Doing a maths degree in college.

Neodymium

Hi everyone, I hope you can help me with a few questions that I have regarding studying maths as a degree in college. I've read the sticky about doing maths in college, I just have a few more questions.

I'm in sixth year at the moment, trying to figure out whether I should choose to study maths or computer science in college. I have heard that doing a degree in computer science sometimes does not equip you with an adequate level of maths for certain applications in the IT world. I am good at maths in school and really enjoy it, it's my favorite subject. What I am thinking of doing is doing a maths degree in college with the hope of maybe doing a masters in computer science afterwards. At the moment I think this would be the best course of action. By doing maths I would have an indepth understanding of maths (more so than by studying computer science) and I'm keeping all my options open about whether I want to pursue a career in IT or another mathematically based field of work. I think having a degree in maths would be more beneficial for me in the long run and I would not have too much trouble entering the IT world seeing as computer science is essentially an application of mathematics and logical thinking.

I'm thinking about doing the Mathematical Sciences degree in UCC as it has a broad choice of options in first year, allowing you to specialise in subsequent years. I don't do applied maths however as it's not offered in my school, and I'm wondering would I be able to cope or is the applied maths stuff thought assuming no prior knownledge? I am doing physics which would include doing some mechanics which I am good at. Would this be any advantage to me?

Thank you very much for reading, I'd be delighted if anyone could give their thoughts on doing a maths or computer science degree.

sionnachrua

I don't know very much about this whole thing, so don't take my word as gospel. I'm in my final year studying pure maths, and I had an offer from the computer science dept. looking for someone with maths to work on a large scale research project. When I talked to the guy in charge he was saying that a lot of those who come out of computer science dislike maths - are great at programming but don't understand enough about the maths behind it. I don't know very much about programming - I did one or two basic courses in programming with things like Maple and R - but I was assured I could pick it up easily enough.

Basically it's said that if you study pure maths then you have the logical reasoning power and the ability to think abstractly that would make a good computer scientist. Then again if you do a computer science degree and you love and are good at maths then you have an advantage on most other people in your class.

I don't know much about the Mathematical Sciences course in UCC, though I did hear there are a lot of options when you start that way. I would recommend getting into pure maths along the way - if you enjoy maths then it's great, a real challenge.

cavedave

I am no expert on this so check everything I say independantly.

It sounds like what you want is a first year of Maths, Computer science and maybe something else. UCD science used to do this but now Cs is its own course. Trinity CS get a maths degree at the end of their course (or at least did up to a few years ago).

One possibility is Mathematical Science in UCD. I dont know much about the course. It is fairly new. But go online and have a look at the exam papers to see if it looks like your sort of thing.

One thing to consider is statistics. Which may be in the sweet spot between computers and pure maths for you. Actuary is full of really clever people and it pays well, it may be too regimented and uncreative for some though.

Id have a look at the exam papers online for courses, sometimes what the booklet says you learn and what you actually learn are very different. The test even if you dont know whats its asking will give you an idea of the type of questions it asks. MAybe even call into a few of the universities. Its pretty intimidating but you'd be surprised how useful sticking your head into the lecture theatre to see what actually goes on. And I dont mean on one of the open days.

equivariant

cavedave wrote: »

One thing to consider is statistics. Which may be in the sweet spot between computers and pure maths for you. Actuary is full of really clever people and it pays well, it may be too regimented and uncreative for some though.

Don't want to get into a big row about this, but I have to comment on that part of your post. If OP is interested in maths and/or computing then (s)he whould do one of those subjects, not something else altogether (statistics).

@OP: If you really like maths, then do that. My impression is that it is easier to learn computing later, rather than the other way around. NUIG has a degree in maths and computing with a substatial pure mathematical component which you could consider if you really want to combine the two. The maths science degree at UCC is a good degree as well, and Trinity, UCD and Maynooth have solid degree programmes in pure mathematics.

cavedave

equivariant

Don't want to get into a big row about this, but I have to comment on that part of your post. If OP is interested in maths and/or computing then (s)he whould do one of those subjects, not something else altogether (statistics).

Do you actually think statistics is something else altogether from maths and computing?

Fremen

cavedave wrote: »

Do you actually think statistics is something else altogether from maths and computing?

I've worked in both maths and stats, and I've got a little background in computing. You could argue that stats is just maths in disguise, implemented on computers. That misses the point to some extent. There's a large enough gap between theory and practice that stats has a very different flavour to maths.

For instance, in the theory of Markov processes, a theoretical analysis of the Metropolis-Hastings algorithm can tell you whether or not your Markov chain will hit equibrilibrium geometrically quickly. In practice, the algorithm can still take the lifetime of the universe to run properly, so you need all sorts of hacks and tricks that a mathematician wouldn't really bother with.

Another point of contrast is that statisticians tend to focus on the average case ("will this method typically work?"), whereas mathematicians look at extreme cases ("what is the most pathological thing that can go wrong with this method?"). Statisiticians think in terms of "for most X, in practice", whereas mathematicians think of "for all X".

OP: Applied maths is a big advantage, since there's a significant overlap between first-year mechanics and LC applied maths (or at least there was in my day). It would make the learning curve a little less steep, but it's not essential.

It's hard to know what you might like without actually doing it. You might find the constsnt theorem/proof structure of maths classes tedious, or you might love it. You should consider taking a course that has broad options at the beginning but that allows for specialisation later, once you know what you like.

You should look up the difference between computer science and software engineering, too. CS is a theoretical subject. There are arguably few true CS jobs out there. Software engineering is a different kettle of fish - it's all about designing and managing projects, using the right language, and so on. The bulk of IT jobs would be for software engineers (though IMHO thouse jobs could be a little dull). Maths would help with CS, but it wouldn't necessarily be massively helpful for software engineering.

cavedave

Firemen that is a could summary of the links and differences between maths,stays and computers at least ay college course level.


Say the op gets into ucd arts rather than mathematical science they could do three of maths, stats, mathematical physics, computers as well as traditional arts fair like philosophy etc. The idea that you can only do maths through science (at least when I was at college) or from starting off with solely maths type subjects is wrong

equivariant

cavedave wrote: »

Do you actually think statistics is something else altogether from maths and computing?

Most (but not all) professional statisticians that I know do not have a very deep knowledge of mathematics. That is not a criticism, just an indicator that the subjects are quite different. In my experience statisticians think quite differently to mathematicians. I don't know as much about cs so I'll leave others to comment on that although my impression (on limited evidence I admit) is that many computer scientists have more in common with mathematicians than statisticians do

fergalr

I'm just going to start by responding to some comments:

cavedave wrote: »

Trinity CS get a maths degree at the end of their course (or at least did up to a few years ago).

I don't think this is correct. The engineers do, or at least did, and there's a stream of engineering that does computer engineering. When I did CS in TCD (finished 2004) CS people certainly didn't get a math degree; and wouldnt have, in my opinion, merited one.

cavedave wrote: »

One thing to consider is statistics. Which may be in the sweet spot between computers and pure maths for you.

I would definitely not suggest a stats degree as a sweet spot between CS and maths; thats just not how I would think of the relationship between those subjects.

sionnachrua wrote: »

I don't know very much about programming - I did one or two basic courses in programming with things like Maple and R - but I was assured I could pick it up easily enough.

I think a mathematician will definitely pick up *simple* programming easy enough - especially if they've done a few courses in it, in their degree. (I think they often see some 'C' programming?).
But there's a vast gulf between basic programming, and the sort of skills that a leet software developer will have. I'm still learning to code, and I've written quite a bit of software, at this stage; I started in secondary school. There's just a huge amount to learn, to get fast and skilled at developing good software, and mathematicians don't learn that at college, as part of their course. (Although, neither do CS people, really - but they've more free time, in and around their course, to work on it, and spend more time doing software projects, so the better ones tend to pick up more software dev skills).



Now, to the question the OP is asking.
Its a very hard question.
Its something I've thought about a lot.

I did CS in college. I wondered, during it, if I should have done maths instead. I think I'm happy overall I did CS, and it was the right decision - primarily because I enjoyed the material a lot, and because I had more 'free time' to work on self directed learning, and do my own reading, than I think I would have had in a maths degree - but its a tight call. I really like algorithms, learning about computer systems, and I really like the practice of programming, and building software; so I enjoyed CS a lot, which counts for a lot in an undergrad.

I'd definitely have been served better with more maths, and less computer hardware, in my degree; I felt that CS in trinity happened to have a lot of hardware in it.

I'm studying for a PhD at the moment, that has more maths around it than much CS postgrad work does. I've seen machine learning, stats, and work with graphs/networks a lot. I've got to read a lot of papers that feature math. I've sat in on a few maths courses, too, and done some reading, to learn more. I did a good bit of basic linear algebra in my undergrad, working with computer graphics; we had a few courses on linear algebra, basic calculus, stats, lots of boolean algebra: but to be completely clear about something, you definitely see much, vastly, less math in most CS courses than in most math courses; or even in engineering courses.


Sometimes I think you get more comfortable with what you do see; I sometimes wonder if in a maths course, they cover so much material, it hurts the opportunity to get a deep understanding of it; but maybe not. I think I'm glad I didn't do engineering; engineers sometimes get a pass degree in maths (think they do in trinity, anyway) but I know some smart people who felt that they covered too much ground, too superficially.

I think, overall, maths degrees are probably harder than CS degrees; that's the impression I get - although a lot depends on what you make of it, of course.
I also think - and this is a different point - that the material covered in a maths degree is generally harder to pick up after undergrad, for a CS person, than the material covered in a CS degree would be for a mathematician.


If you wanted to work in more researchy/sciencey/hard-core-CS-y end of computer science, you would probably be best served by doing, as you suggested, a math undergrad, followed by a CS MSc; especially if you chose programming options, and worked at software development during your spare time in college, or summers.

This will probably most expand your intellectual horizon; but it might be more work, and leave less time for self-directed learning than a CS degree would - depends on the course in particular.

If all you want to do is be a software developer, well, most software developers wouldn't use all the extra math you'd do in a math degree, and you'd be better off doing straight CS, and working on the software development.

I think having a degree in maths would be more beneficial for me in the long run and I would not have too much trouble entering the IT world seeing as computer science is essentially an application of mathematics and logical thinking.

As things stand, you wouldn't currently have much trouble entering the IT world, with a degree in maths; an MSc in software/CS would go a long way.

You'd probably lose out in many jobs, at the start of an IT career, to the better CS students, because they'll have spent more time on software dev, which is the employable skill most people in the IT world are looking for.

But in the long run, or if you want to do more mathematical work, or become a very hardcore CS person, the maths degree will be more beneficial.

It might be more beneficial intellectually. But maybe so would a liberal arts degree - its hard to say!


A lot depends on you, and on the specific courses you are thinking of doing - what do you want from college? How much do you want to be immeadiately employable afterwards, vs. how much do you want to spend on laying fundamentals for a long career?

How much free time do you want during college? Do you want to do a harder course, or a more enjoyable one? Are you willing/able to do extra study post grad?


Lots to think about there.

One last piece of advice:
Have you done any programming yet? If not, I would strongly suggest doing some, before choosing to do a CS degree.
I love it; but I had some classmates that started CS and discovered they hated it.
Also maybe have a look at an introductory algorithms lecture online, on youtube, or iTunes-U; maybe do the same for a few maths courses, to get an idea of how the subject goes - but don't expect to understand that much, you are just trying to get a feel for it.

Neodymium

fergalr wrote: »

I'm just going to start by responding to some comments:


I don't think this is correct. The engineers do, or at least did, and there's a stream of engineering that does computer engineering. When I did CS in TCD (finished 2004) CS people certainly didn't get a math degree; and wouldnt have, in my opinion, merited one.


I would definitely not suggest a stats degree as a sweet spot between CS and maths; thats just not how I would think of the relationship between those subjects.



I think a mathematician will definitely pick up *simple* programming easy enough - especially if they've done a few courses in it, in their degree. (I think they often see some 'C' programming?).
But there's a vast gulf between basic programming, and the sort of skills that a leet software developer will have. I'm still learning to code, and I've written quite a bit of software, at this stage; I started in secondary school. There's just a huge amount to learn, to get fast and skilled at developing good software, and mathematicians don't learn that at college, as part of their course. (Although, neither do CS people, really - but they've more free time, in and around their course, to work on it, and spend more time doing software projects, so the better ones tend to pick up more software dev skills).



Now, to the question the OP is asking.
Its a very hard question.
Its something I've thought about a lot.

I did CS in college. I wondered, during it, if I should have done maths instead. I think I'm happy overall I did CS, and it was the right decision - primarily because I enjoyed the material a lot, and because I had more 'free time' to work on self directed learning, and do my own reading, than I think I would have had in a maths degree - but its a tight call. I really like algorithms, learning about computer systems, and I really like the practice of programming, and building software; so I enjoyed CS a lot, which counts for a lot in an undergrad.

I'd definitely have been served better with more maths, and less computer hardware, in my degree; I felt that CS in trinity happened to have a lot of hardware in it.

I'm studying for a PhD at the moment, that has more maths around it than much CS postgrad work does. I've seen machine learning, stats, and work with graphs/networks a lot. I've got to read a lot of papers that feature math. I've sat in on a few maths courses, too, and done some reading, to learn more. I did a good bit of basic linear algebra in my undergrad, working with computer graphics; we had a few courses on linear algebra, basic calculus, stats, lots of boolean algebra: but to be completely clear about something, you definitely see much, vastly, less math in most CS courses than in most math courses; or even in engineering courses.


Sometimes I think you get more comfortable with what you do see; I sometimes wonder if in a maths course, they cover so much material, it hurts the opportunity to get a deep understanding of it; but maybe not. I think I'm glad I didn't do engineering; engineers sometimes get a pass degree in maths (think they do in trinity, anyway) but I know some smart people who felt that they covered too much ground, too superficially.

I think, overall, maths degrees are probably harder than CS degrees; that's the impression I get - although a lot depends on what you make of it, of course.
I also think - and this is a different point - that the material covered in a maths degree is generally harder to pick up after undergrad, for a CS person, than the material covered in a CS degree would be for a mathematician.


If you wanted to work in more researchy/sciencey/hard-core-CS-y end of computer science, you would probably be best served by doing, as you suggested, a math undergrad, followed by a CS MSc; especially if you chose programming options, and worked at software development during your spare time in college, or summers.

This will probably most expand your intellectual horizon; but it might be more work, and leave less time for self-directed learning than a CS degree would - depends on the course in particular.

If all you want to do is be a software developer, well, most software developers wouldn't use all the extra math you'd do in a math degree, and you'd be better off doing straight CS, and working on the software development.




As things stand, you wouldn't currently have much trouble entering the IT world, with a degree in maths; an MSc in software/CS would go a long way.

You'd probably lose out in many jobs, at the start of an IT career, to the better CS students, because they'll have spent more time on software dev, which is the employable skill most people in the IT world are looking for.

But in the long run, or if you want to do more mathematical work, or become a very hardcore CS person, the maths degree will be more beneficial.

It might be more beneficial intellectually. But maybe so would a liberal arts degree - its hard to say!


A lot depends on you, and on the specific courses you are thinking of doing - what do you want from college? How much do you want to be immeadiately employable afterwards, vs. how much do you want to spend on laying fundamentals for a long career?

How much free time do you want during college? Do you want to do a harder course, or a more enjoyable one? Are you willing/able to do extra study post grad?


Lots to think about there.

One last piece of advice:
Have you done any programming yet? If not, I would strongly suggest doing some, before choosing to do a CS degree.
I love it; but I had some classmates that started CS and discovered they hated it.
Also maybe have a look at an introductory algorithms lecture online, on youtube, or iTunes-U; maybe do the same for a few maths courses, to get an idea of how the subject goes - but don't expect to understand that much, you are just trying to get a feel for it.

Wow Thanks so much fergalr. Thank you so much, you have definitely given me lots to think about and lots of info.

I have done quite a bit of programming, it basically consumes all of my free time. I started learning some html and css towards the beginning of 2011 (I know they're not programming languages) then I moved onto learning javascript at the start of the summer. I taught my self these by doing some online tutorials and a lot of trial and error. I ended up making a website (studyscience.ie) for leaving cert science notes. It's nothing special it's just something I made for practice. I've moved on now to learning java and I love it. I've been doing Stanford University's introduction to programming course and I got a java programming book. I love it. What I love programming is when you're faced with a problem which seems impossible (to me anyway) when you first look at it, but at the end it's really just lots of small problems knitted together. I love the feeling when it all comes together at the end and my code works. With maths it's kind of similar. I get the same kind of feeling when I solve a fairly hard question (at L.C level).

I think I'm going to go for computer science. I really love programming and I'm fascinated about learning more and more. Thanks again to everyone for replying. Best of luck with your PhD fergalr

fergalr

Neodymium wrote: »

Wow Thanks so much fergalr, your better than any guidance counselor that I have ever spoken to. Thank you so much, you have definitely given me lots to think about and lots of info.

Well, I hope the information helps you make the right decision, and doesn't horribly mislead you into making a bad choice - talk to as many people as you can!

There's lots of good advice on this thread: I think Fremen's post in particular is very good, and the point about how CS is different from software engineering is also worth thinking about.

I wrote a post on this topic, over in the Development forum, a while ago - I actually see you've 'thanked' it: http://www.boards.ie/vbulletin/showpost.php?p=73958125&postcount=8

This distinction between CS and software engineering is pretty important; a lot of universities will teach CS, at a level more 'theoretical' than most software developers are going to use, day-to-day. They'll often have a module, or two, on software engineering, but they are really geared up to teach CS.
Personally I think thats time well spent, before doing a career in software.

That's also why I'd be very positive towards doing a maths degree - its hard to go wrong, spending your undergrad learning broad fundamentals.


An important point to remember is that maths would also equip you for study in other advanced areas, much more so than CS would - if you later decided you really wanted to go into physics, or statistics, for example - or if you later decided to work in an area like the more mathematical parts of finance.


Now, as a good CS person, you could probably get interesting work in those areas, but it'd probably be supporting other people, who had done maths.


On the other hand, as things currently stand, you would probably be more instantly employable, in software, with a CS degree - so there's tradeoffs, and it depends on your career goals; which are hard to decide, when you are in leaving cert.


On the guidance counselor issue, well, my guidance counselor in secondary school was a nun, who was very nice, but realistically couldn't have been expected to understand the finer distinctions between CS and Maths; I think guidance counselors in general have a fairly impossible job.

It's good to talk to as many people, that have done the things you are deciding between, as possible; and take any single individual's advice with a grain of salt.

Neodymium wrote: »

I have done quite a bit of programming, it basically consumes all of my free time. I started learning some html and css towards the beginning of 2011 (I know they're not programming languages) then I moved onto learning javascript at the start of the summer. I taught my self these by doing some online tutorials and a lot of trial and error. I ended up making a website (studyscience.ie) for leaving cert science notes. It's nothing special it's just something I made for practice. I've moved on now to learning java and I love it. I've been doing Stanford University's introduction to programming course and I got a java programming book. I love it. What I love programming is when you're faced with a problem which seems impossible (to me anyway) when you first look at it, but at the end it's really just lots of small problems knitted together. I love the feeling when it all comes together at the end and my code works. With maths it's kind of similar. I get the same kind of feeling when I solve a fairly hard question (at L.C level).

Yeah, that feeling of accomplishment is good. I think its a big asset, if you like that feeling - it'll be helpful for pushing through times of frustration!

If you are already doing some programming, then it sounds like you are in a pretty good place, and know what you are getting yourself in for. The Stanford intro programming courses look like pretty good stuff, and are reasonably representative of what you'll see in the better 'intro to programming' courses here.

Neodymium wrote: »

I think I'm going to go for computer science. I really love programming and I'm fascinated about learning more and more. Thanks again to everyone for replying.

Sounds like a great attitude to have, whatever you decide to do!

I wouldn't make any decisions yet, if I were you - there's probably lots of research you should still do.

For example, if you are likely to go to a particular university (I see you mention UCC, which I've no experience with), make sure to check out what the courses are like in that university. If there's an open day, where you could talk to students currently in the courses you were thinking of, that'd be worth it, too.

If the math course happens to be of a higher standard, or have a better looking syllabus, than the CS course, that might swing your decision towards maths, or vicea versa. Maybe there's a course you can do which allows you take some of each, thats worth considering - and so on.

Neodymium wrote: »

Best of luck with your PhD fergalr

Thanks - I think phd students need all the luck we can get :pac: