Computer Science Canada The amount of mathematics in CS... |
| Author: | Saiak [ Sun Mar 22, 2009 6:02 pm ] |
| Post subject: | The amount of mathematics in CS... |
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. |
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| Author: | jbking [ Sun Mar 22, 2009 6:35 pm ] |
| Post subject: | Re: The amount of mathematics in CS... |
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. |
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| Author: | Brightguy [ Sun Mar 22, 2009 6:44 pm ] |
| Post subject: | Re: The amount of mathematics in CS... |
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. |
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| Author: | BigBear [ Sun Mar 22, 2009 7:29 pm ] |
| Post subject: | RE:The amount of mathematics in CS... |
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 |
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| Author: | saltpro15 [ Sun Mar 22, 2009 7:51 pm ] |
| Post subject: | RE:The amount of mathematics in CS... |
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... |
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| Author: | Prabhakar Ragde [ Sun Mar 22, 2009 7:51 pm ] |
| Post subject: | Re: The amount of mathematics in CS... |
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. |
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| Author: | jbking [ Sun Mar 22, 2009 8:28 pm ] |
| Post subject: | Re: The amount of mathematics in CS... |
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. |
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| Author: | Prabhakar Ragde [ Sun Mar 22, 2009 8:55 pm ] |
| Post subject: | Re: RE:The amount of mathematics in CS... |
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. |
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| Author: | [Gandalf] [ Mon Mar 23, 2009 1:17 am ] |
| Post subject: | Re: The amount of mathematics in CS... |
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. |
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| Author: | jbking [ Mon Mar 23, 2009 8:50 am ] |
| Post subject: | Re: The amount of mathematics in CS... |
[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. |
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| Author: | A.J [ Mon Mar 23, 2009 9:14 am ] |
| Post subject: | RE:The amount of mathematics in CS... |
One would require math for computer science. How much math required depends on how much you want to specialize in your field. |
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| Author: | jernst [ Mon Mar 23, 2009 9:21 am ] |
| Post subject: | Re: RE:The amount of mathematics in CS... |
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. |
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| Author: | A.J [ Mon Mar 23, 2009 9:29 am ] |
| Post subject: | Re: The amount of mathematics in CS... |
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  |
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| Author: | bugzpodder [ Mon Mar 23, 2009 10:02 am ] |
| Post subject: | RE:The amount of mathematics in CS... |
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 |
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| Author: | btiffin [ Mon Mar 23, 2009 11:07 am ] |
| Post subject: | RE:The amount of mathematics in CS... |
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 |
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| Author: | Prabhakar Ragde [ Mon Mar 23, 2009 11:45 am ] |
| Post subject: | Re: The amount of mathematics in CS... |
[quote="[Gandalf] @ Mon Mar 23, 2009 1:17 am"] I've looked into this... From what I can tell this is only true for Waterloo's BMath in CS.[/quote] No, it is true for the BCS as well. The BMath/CS has even more math. --PR |
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| Author: | [Gandalf] [ Mon Mar 23, 2009 3:17 pm ] |
| Post subject: | RE:The amount of mathematics in CS... |
Can you point me to some resource that can reasonably lead me to believe that CS in general at Waterloo involves more math than "any other university where CS is part of the Science Faculty"? Anything anecdotal even? Sorry ahead of time for sort of sidetracking this topic a bit.  |
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| Author: | Leela [ Mon Mar 23, 2009 3:23 pm ] |
| Post subject: | Re: The amount of mathematics in CS... |
Don't really want to open a new topic, as my questions are very similar to the ones posted here. I presently finish up my correspondence high-school Calculus and Vectors course and really enjoy every bit of it... that is not related to the application of vectors. I mean I'm ok with vectors in general, but for some reason, all problems related to the application of vectors to real life situations freak me out (force and work problems, for instance). Maybe because it's more physics, than math, and I hate physics... Don't know. Hence, the question - how often do you encounter the vector theme, doing a degree in CS? Another question - how horrible is MAT137 at UofT. I'm taking it this summer. |
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| Author: | Dark [ Mon Mar 23, 2009 3:37 pm ] |
| Post subject: | Re: RE:The amount of mathematics in CS... |
BigBear @ Sun Mar 22, 2009 7:29 pm wrote: 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 I'm sure Physics would also be helpful |
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| Author: | saltpro15 [ Mon Mar 23, 2009 4:21 pm ] |
| Post subject: | Re: RE:The amount of mathematics in CS... |
Prabhakar Ragde @ Sun Mar 22, 2009 wrote: 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). . phew, that just took a big worry off my mind, thanks a lot!  not that I don't like math or do poorly in it, I just don't want to spend all that money to find out I'm doing more math than programming, I prefer concept-oriented math anyway, but I"m losing my train of thought and just gabbling so I will shut up now, thanks again Prabhakar  |
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| Author: | jbking [ Mon Mar 23, 2009 5:53 pm ] |
| Post subject: | Re: RE:The amount of mathematics in CS... |
[quote="[Gandalf] @ Mon Mar 23, 2009 1:17 pm"]Can you point me to some resource that can reasonably lead me to believe that CS in general at Waterloo involves more math than "any other university where CS is part of the Science Faculty"? Anything anecdotal even? Sorry ahead of time for sort of sidetracking this topic a bit. [/quote]
Ok, I'll give a couple of examples here using Waterloo and Guelph though I imagine if one was curious they could go look up any other university to find this stuff out. Anyway, on to the summary here: Waterloo: 7 Math courses consisting of 2 Calculus, 2 Algebra, 2 Statistics, and one Combinatorics Pulled from http://ugradcalendar.uwaterloo.ca/?pageID=655 Guelph: For the honors program there is one Math and one Statistics Pulled from http://www.uoguelph.ca/registrar/calendars/undergraduate/current/c10/c10bcomp-info.shtml Granted Guelph could be an anomaly here, but it is something... Toronto looked to be close to Waterloo in having about 7 Math courses for some options within the CS major I think. |
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| Author: | jernst [ Mon Mar 23, 2009 9:07 pm ] |
| Post subject: | Re: The amount of mathematics in CS... |
WLU, from when i went there, 2 years ago was something like this: 2 calculus, 2 algebra, one statistics |
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| Author: | Tony [ Mon Mar 23, 2009 9:34 pm ] |
| Post subject: | RE:The amount of mathematics in CS... |
Looking at just the designated MATH courses, you'd miss a lot of Math present in the program; at least that's the case for Waterloo (I can't be certain about other schools). Just about all courses under the title of CS have some amount of Math -- from simple Induction to having a full out Logic course (a branch of Math in its own right) as a required CS245. |
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| Author: | [Gandalf] [ Mon Mar 23, 2009 11:52 pm ] |
| Post subject: | Re: RE:The amount of mathematics in CS... |
jbking @ 2009-03-23, 5:53 pm wrote: Granted Guelph could be an anomaly here, but it is something... Toronto looked to be close to Waterloo in having about 7 Math courses for some options within the CS major I think.
Yes, let's look for a counterexample shall we... U of T: From http://www.artsandscience.utoronto.ca/ofr/calendar/prg_csc.htm, you require 4.0 credits of math and statistics courses for the "Foundations Area" specialist. Waterloo: From http://www.cs.uwaterloo.ca/current/programs/require/2008-2009/bcs.pdf, you require 3.5 credits of math and statistics courses to graduate with a BCS in CS. Waterloo: From http://www.cs.uwaterloo.ca/current/programs/require/2008-2009/bmath.pdf, you require 6.0 credits of the math to graduate, unless I'm reading it wrong. U of T: From http://www.artsandscience.utoronto.ca/ofr/calendar/prg_csc.htm, 7.0 math credits are necessary for the "Computer Science & Mathematics" program, which is closer to what a BMath is than the others anyway. I think it would be fair to say that the content in the courses offered at both universities was comparable. Please be careful when you use words like "any" and "all". |
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| Author: | Dan [ Tue Mar 24, 2009 12:01 am ] |
| Post subject: | RE:The amount of mathematics in CS... |
Lakehead requires 5 FCE credits in math to graduate with a HBSc in computer sci...... |
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| Author: | jbking [ Tue Mar 24, 2009 8:42 am ] |
| Post subject: | Re: The amount of mathematics in CS... |
*sigh* I don't remember there being a BCS at Waterloo when I was there. Another point is the question regular compared to Honor's, just to get a little nit-picky on some minor points here. Thanks for the examples Gandalf, as I think my initial reply was based off of conversations had 15 years ago now so that information may be a little out of date now as I remember somebody wanting to go to Simon Fraser because it required less Math. |
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| Author: | Vermette [ Tue Mar 24, 2009 9:29 am ] |
| Post subject: | RE:The amount of mathematics in CS... |
Windsor requires 6 courses from the Math Department in the Honours CS stream: 1 Algebra, 2 Calculus, a 100 level Foundations course (Induction, Set Theory, Propositional logic etc), Stats, and Analysis. I'm excluding any material covered in CS department courses. |
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| Author: | Prabhakar Ragde [ Tue Mar 24, 2009 9:36 am ] |
| Post subject: | RE:The amount of mathematics in CS... |
Not everyone takes a Specialist stream at U of T -- that's their premium brand. As far as I can tell, the straight Major requires one calculus, one algebra, and one probability/stats. They have a CS course that is covering similar ground to our Math 135, also, and no real equivalent to our CS 245. I also looked at McMaster (I didn't do much of this looking around, because none of these places make searching for this information very easy) and counted three or four math courses. UBC B.A., 4 courses. UBC B.Sc has more, but they're weirdly distributed -- 3 calculus (these are largely irrelevant to CS), one algebra, one probability, and two free-choice. Waterloo: two calculus (many CS students take Calc 3 also), two algebra, one probability, one statistics, one discrete math (which is head and shoulders above discrete math courses elsewhere), plus the option to take advanced versions of all of these. And an explicitly mathematical approach to first-year CS, as well. |
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| Author: | Dark [ Tue Mar 24, 2009 3:43 pm ] |
| Post subject: | RE:The amount of mathematics in CS... |
I know at Ryerson, (where I will probably be going in the fall of 2009), you need 6 maths. MTH 110 - Discrete Mathematics I MTH 210 - Discrete Mathematics II MTH 207 - Calculus & Computational Methods I MTH 310 - Calculus & Computational Methods II MTH 108 - Linear Algebra MTH 304 - Probability and Statistics I |
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| Author: | [Gandalf] [ Sun Mar 29, 2009 5:15 am ] |
| Post subject: | Re: RE:The amount of mathematics in CS... |
Prabhakar Ragde @ 2009-03-24, 9:36 am wrote: I also looked at McMaster (I didn't do much of this looking around, because none of these places make searching for this information very easy) and counted three or four math courses.
I think all this comes down is what you're accustomed to, and a good Google search will usually do the trick. Prabhakar Ragde @ 2009-03-24, 9:36 am wrote: Not everyone takes a Specialist stream at U of T -- that's their premium brand. As far as I can tell, the straight Major requires one calculus, one algebra, and one probability/stats. They have a CS course that is covering similar ground to our Math 135, also, and no real equivalent to our CS 245.
Not everyone takes the BMath at Waterloo either, that's their premium brand. I doubt if you were to check the statistics you'd find a large difference in the percentages of CS students who take those programs (BMath and Specialist). So we're still at Waterloo not having more math in CS than every other university. I don't see how you can continue defending that clearly exaggerated and groundless comment. No real equivalent to Waterloo's CS245, "Logic and Computation"? Sounds like U of T's CSC236, "Introduction to the Theory of Computation". The option to take advanced versions of certain courses you say? There's also CSC240, "Enriched Introduction to the Theory of Computation". Plus, where Waterloo has one course that another university doesn't, another university will have a course that Waterloo doesn't. Math and CS included. |
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| Author: | Prabhakar Ragde [ Sun Mar 29, 2009 7:45 am ] |
| Post subject: | Re: RE:The amount of mathematics in CS... |
Gandalf @ Sun Mar 29, 2009 5:15 am wrote: Prabhakar Ragde @ 2009-03-24, 9:36 am wrote: I also looked at McMaster (I didn't do much of this looking around, because none of these places make searching for this information very easy) and counted three or four math courses.
I think all this comes down is what you're accustomed to, and a good Google search will usually do the trick. There is no need to be condescending. A Google search will not quickly deliver the full picture (as the rest of your message makes clear). Quote: Prabhakar Ragde @ 2009-03-24, 9:36 am wrote: Not everyone takes a Specialist stream at U of T -- that's their premium brand. As far as I can tell, the straight Major requires one calculus, one algebra, and one probability/stats. They have a CS course that is covering similar ground to our Math 135, also, and no real equivalent to our CS 245.
Not everyone takes the BMath at Waterloo either, that's their premium brand. I doubt if you were to check the statistics you'd find a large difference in the percentages of CS students who take those programs (BMath and Specialist). So we're still at Waterloo not having more math in CS than every other university. I don't see how you can continue defending that clearly exaggerated and groundless comment. I didn't make the comment -- it was made by a former UW student who graduated at a time when it was true. We have since reduced the requirements in both Math and CS to allow for more flexibility and the possibility of joint programs such as Bioinformatics and CFM. In what I've said above, I've been comparing the BCS (not the BMath/CS) to other institutions, and for U of T, the fairest comparison is to the Major program. We have no equivalent of the Specialist program in terms of diploma recognition, though I would argue that the quality of our Math courses, the explicit connections made in the curriculum, the advanced Math/CS courses, the possibility of joint/double majors (CS/C&O is common), and the general effect of being in a Faculty of Mathematics (many BCS students take Calc 3, for example, even though it is not required) combine to lift our connections to math above those that you would encounter in other CS programs. Quote: No real equivalent to Waterloo's CS245, "Logic and Computation"? Sounds like U of T's CSC236, "Introduction to the Theory of Computation". I teach CS 245 and I am old friends with the developer of CSC236, and they are different courses. CS 245 is a course in mathematical logic and its relationship to computer science, and is considerably more mathematical than both CSC236 (or, for that matter, than the nonmajor PMath 330 at UW). The closest UT equivalent to UW's CS 245 is CSC330 (not required). CSC236 covers algorithm correctness and analysis and the basics of formal languages, material that we at UW cover in CS 136 and CS 241. Quote: Plus, where Waterloo has one course that another university doesn't, another university will have a course that Waterloo doesn't. Math and CS included. If you're going to dismiss Waterloo as no better than anywhere else on the grounds that everyone requires 40 courses or equivalent for a degree, there's not much I can say to change your mind. I am not knocking UT; it's a good program, though I would suggest that their focus really is on their grad program and on the select number of their undergraduates that they can convince to attend grad school with them. (Waterloo may be headed in this direction as well.) I also think that aspects of Waterloo's reputation are exaggerated, and I have no interest in perpetuating mythology. The fact that our ACM Programming Contest teams have historically done well, for example, says nothing about the quality of our education, since the particular skills involved in a programming contest are a small fraction of the skill-set that should be imparted by a CS program, and the individuals on those teams exercising those skills did not necessarily pick them up in UW classrooms. Nor is every course at UW a life-changing experience; as at other places, there is far too much indifferent teaching and watering-down of content for the sake of expediency. However, when it comes to the influence of math and its integration into the CS curriculum, few institutions can match UW, and none with comparable numbers of students. (edit: hit Submit instead of Preview, had to fix tags) |
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