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Pure Maths as a Degree

  • 03-01-2007 10:08pm
    #1
    Registered Users Posts: 219 ✭✭rjt


    So, as the CAO deadline is approaching, I really need to make a final decision about courses. My intention is to do a pure maths degree (probably in Trinity), but I thought that it'd be wise to ask some current students before signing my future away.

    Basically, what are the pros and cons of doing a degree in pure maths? Which colleges are best? Are the potential career options really as broad as the open days always insist? Also, how difficult are the courses? I'm pretty good at maths and problem solving (doing well in school and the Irish Maths Olympiad), and from what I've seen of the first year course (I've done some Linear Algebra), it certainly seems do-able. But does it get much more difficult as it progresses?

    And as a slight aside to any Trinity students, how hard is it to get a Foundation Scholarship? I'd love to be able to live near campus, but can't really afford it.

    :)


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Comments

  • Closed Accounts Posts: 1,498 ✭✭✭paddyc


    in my experience and i didnt do pure maths but there was a lot of it... if you can do all the past papers in the library you'll get a first...
    as simple as that..

    get a part time job.. you'll be able to live in town then


    cheers paddy


  • Moderators, Social & Fun Moderators Posts: 10,501 Mod ✭✭✭✭ecksor


    Ok, there's not many degrees that are really in "pure maths" as such, they tend to combine pure maths, applied maths, computing, statistics in various doses and combinations and in fact it's not clear to a school leaver what a lot of these differences are a lot of the time although the mixture is probably quite important to how much the course will be enjoyed by the student.

    I take it you mean that you're doing a degree in a single subject titled "mathematics" ?
    rjt wrote:
    Basically, what are the pros and cons of doing a degree in pure maths?

    That probably depends upon the person. My own personal experience is that I'm in my final year of a maths degree which was 50/50 between pure and applied before this year (i.e, no computing, no statistics) and I'm taking almost all pure maths modules for this year.

    Pros for me are that I find the subject very interesting and I enjoy it. Pros from the point of view of other people is that people tend to regard a maths degree highly (and usually overestimate how intelligent you must be if you tell them what you're studying).
    Which colleges are best?

    I'm studying in England, but I checked out most Irish courses before moving. TCD seems pretty comprehensive and challenging with a wide range of options (and an International reputation if that sort of thing appeals to you). The 3 year BA in Maynooth looked like a very good degree option to me, especially if you're planning to do mostly pure topics. I would personally have applied to one or both of those if I'd stuck around.

    The other NUIs seemed decent, as did DCU. DIT's new degree has a nice range of options but is a very new course which might be a good thing or a bad thing. Their class size is tiny.

    The only maths degree around that made me cringe and say "no way" was UL, which at the time appeared to be mostly vocational modules designed for job use.

    Recommending a maths degree is tricky though, as I say above, the different emphasis that universities put on different areas will suit some more than others. Some might like the practical nature of the UL course, but for most people who simply like maths it seemed to me to be a pretty boring course and a vocational outlook is shortsighted IMO. Your mileage may vary. Unfortunately, secondary school doesn't normally prepare a leaver to make an informed choice.
    Are the potential career options really as broad as the open days always insist?

    Yes. However, there's a nice confusing situation where we keep getting told that there's a shortage of maths graduates, and yet it appears that all the maths graduates end up in jobs that don't necessarily require a maths degree, so I'm never quite clear on what they mean there (instead of saying there's a shortage of numerate graduates).

    Typical destinations for my classmates seem to be accountancy training or management training. Many seem to end up in accounting, finance, insurance, actuary training, banking or some form of IT or Programming. These may not appear to be particulary sexy options (unless you like money and/or computers). There are interesting jobs to be had, but because they're not "commodity" type professions then it's hard to list them as options for someone who won't graduate for a few years. For example, I've recently found a company who makes use of mathematics for testing of some specialised online facilities which I personally find very very interesting, but there's maybe 3 companies in the world that do it so it's not going to appear on a prospectus. I'm a bit vague here but hopefully you get the point.

    Perhaps the relevance of a lot of things become apparent once you identify an area you're interested in working in. For example, I originally got into maths in my last job because I needed a better grounding to understand subjects like cryptography, risk analysis and some aspects of theoretical computer science. In that situation, it definitely has job relevance.
    Also, how difficult are the courses? I'm pretty good at maths and problem solving (doing well in school and the Irish Maths Olympiad), and from what I've seen of the first year course (I've done some Linear Algebra), it certainly seems do-able. But does it get much more difficult as it progresses?

    Yes, but there's a rule I came across before that I like which is:

    Last year's maths is easy.
    This year's maths is hard.
    Next year's maths is impossible.

    Judging by the above, if you keep up with your work then you should be capable of doing it.

    I think this thread might make a good sticky if we get a few more responses and opinions.


  • Business & Finance Moderators, Entertainment Moderators Posts: 32,387 Mod ✭✭✭✭DeVore


    I have a degree in Pure Maths from Trinity. Not a very good one and its a bit dogearred but none the less... :)

    Firstly, print out what Ecksor just wrote, photocopy it down to A8 and stick it on any glasses you might wear. Its golden advice.

    I found the standard of lecturing in TCD to be highly variable but occasionally very poor. That said I went to Belvedere College and was taught by John "titch" Brown who was brilliant so perhaps I am being harsh on TCD, I have no idea that lecturing in any other college is any better.

    The course itself was interesting and varied. Quite a lot of it was "self taught"
    and if you work you'll do fine. Some of it was rote learning, some of it was rote learning because we simply didnt understand a topic intrinsically and some of it was genuinely interesting. The course if wide and after a generalistic first year, you can specialise quite deeply.

    15 years out I am very glad I picked it despite the heart ache between TCD and I. I have always said that you train to be a dentist, an accountant, an engineer... but you are born a Mathematician. That is still exceedingly true imho.
    You will learn about tensors, lambda-calculus and n-dimensional vector geometry. You'll probably never use a fraction of it again but what it teachs you is a rigourousness of approach, a discipline of logic and a robustness of thought that can be applied to just about any given problem. Thats why employers are always looking for Maths graduates, thats why they work in various different fields. If you are smart... Maths will razor-sharpen your thinking.

    Do not go into accounting. No offence to accountants but thats like getting Deep Thought to add up your groceries.
    People who left my year went to NASA, The Met Office, Encryption (setting up Iona, Trintech and Baltimore along the way), programming, teaching and banking. I dont think its a limiting degree, in fact I think that if you go into say Engineering then you can only ever really be an engineer without retraining. Maths allows you to decide later on where you want to apply your mind.

    As an employer... unless I needed a specific degree (ie Engineering etc) I wouldnt have cared enormously what the base degree was provided it was a decent final year result. That shows the person can learn hard things. After that I'm much more interested in whether this person can get along with the team, seems enthusiastic, good people skills etc.

    So there you go, thats my 1/50th of a dollar.

    DeV.


  • Posts: 16,720 ✭✭✭✭ Landyn Many Stipend


    Some links below.

    1. An old thread (2004) asking the difference between Maths Degrees in various colleges.
    2. A comparison of Theoretical Physics and Mathematics in Trinity.
    3. First thread about Schols Exams in Trinity
    4. Second thread about Schols.
    5. Third thread about Schols.

    There are a few people doing Maths or Theoretical Physics over on the TCD board, so if you get any specific Trinity questions you can always wander over.


  • Moderators, Science, Health & Environment Moderators, Social & Fun Moderators, Society & Culture Moderators Posts: 60,076 Mod ✭✭✭✭Tar.Aldarion


    Stellar advice here, good luck rjt. You have the same question on your plate that I did a few years ago. I wanted to be an astronaut, but something let me down and I can't be one, so it was mathematics, physics, computers or engineering that was next to choose from, maybe still go to NASA ;). I chose engineering(Electronic and computer as it has all four.) as I thought it would give me better job opportunities.
    All, I can really say is that if you enjoy maths, feel a buzz getting something difficult right, you should go for it.
    There are a lot of pros to it, so you won't be signing your life away.
    At the age of choosing it is impossible to know what to go for, so just go for what you think you will like, and if you like a few things, you will just be left wondering should you have done the other ones instead. (:


    EDIT: just clicked on one of your links there myth, I went to secondary with that seamusK, weird.
    Seems he changed from Theoretical physics to pure mathematics, the things you learn on boards...
    (Oh, and he can handle the workload so can you OP :P)


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  • Registered Users Posts: 3,608 ✭✭✭breadmonkey


    Great thread!


  • Closed Accounts Posts: 2 Brendan Boulter


    I wanted to be an astronaut, but something let me down and I can't be one, so it was mathematics, physics, computers or engineering that was next to choose from, maybe still go to NASA ;).

    Hi,

    My first "real" job after graduating with a few maths degrees was with the European Space Agency. I worked on a number of their major scientific satellite programs and the work was really interesting and enjoyable.

    The career prospects for mathematicians are very varied. The best career advice is to go for something that you enjoy, something that you are good at and something that you have a passion for.

    Brendan


  • Registered Users Posts: 13,746 ✭✭✭✭Misticles


    i do the maths science degree in dit!! i love it!! maths and some computers and the options for third year are very interesting, cryptology etc
    im in 2nd year at the minute, 11 in my class. it can be hard but its all part and parcel of college! :D


  • Closed Accounts Posts: 1,504 ✭✭✭Nehpets


    I am interested in maths in school. I do applied maths too. I am in no way amazing at it but I like it :s Someone mentioned above that you could go into IT. Would a maths degree hold up as well as a computer science degree? (for programming, not networking etc. obviously). The points are high I assume, I'm too lazy to go check them right now :D

    "unless you like money and/or computers"

    I like both! muhahaha

    I know the OP specified TCD, but does anyone have experience with UCD and maths?


  • Registered Users Posts: 351 ✭✭Slippers


    If you do Omnibus entry Science in UCD (CAO: DN008) you can try lots of subjects before you decide what to do at the end of second year. I started in 2003 so I have no experience of the Horizons system but I expect it means there is more choice.

    At the beginning of 1st Year I went to Experimental Physics lectures, Biology lectures, Chemistry lectures and one Chemistry lab class before settling on Honours Mathathematics, Computer Science, Geology and Mathematical Physics. At Christmas I also did the Pass Maths exam (multiple-choice exam, which was nice) in case I wanted to drop down from Honours Maths. I dropped down after Christmas.

    In 2nd Year I did Computer Science, Pass Maths (called General Maths in 2nd Year) and Statistics.

    In 3rd Year I did a Single Subject General Degree in Statistics which included eight Statistics units and two General Maths units (one or both could have been Computer Science instead). I could have done a Two Subject General Degree in any two of my 2nd Year subjects or a Topical Degree in Applied and Computational Mathematics which would have been bits of Maths, Statistics and Mathematical Physics. I was also meant to have German in 3rd year but there weren't enough people and I had to do Combinatorial Mathematics which I failed. If I had passed one more unit I would have gotten into 4th Year.

    One thing I didn't know until I was holding it in my hands is if you don't get into 4th Year you don't get your subject on your Degree, it just says Science. I'm not 100% sure it says it on the Honours Degrees but I was surprised and disappointed.

    You could do Single or Joint Honours. If you never make up your mind you could do both Maths and Computer Science until the end of 4th Year. Points last year were 320 and you can even get in with only five subjects if you have three higher level Cs or something like that. I did Ordinary level Maths in the Leaving Cert and found the Mathematical Physics to be harder than the Honours Mathematics.

    Here is a link to PDF versions of the Faculty Booklets.
    www.ucd.ie/registrar/booklets.htm
    They don't produce them any more but they were vital in my understanding my choices.


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  • Registered Users Posts: 219 ✭✭rjt


    Thank you all for your responses :)

    ecksor: Yeah, by "pure maths" I simply meant "mathematics on its own" (rather than TP or Mathematical Sciences or somesuch).

    Quick question to Brendan (or anyone else who feels like answering): You say you worked at the ESA, what kind of work did you do and what areas of maths did you apply most? Would employment opportunities in that area be good?

    Slippers: I was looking at UCD, but to be honest,their arts programme confused me slightly, and there is no Mathematics-only course in the prospectus (although Mathematical Sciences is down as one of my options). Would you recommend going in through General Science instead?

    Also, a general question, after a degree, is there much opportunity to pursue academic research (in maths or sciences)? I have nightmares about ending up sitting at a task performing tedious calculations for some business. I'd much prefer to feel that my work was going somewhere (rather than just raising profit for a company!). Am I dreaming, or are such positions available?


  • Closed Accounts Posts: 1,475 ✭✭✭Son Goku


    rjt wrote:
    Also, a general question, after a degree, is there much opportunity to pursue academic research (in maths or sciences)? I have nightmares about ending up sitting at a task performing tedious calculations for some business. I'd much prefer to feel that my work was going somewhere (rather than just raising profit for a company!). Am I dreaming, or are such positions available?
    Yeah, such positions are in fact under staffed in Britain and Ireland. Particularly Southern Britain.


  • Registered Users Posts: 219 ✭✭rjt


    Son Goku wrote:
    Yeah, such positions are in fact under staffed in Britain and Ireland. Particularly Southern Britain.

    Excellent. Would these positions mostly be as post-grads in universities?


  • Closed Accounts Posts: 1,475 ✭✭✭Son Goku


    rjt wrote:
    Excellent. Would these positions mostly be as post-grads in universities?
    If you're just talking about Postgrads then there is a tremendous amount of positions available after your degree. If you get a First in your degree, it is practically a certainty that somewhere in the British Isles would accept you.

    After postgrad, i.e. postdoc, there is still currently an open job market for pure and applied math. Most people leave after PhD to go to finance and industry, so that leaves positions open.

    With regards to different Colleges, the modules in NUI Maynooth, seem to follow what is called the Bourbaki tradition. Kind of the "old school" way of doing maths (Although not old school material, Maynooth's final year actually offers the most advanced stuff). Basically the teach stuff that lends itself to theorem proving and axioms.

    The other Colleges offer a modern take on maths. Particularly things like a course purely on group representation, e.t.c. that are more about content than proofs, tie in with other areas and are a bit less dry.

    People are usually suited to one of these approaches to maths, although it's hard to say which without an indication of your tastes.

    You said you did some Linear Algebra. Did you enjoy it?


  • Registered Users Posts: 351 ✭✭Slippers


    rjt wrote:
    I was looking at UCD, but to be honest,their arts programme confused me slightly, and there is no Mathematics-only course in the prospectus (although Mathematical Sciences is down as one of my options). Would you recommend going in through General Science instead?
    If you do Omnibus Science you pick which degree you are going to do at the end of 2nd Year. If you pick "Mathematics" as your degree you can have all your modules in 3rd and 4th Year be "MATH" modules. There is not enough of them in 1st and 2nd Year to do nothing but "MATH" so you would have to do some others, like "MAPH" or "STAT" ones. I found maths physics to be entirely mathematics so between maths, maths physics, statistics and some of the data structures & algoriths courses from computer science you shouldn't have to do much in 1st and 2nd Year that's not maths.

    If you do Mathematical Science you can switch to Omnibus Science and do a degree in "Mathematics" at any time. Also, in Omnibus Science, for some of the denominated entry degrees you can copy the choices the denominated entry students are forced to make in the different years.

    I found a current booklet: www.ucd.ie/science/science_at_ucd.pdf
    Unfortunately it only covers 1st Year but the later years won't have changed much from the older booklets I linked to earlier.

    In 05/06, 4th year Maths students could pick eight of these twelve MATH units:

    Ring Theory
    Group Theory
    Combinatorics
    Measure Theory
    Differential Geometry
    Functional Analysis
    Numerical Analysis
    Financial Mathematics
    Topology
    Commutative Algebra
    Several Complex Variables
    Special Topics


  • Registered Users Posts: 219 ✭✭rjt


    Son Goku wrote:
    If you're just talking about Postgrads then there is a tremendous amount of positions available after your degree. If you get a First in your degree, it is practically a certainty that somewhere in the British Isles would accept you.

    After postgrad, i.e. postdoc, there is still currently an open job market for pure and applied math. Most people leave after PhD to go to finance and industry, so that leaves positions open.

    With regards to different Colleges, the modules in NUI Maynooth, seem to follow what is called the Bourbaki tradition. Kind of the "old school" way of doing maths (Although not old school material, Maynooth's final year actually offers the most advanced stuff). Basically the teach stuff that lends itself to theorem proving and axioms.

    The other Colleges offer a modern take on maths. Particularly things like a course purely on group representation, e.t.c. that are more about content than proofs, tie in with other areas and are a bit less dry.

    People are usually suited to one of these approaches to maths, although it's hard to say which without an indication of your tastes.

    You said you did some Linear Algebra. Did you enjoy it?

    Yeah, I did. Most of what I've done so far is vector based stuff, and the real basics (Gaussian elimination and such), but I hope to progress more after my mocks (given that I've finished the secondary course, I'll probably bring in some linear algebra stuff to work on in school).

    I particularly liked how it tied in (often in surprising places), like the proofs of Cauchy-Schwartz and the Triangle Inequality with vectors (and after seeing the long non-vector proof of Cauchy-Schwartz, I quite liked the vector version!).


  • Registered Users Posts: 2,149 ✭✭✭ZorbaTehZ


    I'm really interested in doing a pure Maths degree, but I was always put off it since I thought there was little or no career opportunities out of it. Nice thread gave me a lot to think about :D


  • Registered Users Posts: 351 ✭✭Slippers


    If you want to see someone who went far with a Maths degree have a look at this:
    en.wikipedia.org/wiki/James_Harris_Simons


  • Closed Accounts Posts: 1,475 ✭✭✭Son Goku


    rjt wrote:
    Yeah, I did. Most of what I've done so far is vector based stuff, and the real basics (Gaussian elimination and such), but I hope to progress more after my mocks (given that I've finished the secondary course, I'll probably bring in some linear algebra stuff to work on in school).
    You sound like you're very suited to mathematics. Especially this:
    I particularly liked how it tied in (often in surprising places), like the proofs of Cauchy-Schwartz and the Triangle Inequality with vectors (and after seeing the long non-vector proof of Cauchy-Schwartz, I quite liked the vector version!).
    If you actually have a taste for proofs and are surprised by results, I think you have the interest needed to see a degree through.
    (As a side note, Linear Algebra is basically the mathematics of Quantum Mechanics)


  • Registered Users Posts: 8,391 ✭✭✭spacecoyote


    well i graduated from Trinners with a Maths degree in 1999, albeit a fairly mediocre one, as i was a lazy b*stard who enjoyed college life a bit too much.

    It is not an easy degree, and even if you do find everything up to your leaving cert quite easy it will not prepare you for the depths in which you will delve into different areas of maths. It is hard work, but your first year is quite broad so you should get a good idea about which direction you would like to take. You'll study pure maths subjects as well as statistics, mechanics (similar to applied maths), computer programming. A good understanding of the subjects will be necessary but you'll find in a lot of cases a phenomenal memory can be enough to get you an extremely good degree (i've seen guys get gold medals without having a clue what they just wrote on a paper!!!).

    The majority of people who studied with me have either gone onto further studies or down the actuarial route. I can tell you from experience that if you want to go down the financial line, a maths degree can be met with some confusion. Its been said to me in interviews: "....yes, a maths degree is a fantastic qualification but its quite specialised...would you not have thought of a more general qualification". Thats why a number of people in my class, and other classes headed over to edinburgh afterwards to do the financial maths postgrad over there. I personally did a general business postgrad to get a more "rounded" education. I currently work as a trader, and i know a few others working in similar areas.

    It is a very interesting course and can be very rewarding if you put the work in. As has been previously stated, you may never use a lot of what you learn again but it will all stand to you in the long run.

    Good luck with whatever you choose. If you go for maths I don't think you'll regret it!


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  • Registered Users Posts: 2,604 ✭✭✭xOxSinéadxOx


    so what's the difference between mathematical science, mathematical studies and mathematics?:confused:


  • Registered Users Posts: 379 ✭✭King John V


    In nuig, mathematics is pure honours, mathematical studies can lead to honours as well but isn't regarded as highly as pure honours in the maths community. It's still more than good enough for secondary school teaching. Finally, mathematical science is a pass level subject. You can still get an overall level 8 honours degree with it though. Hope this helps :).


  • Closed Accounts Posts: 24 flint_72


    hay,i hope im not going too much off on a tangent,bu anyway im more interested in Theoretical Physics in Trinity that just maths as such.Bu i saw some1 here say they worked for a space agency.i suppose rather than workin in NASA,what would interest me would b 2 work in CERN! sounds like fun :P. I dont suppose any1 here knows of any1 working there r more what the chances of getting that kinda work are? N i no that Ireland doesnt give them any money :P.


  • Closed Accounts Posts: 649 ✭✭✭fillmore jive


    well i know in ucd they have some type of summer internship in cern. a couple of the post grads in the physics building did it, youre better off going in and asking some of the particle and atomic physics lecturers about it, theyll be more than happy to help.


  • Closed Accounts Posts: 12,382 ✭✭✭✭AARRRGH


    What do you guys think of the Open University maths courses?


  • Closed Accounts Posts: 5 bilboa88


    I'm planning on listing maths as my first choice on my CAO this year. I have a strong interest in it, mainly on the pure side and am unsure what university I should apply to. I've heard that NUIM has a course with a strong emphasis on the pure side of things AND it's only 3 years too. However, a lot of people I talk to seem to think TCD is better. I know UCC , UL And NUIG all have good degrees too but I'm pretty sure I'll be staying in Dublin if possible. Has anyone got experience of these degrees ? If so, what are the career options that most people in your year took ( Hope that isn't too rude! ) ? And what are your opinions on the academic route ? What's it like ?


  • Registered Users Posts: 2,149 ✭✭✭ZorbaTehZ


    Have a look at this sticky, it might answer some of your questions.


  • Registered Users Posts: 2,481 ✭✭✭Fremen


    I did a joint hons. in maths and computer science at UCD. What you'll cover will be quite different to what you did at school. One word of warning: I'm not sure if anyone on this forum will agree with me, but in a certain sense I found studying maths to be kind of a lonely experience. Keep in mind that you won't be able to talk to *anyone* outside your course about what you're doing. After second year, I couldn't explain to outsiders what my classes were even about.

    Lots of maths students go into banking, actuary, certain types of IT or academia. Personally, I went over to London and am doing a masters in financial maths now (trying to get into a phd at oxford at the moment). Anything which uses numbers, really. Accountancy is another path, or maybe engineering if you go heavily into the mathematical physics side later on. Almost all these things require some sort of further study, though.


  • Closed Accounts Posts: 5 bilboa88


    Thanks!


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  • Registered Users Posts: 4,944 ✭✭✭Jay P


    ZorbaTehZ wrote: »
    Have a look at this sticky, it might answer some of your questions.

    That's a link to this page! :D

    This must be the best thread I have read in a long time. It's all still confusing though :(


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