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Pure Maths as a Degree
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Hi lads, just wondering if i can get some advice.
Here's my situation:
I always liked maths and physics in school. Got an A1 in LC higher physics and an A2 in LC higher maths (slightly disappointed with this tbh) and always found maths, in particular, easy.
Anyway, wouldn't you know, i did a completely nonmaths based course in college, worked a bit but now i often do think about doing a maths or maths/physics degree.
The thing is it's quite a while since i did the LC and, looking through this forum, some of the maths kinda scares me (despite the above). OK maybe it's because it's college maths that i've never done is this understandable?
Any suggestions as to how to get back into the maths/physics thing?
Any books/websites i could take a look at.
And how difficult would you imagine it would be to go back to do a Maths degree.
Thanks.0 
take everything wrote: »Hi lads, just wondering if i can get some advice.
Here's my situation:
I always liked maths and physics in school. Got an A1 in LC higher physics and an A2 in LC higher maths (slightly disappointed with this tbh) and always found maths, in particular, easy.
Anyway, wouldn't you know, i did a completely nonmaths based course in college, worked a bit but now i often do think about doing a maths or maths/physics degree.
The thing is it's quite a while since i did the LC and, looking through this forum, some of the maths kinda scares me (despite the above). OK maybe it's because it's college maths that i've never done is this understandable?
Any suggestions as to how to get back into the maths/physics thing?
Any books/websites i could take a look at.
And how difficult would you imagine it would be to go back to do a Maths degree.
Thanks.
Or perhaps the Open University might be an option which again allows some flexibility from what I recall. Or one could do a maths module from it as a taster.
Others may have better ideas but just thought I'd throw out some thoughts.0 
take everything wrote: »Hi lads, just wondering if i can get some advice.
Here's my situation:
I always liked maths and physics in school. Got an A1 in LC higher physics and an A2 in LC higher maths (slightly disappointed with this tbh) and always found maths, in particular, easy.
Anyway, wouldn't you know, i did a completely nonmaths based course in college, worked a bit but now i often do think about doing a maths or maths/physics degree.
The thing is it's quite a while since i did the LC and, looking through this forum, some of the maths kinda scares me (despite the above). OK maybe it's because it's college maths that i've never done is this understandable?
Any suggestions as to how to get back into the maths/physics thing?
Any books/websites i could take a look at.
And how difficult would you imagine it would be to go back to do a Maths degree.
Thanks.
It's very doable at any age. When I was a third year undergrad, there were these two old biddies who came to my lectures on metric spaces and logic. They seemed to cope as well as anyone else. Check out the linear algebra lectures at http://www.khanacademy.org/ and the MIT introduction to calculus lectures to see what you'd be up against
http://ocw.mit.edu/courses/mathematics/1801singlevariablecalculusfall2006/videolectures/
(I haven't looked at the MIT lectures, so I can't promise they're any good).0 
It's very doable at any age. When I was a third year undergrad, there were these two old biddies who came to my lectures on metric spaces and logic. They seemed to cope as well as anyone else. Check out the linear algebra lectures at http://www.khanacademy.org/ and the MIT introduction to calculus lectures to see what you'd be up against
http://ocw.mit.edu/courses/mathematics/1801singlevariablecalculusfall2006/videolectures/
(I haven't looked at the MIT lectures, so I can't promise they're any good).
Also, my guess is jumping back into physics would be less hard. For example, my impression from talking with a good friend who was a TP (theoretical physicist in TCD) was in first year, one just did the Leaving Cert course in more detail. I'm not sure how many people did it from scratch but I think it was seen as possible  I know a friend who did biology who hadn't done it for the L. Cert and another person who hadn't done chemistry who picked it up (and did well in biochemistry). While with maths you are more expected to know a lot of the L. Cert stuff. Of course, some textbooks may start from precollege level. I remember there was an engineering textbook for the methods course and the stuff we would have done in first year in college was many chapters in so probably one could work one's way up from the start.
I'm not trying to be negative  just showing there could be problems.0 
I agree. You need to be very committed, and need to get right back on top of Leaving cert material. You'd need to be at higher level A1/A2 standard before starting, but certainly possible if you want it enough.0

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Getting back into it is the key. But if you were decent at maths I wouldn't be worried about starting a pure maths degree from scratch. You're either going to cover stuff you've seen before more rigorously and then stuff no one has seen before. So you'll get the refresher and the new stuff will just be that, new.0

I agree. You need to be very committed, and need to get right back on top of Leaving cert material. You'd need to be at higher level A1/A2 standard before starting, but certainly possible if you want it enough.
This may sound cliche but the thing i got from maths was its elegance and rigour. I got a buzz from that.
I've always valued understanding over memorization (not sure what's valued at college level tbh).
Having said that, because i haven't done any in a good few years, i'm worried the natural interest may have waned. I'll look through that Khanacademy and MIT stuff and see if i can get into it properly again.
I hope the (nonmaths) stuff i've done over the last few years hasn't killed that desire.0 
Think that says it all really. If that's what you value in your previous experiences of maths then I would definitely recommend you study pure maths.0

take everything wrote: »This may sound cliche but the thing i got from maths was its elegance and rigour. I got a buzz from that.
I've always valued understanding over memorization (not sure what's valued at college level tbh).
But at the same time, to enjoy maths, I think one has to work hard at it or at least be disciplined. A lot of people in the course I did ended up learning off stuff at various stages as they hadn't kept up  you can't rely on natural talent alone generally, it takes discipline not to fall behind and then end up simply going to lectures to take notes without really processing the information. Of course, keeping up for the full year isn't always necessary e.g. one may be able to get a good result without knowing the last few weeks of a course if one has a good grasp of the stuff before it.0 
Sounds like maths would be a good course, then. That's the nice thing about maths.
But at the same time, to enjoy maths, I think one has to work hard at it or at least be disciplined. A lot of people in the course I did ended up learning off stuff at various stages as they hadn't kept up  you can't rely on natural talent alone generally, it takes discipline not to fall behind and then end up simply going to lectures to take notes without really processing the information. Of course, keeping up for the full year isn't always necessary e.g. one may be able to get a good result without knowing the last few weeks of a course if one has a good grasp of the stuff before it.
Alright thanks.
That's the scenario i'm afraid of resorting to learning rather than understanding.
That kinda defeats the purpose do these students become disillusioned?
I appreciate the point about discipline.
Interest allied to good discipline can stave off the above scenario i suppose.0 
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But on the other hand you will definitely learn something off for some exam at some point. There's no shame in that. You run out of time studying and there simply isn't a few hours to fully understand some theorem or something and you learn off the proof. I did a very rigorous course in probability theory in DCU and there were so many proofs on the second component of the module that I remember having to learn off a few at the end that I just didn't have time to revise. Of course one came up and I didn't intuitively understand what I was doing and lost some marks but such is life No shame in it, you can always go back to it after and correct your understanding.0

One point about disillusionment, FWIW: I transferred at Xmas of first year so I found I was a bit lost in some courses and did get a bit disillusioned about going to lectures just to take notes. So for various courses, I simply stopped going to the lectures and then copied the notes later. So that stopped me from getting disillusioned.
I'm not sure what other people thought i.e. whether they were disillusioned or not. The male maths students weren't necessarily the most communicative about feelings or weaknesses, etc and the conversations with the girls tended to be on other stuff (probably generalising a bit there!). Possibly some didn't have the "allergy" to learn stuff off that I had. Some also had great memories for that sort of thing. Some of the lecturers were quite strict with regard to marking e.g. one error in a proof and one got no marks, or so I heard, to avoid people learning stuff off (but still loads did). I remember hearing of one case where one guy had learned off a theorem but there was a page missing in what he had learned!0 
Some of the lecturers were quite strict with regard to marking e.g. one error in a proof and one got no marks, or so I heard, to avoid people learning stuff off (but still loads did).
Hmm. I wasn't aware that anyone was that strict!
The purpose of bookwork questions though is to 'encourage' students to study proofs carefully and understand them. If they are not able to reproduce the proofs reasonably accurately on exam scripts then this indicates that they haven't mastered the basic principles. I would have thought that normal practice was that if a purported proof went some of the way, establishing some of the necessary steps but messing up others it would receive partial credit. But what is written should make some sort of sense  if it seems merely a parody of the standard proof which makes no logical sense whatsoever in itself, then it establishes nothing, and deserves no credit (even if it might have some words or formulae in common with some standard proof).
Responding to take everything, I would have thought that those who learned off proofs by rote memorization without studying them carefully would become disillusioned. Courses in subsequent years are taught on the basis that students have studied and understood what has been presented to them in earlier years, and have at least some sort of overview of at least the basic principles of what they have supposedly learned. Some may achieve that understanding easily, others only after much effort. So whilst rote memorization of the words and formulae of a proof may get someone over an immediate hurdle, in the shape of an examination the next day, in the longer term it is surely fruitless. So I would expect that those who rely on rote memorization and cramming (without attempting to master the basic principles, or validate the logic of the arguments) would find themselves increasingly unable to cope with the more theoretical and intricate material presented in later years, and would become increasingly more disillusioned as a result.
But those with an aptitude for mathematics who keep in touch with the course material should find it easier than other courses, as much of what they are taught should seem obvious and commonsensical, and the material they are expected to master should seem coherent and logical, and not an assemblage of random facts.0 
kangaroo wrote:Some of the lecturers were quite strict with regard to marking e.g. one error in a proof and one got no marks, or so I heard, to avoid people learning stuff off (but still loads did).
The purpose of bookwork questions though is to 'encourage' students to study proofs carefully and understand them. If they are not able to reproduce the proofs reasonably accurately on exam scripts then this indicates that they haven't mastered the basic principles. I would have thought that normal practice was that if a purported proof went some of the way, establishing some of the necessary steps but messing up others it would receive partial credit. But what is written should make some sort of sense  if it seems merely a parody of the standard proof which makes no logical sense whatsoever in itself, then it establishes nothing, and deserves no credit (even if it might have some words or formulae in common with some standard proof).
But when I was in TCD maths, exams were somewhat eccentric. For example, for many exams, you weren't told at the top of the page how many questions to answer. I'm not sure we were ever told what to do (I didn't go to all the lectures for one reason or another). What I picked up was that it was marked out of what the best person who sat the exam did which seemed to make sense from the results I saw. I know for schol in my year one guy answered all ten questions.
Also, I heard that one lecturer used the following method to "normalize" the results for exams with 6 questions: for two part questions, each part got 7 rather than 8 marks  you were only marked out of 16 if you got both parts of the question correct. Perhaps this is fair for the top people but a bit tougher for people further down. He seemed a tough marker e.g. for schol. in my year, best was 73, next was 59 and next was only 50.
A friend got 69.2% in his finals but wasn't marked up to a first. In DCU (not a maths course), my sister was told that everyone (in the college?) that got 68% was automatically moved to a first. In TCD Maths, they were big into not devaluing the value of a grade but also it was all a bit impersonal. I heard people had complained that the mathematical physics course in first year was very hard (with a high failure rate) but the lecturer said he had to keep up to European standards. It was a bit like the survival of the fittest. Which is fair to some extent but the course would have been challenging if one hadn't done either Physics or Applied maths for the L. Cert. I remember seeing the results for another finals course (3rd year/4th year) and more than half had got F3's (less than 30%) which would ruin your average. These were people who had got through first and second year. One person got a first but I found out she had an eyesight problem and so got 4 hours instead of 3 for exams in a quite room (even though she didn't really need the extra time once the print was clear to her which she said it was). Things may be a bit easier now.
Anyway, I was just making an aside. Your point about an attempted proof having some logic or being partially correct getting some marks seems fairer and may be the way most or all lecturers mark now.0 
take everything wrote: »Hi lads, just wondering if i can get some advice.
Here's my situation:
I always liked maths and physics in school. Got an A1 in LC higher physics and an A2 in LC higher maths (slightly disappointed with this tbh) and always found maths, in particular, easy.
Anyway, wouldn't you know, i did a completely nonmaths based course in college, worked a bit but now i often do think about doing a maths or maths/physics degree.
Thanks.
Thought I would respond to this as I was in a similar enough situation. A1 in LC maths, always my favourite subject but ended up going for something completely different in college.
Started an Open University maths degree last year (age 26) and whilst I do love it, I know that I would have been much, much better at it had I started it years ago. I don't feel that my brain is as sharp as it would have been coming straight out of school and while my interest is high, it probably isn't as high as it would be were I not trying to balance a fulltime job as well.
Now don't get me wrong, it is great fun, and I am pretty sure that if I could actually go back to college properly and throw myself into it, it would be absolutely brilliant. But it is difficult when out of the old studying mindset.0 

Hi im currently a 5th year student and thinking about studying maths in college. I was just wondering does anyone know if the ucc course is good for pure maths. Also from what i gathered from the internet the trinity maths course seems to be more physics based. Is this true? Is it like impossible to get into one of the top english couses and is there any point in going to england at all with the cost and other cons?0

Hi im currently a 5th year student and thinking about studying maths in college. I was just wondering does anyone know if the ucc course is good for pure maths. Also from what i gathered from the internet the trinity maths course seems to be more physics based. Is this true?
It has changed a bit since I was there. When I was there the mathematical physics/mechanics course was a year long course  1/6 of first year.
Now it is 5 credits out of 60 or 1/12 of first year for people who decide to continue on with statistics and mathematical computing in the second half of first year. Details are at: http://www.maths.tcd.ie/undergraduate/mathematics/regulations/index.php?file=jfmath One doesn't have to do any mathematical physics courses in the years after that. It is a different lecturer from when I was there. The people who only do the half year course have a different exam. So they could well be more conscious now of people who haven't done either Applied Maths or Physics for the L. Cert.
Be conscious that looking at the terms for lots of things with maths (or physics) can look scary if one hasn't studied them yet.
Anyway, other people might have other experiences to share from TCD or other maths courses  one might have to do mathematical physics/modelling of physical systems in a lot of courses at least initially. It can be interesting to see maths applied.0 
Given I mentioned something on this, I thought I'd clarify.
It has changed a bit since I was there. When I was there the mathematical physics/mechanics course was a year long course  1/6 of first year.
Now it is 5 credits out of 60 or 1/12 of first year for people who decide to continue on with statistics and mathematical computing in the second half of first year. Details are at: http://www.maths.tcd.ie/undergraduate/mathematics/regulations/index.php?file=jfmath One doesn't have to do any mathematical physics courses in the years after that. It is a different lecturer from when I was there. The people who only do the half year course have a different exam. So they could well be more conscious now of people who haven't done either Applied Maths or Physics for the L. Cert.
Be conscious that looking at the terms for lots of things with maths (or physics) can look scary if one hasn't studied them yet.
Anyway, other people might have other experiences to share from TCD or other maths courses  one might have to do mathematical physics/modelling of physical systems in a lot of courses at least initially. It can be interesting to see maths applied.
Thanks loads. TBH i have no real interest in continuing physics at 3rd level so im really looking for a pure maths course so this is good help. Im just really looking to see if theres any reason that i shouldnt go to ucc.0 
Thanks loads. TBH i have no real interest in continuing physics at 3rd level so im really looking for a pure maths course so this is good help. Im just really looking to see if theres any reason that i shouldnt go to ucc.
Forgot to say: one disadvantage to going to the UK is that they will have done some stuff for A levels not in the L. Cert course. Not sure how big a problem it is but it's nice not to feel behind starting a course. Maybe some people would be disciplined and could catch up during the summer before starting the course. Although it's easier said than done  I know people including myself who hoped to do some studying over the summer between years but didn't.0 
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Ok, thanks, one small clarification: when I said people who go on to do statistics and mathematical computing, that is not all of the course, only 10 out of the 30 credits in the second part of first year. One can do virtually all pure maths in second year (it's a bit unclear if one has to do a stats course): http://www.maths.tcd.ie/undergraduate/modules/index.php?file=sfmaths and all or virtually all pure maths after that: http://www.maths.tcd.ie/undergraduate/modules/index.php?file=jsmaths (technically some courses might be considered "methods" courses rather than pure maths  most of leaving cert maths is methods).0

Thanks again. Is it that important in terms of post grad oppurtunities to have gone to a college with more renown like trin or does it just exclusively depend on your grade
I think there might be bigger variation in the UK in terms of the colleges and how they are viewed. I think the standard demanded may vary  somebody (from the UK, studying at TCD) told me once he saw something in the Times Education Supplement that 90s% in QUB was like 60s% in TCD. I never saw this and tend to doubt that such indepth comparisons were ever done but who knows.
Anyway, hopefully other people can answer this question better.0 
Thanks again. Is it that important in terms of post grad oppurtunities to have gone to a college with more renown like trin or does it just exclusively depend on your grade
For MSc courses it depends on your college transcript and your ability to write a decent cover letter. For PhD courses, grades are arguably less important since applications are more personal. They'll test you oneonone for knowledge of the specific area you're applying to work in. If you can convince them you know your stuff, you're in. University prestige is only really useful for getting your foot in the door for an interview.
I've said iot before, but I think TCD has a better pure maths degree. In UCD you have to mess around in first year doing other things like experimental physics or computer science (or at least you did when I was there). TCD has weaker algebra courses, lacking Galois theory and Ring theory, but on the whole I think it's a more complete degree.0 
I've said iot before, but I think TCD has a better pure maths degree. In UCD you have to mess around in first year doing other things like experimental physics or computer science (or at least you did when I was there). TCD has weaker algebra courses, lacking Galois theory and Ring theory, but on the whole I think it's a more complete degree.0

TCD has weaker algebra courses, lacking Galois theory and Ring theory.
I suggest that it is incorrect to claim that the TCD undergraduate curriculum lacks Galois Theory and Ring Theory.
Abstract algebra has been taught at TCD to 3rd and 4th year students (combined) every other year for decades. Current semesterlong modules are MA3411 and MA3412, last taught in the academic year 200910. These succeed the former yearlong course 311. Topics covered include Galois theory, including in particular the Galois correspondence, calculations of splitting fields of polynomials of low degree with rational coefficients, together with their subfields and associated Galois groups. Also a proof that certain quintic polynomials are not solvable by radicals. There is of course a fair amount of prerequisite material that has to be developed first: finite field extensions and the Tower Law, basic properties of finite algebraic extensions, ruler and compass constructions, finite fields, solvable groups etc. On the basis of a quick glance at the UCD website, I suggest that the ground covered corresponds to the main part of UCD module MATH40300, including the first of the 'possible further topics', namely 'solvability of polynomials by radicals'.
With regard to ring theory, these undergraduate modules have included discussion of rings and modules, Noetherian rings and modules, Hilbert's Basis Theorem, the correspondence between affine algebraic varieties and ideals of polynomial rings in several variables. Hilbert's Nullstellensatz was included in the undergraduate course some years ago.
UCD though has an active research group in algebra, and, on the basis of a quick visit to the UCD maths website, it is clear that that the Level 4 Algebra modules such as MATH40010 (Ring Theory) and MATH40120 (Commutative algebra) go well beyond what is covered in algebra in the TCD undergraduate curriculum, and indeed seem to me to be pitched very definitely at graduate level.0 
My mistake. I just remembered looking through the TCD course list and not seeing it.0

Im currently in first year studying medicine, but to be honest Im not very happy in it. I have always loved maths in school, maths and applied maths were my favourite subjects and by far the ones I excelled in, I always had a natural talent and interest for the subject. They were definitely the subjects I enjoyed the most. I was in a dilemma for ages as to whether to choose maths or medicine. I ended up choosing medcine. I realise now that its not for me and I often say to myself I wish I was doing something mathsy when Im in a physiology lecture or whatever, I kind of miss not being able to work with maths everyday as in school.
But Im torn now as to whether I should change courses and go into mathematical sciences. Ive always heard stories about people who hated the course and thats what put me off in the first place. Plus what career oppurtunities are there out of it? I find statisitics rather dull so I dont know if actuary would be for me. Plus I hate working with computers/learning about them.
Can anyone give me any insight on what I just said or have any comments on the course or what I should do? Its early days I know but I feel I should start really consider this. Thank you for any replies!0 
Im currently in first year studying medicine, but to be honest Im not very happy in it. I have always loved maths in school, maths and applied maths were my favourite subjects and by far the ones I excelled in, I always had a natural talent and interest for the subject. They were definitely the subjects I enjoyed the most. I was in a dilemma for ages as to whether to choose maths or medicine. I ended up choosing medcine. I realise now that its not for me and I often say to myself I wish I was doing something mathsy when Im in a physiology lecture or whatever, I kind of miss not being able to work with maths everyday as in school.
But Im torn now as to whether I should change courses and go into mathematical sciences. Ive always heard stories about people who hated the course and thats what put me off in the first place. Plus what career oppurtunities are there out of it? I find statisitics rather dull so I dont know if actuary would be for me. Plus I hate working with computers/learning about them.
Can anyone give me any insight on what I just said or have any comments on the course or what I should do? Its early days I know but I feel I should start really consider this. Thank you for any replies!
You could fill in a CAO form and keep your options open (of course, you might be able to transfer within your college but it can be nice, if you have the money, to at least have the option of going to another college).
I'm not sure I'll be able to write a long reply now as I could be called away but I had the points to do medicine but didn't regret choosing maths. I was a bit of a fussy student so didn't like to learn too much off without understanding it or too much learning off in general so enjoyed studying maths. I think I would have found studying medicine frustrating trying to cram a lot into the brain and not always having time to think things through or see how they might connect.
I wasn't into computers before I went to college  I was a bit blown away by the jargon I think  but enjoyed them in college.
If you are a bright student who studies, there are other statistics possibilities. But if you definitely don't want a job involving statistics or computers, your career options are reduced compared to many maths students.
You could always do a course e.g. arts degree (Economics, Psychology, etc) or some science degree in some colleges that allows you do other courses/subjects.
It is my opinion that if you want to study maths, it's best to try it when young when your brain is sharp and your memory is very good. It's less of an issue with some other subjects I think  with some subjects you might even be better with a bit of life experience.
I'm sure other people can make other interesting points.0 
Maths sciences at UL. From my experience I can say that the emphasis in the maths sciences degree at UL is on what they call mathematical modelling, i.e. solving real problems using mathematics. Most of the other universities seem to specialise in pure mathematics for its own sake which actually involves little problem solving and lots of proving technical theorems. So if you like solving real problems and using maths to understand things, the UL course is the one.0

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One might say proving a theorem is solving a problem no?0
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