Not good enough for university maths?

I'm currently an A Level student; I've just finished the first year and done my AS exams. I have only recently decided, despite having enjoyed mathematics more than anything else, that maths was what I wanted to do, but after this fairly short while I am already severely doubting my ability to study the subject at a university level... to give a general idea of what I mean by university maths, I think I've enjoyed sufficient academic successes to be shooting for the higher end universities, having performed reasonably well at a pretty awful state school. But I feel that all my achievement in maths is strongly divorced from any notion of mathematical talent; GCSE is of course too easy to consider as an indication of ability or potential university success and my A* predictions and good AS mock performance are almost undoubtedly the result of hard work over true skill. I was way above my peers throughout this year generally but the majority of them did next-to nothing, and I was out-performed or equalled by some in an arguably more indicative Mathematics Challenge (UKMT)
STEP and, to a lesser extent, AEA are meant to weed out the talent from the veterans of regurgitating formulas and recognizing a style of question that you've seen like two dozen times already, and I feel they firmly strand me in the latter category. I either mess up on the plethoras of required details despite understanding in principle, or, in the majority of cases, just don't understand at all; the supposedly lighter introductions such as the booklet "Advanced Problems in Core Mathematics" by Stephen Siklos seldom make complete sense to me (I should note that I have the sufficient knowledge for the majority of the questions, having pre-emptively established a decent grounding in A2 core) and I have been unable to complete any question correctly. I also had a Bronze in the UKMT Maths Challenge, further indicating that I do not possess capability for the insight and structured approach that a good mathematician requires. I have always performed slightly better at the humanities subjects - I stress slightly, at least where the actual exams are concerned - but they bore me practically to tears, and this seems to leave me with the choice of either pursuing something I on the whole detest for the sake of being able to do it at a very good institution, or pursuing what I enjoy and likely not faring nearly as well. Am I being melodramatic, with true mathematical thinking being equally trainable as A level required skills, or is it worth setting my sights on something more manageable?

(edited 9 years ago)

Reply 1

theOldBean

15

Original post by 1 8 13 20 42

I'm currently an A Level student; I've just finished the first year and done my AS exams. I have only recently decided, despite having enjoyed mathematics more than anything else, that maths was what I wanted to do, but after this fairly short while I am already severely doubting my ability to study the subject at a university level... to give a general idea of what I mean by university maths, I think I've enjoyed sufficient academic successes to be shooting for the higher end universities, having performed reasonably well at a pretty awful state school. But I feel that all my achievement in maths is strongly divorced from any notion of mathematical talent; GCSE is of course too easy to consider as an indication of ability or potential university success and my A* predictions and good AS mock performance are almost undoubtedly the result of hard work over true skill. I was way above my peers throughout this year generally but the majority of them did next-to nothing, and I was out-performed or equalled by some in an arguably more indicative Mathematics Challenge (UKMT)
STEP and, to a lesser extent, AEA are meant to weed out the talent from the veterans of regurgitating formulas and recognizing a style of question that you've seen like two dozen times already, and I feel they firmly strand me in the latter category. I either mess up on the plethoras of required details despite understanding in principle, or, in the majority of cases, just don't understand at all; the supposedly lighter introductions such as the booklet "Advanced Problems in Core Mathematics" by Stephen Siklos seldom make complete sense to me (I should note that I have the sufficient knowledge for the majority of the questions, having pre-emptively established a decent grounding in A2 core) and I have been unable to complete any question correctly. I also had a Bronze in the UKMT Maths Challenge, further indicating that I do not possess capability for the insight and structured approach that a good mathematician requires. I have always performed slightly better at the humanities subjects - I stress slightly, at least where the actual exams are concerned - but they bore me practically to tears, and this seems to leave me with the choice of either pursuing something I on the whole detest for the sake of being able to do it at a very good institution, or pursuing what I enjoy and likely not faring nearly as well. Am I being melodramatic, with true mathematical thinking being equally trainable as A level required skills, or is it worth setting my sights on something more manageable?

I am currently a maths undergraduate. Here are my thoughts:
1. Working hard is very important! To quote Dr.Tony Gardiner of Birmingham University, 'Good mathematicians do not find mathematics easy; they simply worry away at a problem until they find out what is going on.'

2. UKMT SMC and BMO1 are not particularly good predictors of how well one will succeed with university maths. This is because SMC/BMO are largely about 'spotting the trick' on questions which require next to no knowledge. At University level, a big part of the course is 'knowing' things - i.e. the statements and proofs of lots of results. [NB: The 'best' predictor of how well you might do in a University course are (i) Your A-level results and (ii) Your STEP III results.]

3. You are supposed to find STEP hard. A candidate who does 2-3 questions fully and another couple of questions 'half-done' will probably get a high mark in the exam. [Edit: When I did STEP II, I only did 2 questions fully in the 3 hour exam (along with various bits and bobs from other questions) and still got a grade 1. Admittedly the exam was harder than usual that year, but this is indicative of the difficulty of the questions.]

4. If you enjoy solving problems then maths is certainly something you should seriously consider. (As is physics/engineering/compsci, but note that it's much easier to change from a maths degree to one of these than it is the other way round.

EDIT: If you have any questions about maths at the undergraduate level, or about STEP for Warwick/Cambridge etc. feel free to quote me. Quoting is better than PM'ing - if you PM me, then you do so at your own risk since I don't always notice them.

(edited 9 years ago)

Reply 2

davros

16

Original post by 1 8 13 20 42

Am I being melodramatic, with true mathematical thinking being equally trainable as A level required skills, or is it worth setting my sights on something more manageable?

Cutting through the waffle ( :smile:

), I think you need to take a step backwards (no pun intended) and not worry too much about STEP at this stage - many people intending to sit STEP next summer won't even have begun their preparation yet!

You say you've "pre-emptively got a good grounding in core topics" but that is not the same as being taught the topics formally and having the interaction and two-way conversations with a good teacher who can explain the subtleties to you. You can bluff your way through A level with a superficial knowledge of C1 - C4 but to tackle STEP you really need an extra level of maturity which comes with having the time to let the ideas settle in your brain.

Have you tried the more difficult extension questions or mixed exercises from your textbook? Have you tried some AEA questions to get in the mood for tackling extended questions on Core topics? How much time are you giving yourself to try to solve some of the problems (it's not unusual to take an hour or more to start with, or even to leave a question for a day or to and then come back to it when you first start out!)?

Relax over the summer and then go back over C3/C4 fully - check your understanding with a teacher when you return to school. Then start thinking about STEP if you're serious!

Reply 3

Smaug123

15

Original post by 1 8 13 20 42

I either mess up on the plethoras of required details despite understanding in principle, or, in the majority of cases, just don't understand at all; the supposedly lighter introductions such as the booklet "Advanced Problems in Core Mathematics" by Stephen Siklos seldom make complete sense to me… and I have been unable to complete any question correctly.

It would be an exceptional candidate who could do STEP well at the end of the first A-level year. It takes the overwhelming majority of people (me included) months of preparation before being able to do STEPs reliably. The fact that you can't do STEP reliably without months of preparation just means you are not in the top 0.1% of the STEP cohort - that's definitely nothing to worry about yet.

Bear in mind also that A-levels are not designed to teach mathematical intuition, but fluency in computation. BMO performance is almost solely about intuition. You're judging yourself based on a property for which you have had essentially no preparation, which is very unfair (especially since almost no-one else has had the preparation either).

Reply 4

bijesh12

13

I've just finished my degree in mathematics and finance. The maths part was about 80% of the course, so the finance was really minor. Anyway I done alevel maths not further maths and I only had a B. In your first year you're most likely to cover further maths in more detail, with the introduction of a few new topics, this obviously does vary from uni to uni.

If you work hard enough, practice questions and the usual stuff u shouldn't be worried. I ended up with a 2:1. But do attend lectures I don't think you can learn some of the stuff with missing PowerPoint slides. I done my dissertation in applied maths-celestial mechanics yet I never done mechanics at alevel. You will be fine, if you ever need any help on modules like stochatics, probability, statistics give me a shout, I love those topics. Gd luck

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Reply 5

bijesh12

13

In your first year you'll kind of realise what you did in alevel becomes your bread and butter and the foundation for your 2nd year.

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Reply 6

Smaug123

15

Original post by bijesh12

In your first year you're most likely to cover further maths in more detail, with the introduction of a few new topics, this obviously does vary from uni to uni.

Depends if OP is aiming for Cambridge (as the STEP might imply). There, further maths is covered in approximately the first two weeks, because STEP has made sure everyone is au fait with further maths.

Reply 7

Mike93L

12

Tbh if do really well at A Level and STEP then you're going to be fine for uni since they're the best indicators you've got. The main thing I'd say is whether you have a passion for maths which you probably do. If you do then natural ability can be outweighed y enthusiasm and hard work.

On a side note, apparently a guy who got one of the best STEP results ever got a third in maths this year.

Reply 8

arrow900

12

Original post by Smaug123

It would be an exceptional candidate who could do STEP well at the end of the first A-level year. It takes the overwhelming majority of people (me included) months of preparation before being able to do STEPs reliably. The fact that you can't do STEP reliably without months of preparation just means you are not in the top 0.1% of the STEP cohort - that's definitely nothing to worry about yet.

Bear in mind also that A-levels are not designed to teach mathematical intuition, but fluency in computation. BMO performance is almost solely about intuition. You're judging yourself based on a property for which you have had essentially no preparation, which is very unfair (especially since almost no-one else has had the preparation either).

Can you please define well?
I don't mean to brag - quite the opposite tbh- but I'm in Year 12 and have just done Step II I think I got 3 fulls and 2-5 marks worth of partials. Is this performance worth mentioning to Cambridge or should I just keep it quiet as I suspect that it may hinder my application?

Also I'm not one of the maths competition dudes, only really wanted to do maths since the start of year 12. I too got a bronze medal in the senior maths challenge.
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(edited 9 years ago)

Reply 9

james22

16

To give some perspective, I never got higher than bronze at the maths challenge, didn't do very well in STEP, and am currently aiming for a 1st in maths at Oxford.

STEP is probably the best inticator of how well you will do (far from perfect though), but it requires loads of practice to be good at.

Reply 10

newblood

19

Original post by arrow900

Can you please define well?
I don't mean to brag - quite the opposite tbh- but I'm in Year 12 and have just done Step II I think I got 3 fulls and 2-5 marks worth of partials. Is this performance worth mentioning to Cambridge or should I just keep it quiet as I suspect that it may hinder my application?

Also I'm not one of the maths competition dudes, only really wanted to do maths since the start of year 12. I too got a bronze medal in the senior maths challenge.
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You did 3 questions fully and on the other 3 questions you aggregated a total of 2-5 marks (or2-5 marks each)?

I would say that is definitely good for a year 12 even for cambridge as that amounts to scraping a 2 if the former and a strong 2 if the latter.

However was it your aim to focus exclusively on only 3 questions...i would argue thats not the best technique if youre not going to put a bit more meat into your partials rather than just scratching the surface.

Are you sitting STEP III tomorrow?

Reply 11

universal_set

14

Original post by bijesh12

I done my dissertation in applied maths-celestial mechanics yet I never done mechanics at alevel. You will be fine, if you ever need any help on modules like stochatics, probability, statistics give me a shout, I love those topics.

Hi Birjesh,

How are you?

This year, I will be doing BSc in mathematics with management and finance at KCL. I have couple of questions & I hope that you are the right person to guide me.

I love mathematics especially pure side of it which leads towards measure theoretic probability & stochastic analysis. After the successful completion of my degree, I will want to do MSc in financial mathematics or in any closed discipline such as applied maths at Oxbridge/LSE/IC iff I am able to get first class honours throughout and overall.

1) what are the chances of getting full scholarship if a person has first class honours in maths from KCL. (Here is the structure of my degree course:
http://www.kcl.ac.uk/prospectus/undergraduate/mathematics-with-management-and-finance/structure ) What are the other factors that can help to get full funding for taught MSc which I should focus during my stay at university at undergrad level?

God forbid, if I don't acquire first class honours in BSc then obviously I will select a job path for myself where I can use my quantitative skills.

2) what are the chances to get a quant job in financial sector? (Considering the highest qualification of a candidate is BSc + one internship + sufficient participation in extracurricular activities)

If you look at my courses of third year then what are the other three modules I should pick from maths option list. (Sorry, I know it is too early to ask such question but I want a clear direction towards my goal). As I said earlier that one day I want to study advanced level probability (abstract) so that I can understand stochastic processes and its analysis as well (in financial context).

Thanks.

P.S. I will appreciate if anyone else can answer my questions.

Reply 12

arrow900

12

Original post by newblood

You did 3 questions fully and on the other 3 questions you aggregated a total of 2-5 marks (or2-5 marks each)?

I would say that is definitely good for a year 12 even for cambridge as that amounts to scraping a 2 if the former and a strong 2 if the latter.

However was it your aim to focus exclusively on only 3 questions...i would argue thats not the best technique if youre not going to put a bit more meat into your partials rather than just scratching the surface.

Are you sitting STEP III tomorrow?

Ahh no I had a small amount of hope about getting a 1 since the boundary often creeps around 60, but judging by that response I guess I am going to have to retake STEP II next year. ( which I hope should appear a lot easier the second time round, assuming I get an offer which I am severely doubting)

No unfortunately as I have not done FP2,FP3 and essentially a large chunk of Further Maths.
Getting an offer would be bliss and I'm so jealous of those of you with offers and even more so those of you studying maths at Oxbridge.

Reply 13

newblood

19

Original post by arrow900

Ahh no I had a small amount of hope about getting a 1 since the boundary often creeps around 60, but judging by that response I guess I am going to have to retake STEP II next year. ( which I hope should appear a lot easier the second time round, assuming I get an offer which I am severely doubting)

No unfortunately as I have not done FP2,FP3 and essentially a large chunk of Further Maths.
Getting an offer would be bliss and I'm so jealous of those of you with offers and even more so those of you studying maths at Oxbridge.

last year a 1 was 80 i believe(81 maybe?) so i think the absolute lowest a 2 would have been is 60. Thats a very good score regardless, especially since youre in year 12. Many people get into cambridge after getting a 2 in year 13 (but they usdually have a 1/S in the other paper) so you should be proud of your achievements!

But i wouldnt look at boundaries prior to 2011. The increase in boundaries since then has been due to the phenomenal increase in the number of people sitting STEP and the awareness as easy access of soutions/pastpapers as the papers havent gotten any easier.

Reply 14

arrow900

12

Original post by newblood

last year a 1 was 80 i believe(81 maybe?) so i think the absolute lowest a 2 would have been is 60. Thats a very good score regardless, especially since youre in year 12. Many people get into cambridge after getting a 2 in year 13 (but they usdually have a 1/S in the other paper) so you should be proud of your achievements!

But i wouldnt look at boundaries prior to 2011. The increase in boundaries since then has been due to the phenomenal increase in the number of people sitting STEP and the awareness as easy access of soutions/pastpapers as the papers havent gotten any easier.

Please can you consider my credentials and tell me whether or not I stand a chance of getting an offer.
The only reason I took STEP was to prove to my parents that I should do Maths a Uni. Dont take this the wrong way I would have probably been stuffing my brain with Analysis, Number Theory and Group Theory had I not been doing STEP papers but with only 3-4 weeks to prepare it was certainly a stupid and naïve decision.
I feel as if I have let myself down.

GCSE: 6A* 3A 1B
A Levels: A* in maths taken 2 years early but only 89% average

AS: Chemistry B/A ( LOW UMS due to one exam going horribly wrong)
Biology B/A (dropping)
Physics Very high A ( ~97%)
Further Maths (~92-94% mainly due to screwing up D1)

Surely these are quite low relatively speaking.
I just wish there were some other way of proving to Cambridge that I really want to study maths there. TBH I can already picture the rejection letter.

Reply 15

newblood

19

Original post by arrow900

Please can you consider my credentials and tell me whether or not I stand a chance of getting an offer.
The only reason I took STEP was to prove to my parents that I should do Maths a Uni. Dont take this the wrong way I would have probably been stuffing my brain with Analysis, Number Theory and Group Theory had I not been doing STEP papers but with only 3-4 weeks to prepare it was certainly a stupid and naïve decision.
I feel as if I have let myself down.

GCSE: 6A* 3A 1B
A Levels: A* in maths taken 2 years early but only 89% average

AS: Chemistry B/A ( LOW UMS due to one exam going horribly wrong)
Biology B/A (dropping)
Physics Very high A ( ~97%)
Further Maths (~92-94% mainly due to screwing up D1)

Surely these are quite low relatively speaking.
I just wish there were some other way of proving to Cambridge that I really want to study maths there. TBH I can already picture the rejection letter.

I am not part of cambridge admissions nor do i attend cambridge so i dont think my input would be very reliable so youre better off asking someone else specifically if you have what it takes to get in.

Reply 16

miml

17

Original post by 1 8 13 20 42

.

I've just finished a degree in straight maths at Warwick.

1) Most students at top universities find A-levels easy, and nailing them is just a case of putting in the effort as I'm sure you already know.

2) STEP/AEA, although good indicators of the 'insight' required aren't necessarily great indicators of ability to succeed on a degree. This depends to a large extent on what you want from your degree - it is if you are aiming for the 80%+ marks that you need to consistently demonstrate that you have that 'insight' that you need for STEP. (Most people at university don't actually want this, but it's worth observing that mathematicians are more likely, for a large number of reasons, to actually want to get 80%+)

TBH it is quite possible to get a respectable (2.1/low 1st) without ever stretching yourself to the same extent as STEP. In fact, to date, STEP II was my hardest exam (taking into account the mathematical maturity at the time).

3) University is just as much about the hard work/memorisation/routine application of A-levels as it is about the insight of STEP. You need both to succeed.

4) UKMT/BMO are irrelevant. I knew a guy who consistently got to BMO2 but struggled with A-levels. I also know a lot more people who never got more than Bronze and got 80+ in all their maths modules.

5) Bottom line is if you are good enough to meet the offer, you're good enough to study there.

(edited 9 years ago)

Reply 17

hassassin04

17

Original post by miml

4) UKMT/BMO are irrelevant. I knew a guy who consistently got to BMO2 but struggled with A-levels. I also know a lot more people who never got more than Bronze and got 80+ in all their maths modules.

I am sorry but I kind of doubt there are a lot of people that get 80+ in all maths modules. Very very few..

Reply 18

davros

16

Original post by arrow900

Please can you consider my credentials and tell me whether or not I stand a chance of getting an offer.
The only reason I took STEP was to prove to my parents that I should do Maths a Uni. Dont take this the wrong way I would have probably been stuffing my brain with Analysis, Number Theory and Group Theory had I not been doing STEP papers but with only 3-4 weeks to prepare it was certainly a stupid and naïve decision.
I feel as if I have let myself down.

GCSE: 6A* 3A 1B
A Levels: A* in maths taken 2 years early but only 89% average

AS: Chemistry B/A ( LOW UMS due to one exam going horribly wrong)
Biology B/A (dropping)
Physics Very high A ( ~97%)
Further Maths (~92-94% mainly due to screwing up D1)

Surely these are quite low relatively speaking.
I just wish there were some other way of proving to Cambridge that I really want to study maths there. TBH I can already picture the rejection letter.

No one can give an exact answer to your question - if you want to apply to Cambridge, then do so - if you don't apply, you can't get an offer!

Make sure your teachers are going to give you appropriate predictions e.g. A*A*A (I'm not sure what the situation is if you've already achieved an early A* in Maths - Cambridge might ask for grades in a further three A levels but you really should email them and ask what their position is!).

I'll give you a couple of other personal observations which you are free to ignore if you want.

You shouldn't be making decisions based on proving to your parents that you should do a particular degree. You choose your degree, not your parents. Having said this, why didn't you just take STEP I this year to use as your "evidence" and then worry about STEP II and STEP III if/when you have an offer to meet?

Getting a "disappointing" grade in STEP II a year early is not the end of the world - any sort of grade at your age is impressive. If you did get a Cambridge offer, they would simply ask you to sit STEP II and III next year anyway, so it's that performance that matters.

You haven't mentioned your module choices, but D1 is really not helpful either for STEP or for maths at a top uni. (I know some schools don't give you a choice, so it may not be your fault!) If you're serious about Cambridge, you want as much Mechanics as possible under your belt, followed by as much stats (this is assuming that you've done all the FP modules). In case you haven't looked at the makeup of the Cambridge Tripos, you do a fair amount of mechanics and probability theory in the first year, so it makes sense to get a good look at that material. Also, as you know, STEP doesn't include Decision maths, so you're limiting your question choice in the entrance exam!!

All in all I'd say you have a very good chance of getting an offer from the achievements you've quoted already, so why not go for it? Then focus on getting the extra bits sorted - the rest of your FM modules and preparation for STEP II and III.