people, which is used to estimate how long, either in terms of time or space, an algorithm needs to execute. A classic example of this is the O(n lg n) that optimal sorting algorithms, MergeSort and HeapSort, have. Parallelized algorithms may be something new here where you may have to consider if you have m processors sorting a list of length n, what is the worst case complexity for some of the better sorting algorithms with this twist. I remember taking a course in Computational Complexity theory that was a lot of fun, especially with the 10 question 2 week take home final where we could get hints for some problems that were in random order of difficulty.

2) Boolean Algebra - Working with gates, e.g. AND, OR, NOT, XOR, NAND, or NOR to name a few, and being able to simplify various expressions may be viewed as advanced Mathematics by some as well as evaluating short-circuit logic in conditions that uses some elements from Boolean Algebra, e.g. true OR anything will be true as well as false AND anything will be false to give a couple examples.

3) Graph Theory problems known for being "NP-complete" - If you get into some complexity areas this can come up like the travelling salesmen problem and trying to find a polynomial solution algorithm if one exists.

4) Numerical analysis - Considering things like least squares as well as the accuracy of floating point number systems. Polynomial interpolation could be another example here. Matlab would be an example of the software used for such problems and is quite Math intensive to my mind. CS 370 was rather hard as I recall though another part may have been learning least squares in a stats course the same semester....

5) Symbolic Computation - Solving differential equations precisely or factoring polynomials or obtaining a gcd may be examples here. Maple is an example of the software used here that is quite different from Matlab though it is also rather Math intensive, particularly for abbreviating things like integrals, sums and products. CS 487 that caused me to remember some things from Math 145, ah the memories....

6) Cryptography - The proof of how algorithms like RSA work involves some classical Algebra involving the Chinese Remainder Theorem.

Or do you mean the more exotic stuff like the "P = NP" type question that is from CS and involves advanced Mathematics concepts.

By Master's in Math do you mean a literal "Masters in Mathmatics" degree or a "Masters in Science with a major in Mathematics"? Theoretically, either may be possible if you have enough of a Math background as I'd imagine if someone had a biochemistry degree they could do a Master's in either biology or chemistry.

At Waterloo, Computer Science is part of the Faculty of Mathematics, so their Computer Science programs are going to involve a lot more Math than any other university where CS is part of the Science Faculty which also has Math, Chemistry, Biology and Physics for main branches.

[Brightguy]

CS could plausibly be considered as just a branch of math. On that point, I think this site's name is misleading - programming.ca would be more accurate.

[BigBear]

The highschool math courses required for Waterloo are Advanced Functions and Calculus, aswell as English and computer science, then 2 more U or M courses to make up you average.

Data is not needed but I have been told it is helpful

[saltpro15]

is there more math in a CS university program or a Software Engineering one? I would assume SE since it's really more of an engineering course...

[Prabhakar Ragde]

jbking @ Sun Mar 22, 2009 6:35 pm wrote:

I remember taking a course in Computational Complexity theory that was a lot of fun, especially with the 10 question 2 week take home final where we could get hints for some problems that were in random order of difficulty.

Hey, that was me, right? One killer exam, if I remember correctly.

[jbking]

Prabhakar Ragde @ Sun Mar 22, 2009 5:51 pm wrote:

jbking @ Sun Mar 22, 2009 6:35 pm wrote:

I remember taking a course in Computational Complexity theory that was a lot of fun, especially with the 10 question 2 week take home final where we could get hints for some problems that were in random order of difficulty.

Hey, that was me, right? One killer exam, if I remember correctly.

Right, that was you.

[Prabhakar Ragde]

saltpro15 @ Sun Mar 22, 2009 7:51 pm wrote:

is there more math in a CS university program or a Software Engineering one? I would assume SE since it's really more of an engineering course...

At UW, there is less math in the SE program, because they had to take some out and condense some (e.g. calculus) to fit in stuff for Engineering accreditation. Also the math courses that CS students take are more concept-oriented (i.e. proof) and less technique-oriented (i.e. here's how to do it, don't worry about why it works). At another university, there would be less math in a CS program than at UW, but probably no less than in whatever their SE program may look like.

[[Gandalf]]

jbking @ 2009-03-22, 6:35 pm wrote:

By Master's in Math do you mean a literal "Masters in Mathmatics" degree or a "Masters in Science with a major in Mathematics"?

Isn't this exclusively based on the structure of the university you attend? Does the name itself imply any real differences?

jbking @ 2009-03-22, 6:35 pm wrote:

At Waterloo, Computer Science is part of the Faculty of Mathematics, so their Computer Science programs are going to involve a lot more Math than any other university where CS is part of the Science Faculty which also has Math, Chemistry, Biology and Physics for main branches.

I've looked into this... From what I can tell this is only true for Waterloo's BMath in CS.

[jbking]

[quote="[Gandalf] @ Sun Mar 22, 2009 11:17 pm"]

jbking @ 2009-03-22, 6:35 pm wrote:

By Master's in Math do you mean a literal "Masters in Mathmatics" degree or a "Masters in Science with a major in Mathematics"?

Isn't this exclusively based on the structure of the university you attend? Does the name itself imply any real differences?[/quote]

Yes, it is based on the structure of the university but there is a slight parsing difference to my mind that can be interesting to some that question the existence of a Math degree like there are Arts and Science degrees. In terms of any real difference like in terms of course material, I don't think there would be much but did want clarification of which parsing did the poster mean.

[A.J]

One would require math for computer science. How much math required depends on how much you want to specialize in your field.

[jernst]

A.J @ Mon Mar 23, 2009 9:14 am wrote:

One would require math for computer science. How much math required depends on how much you want to specialize in your field.

I disagree here. Math has nothing to do with how specialized you are in your field, but rather what field you choose to specialize in. For example consider a person who takes a computer science degree only to become a web developer. There may be the occasional time when you would find it helpful to know what kind of sorting algorithm is faster than another, but beyond that not much. There is very little math required in this field compared with someone specializing in AI for example.

[A.J]

jernst wrote:

A.J @ Mon Mar 23, 2009 9:14 am wrote:

One would require math for computer science. How much math required depends on how much you want to specialize in your field.

Math has nothing to do with how specialized you are in your field, but rather what field you choose to specialize in.

Oops, that's actually what I meant....sorry, I have NO idea how that came out wrong

[bugzpodder]

As someone who is finishing his CS degree in UW, I would say that most of the courses require very little math skills. Anything you need will be given to you in class and is very accessible. It's actually the mandatory 2nd yr math courses that are hard

[btiffin]

from the old guy
Lucky gits.

When I attended UofW all we had access to was BMath. There were no degrees in compsci.

And the Pascal classes in the early 80's, what did we do? Programs for calculating integrals.

Math creeps into a lot more CS than many programmers even realize. Unrealized as most of them "get it" without thinking. Functions and Relations, Matrices, Algebra, good old arithmetic ... and on and on. The more you know, the less you'll need to know you know.

Cheers