Cambridge Demystified - Mathematics

Update (August): I got 4A* and 1,1 in STEP so I will be going to Cambridge in October 2020! I'll be happy to continue answering any questions you might have.
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Hello! This thread is part of a series of threads called Cambridge Demystified, started by Oxford Mum and created to help prospective Cambridge applicants. I'm a Cambridge Mathematics first year student (Gonville & Caius College) and in this thread I'll answer a number of questions about my experience with applying to Cambridge.

Why did you want to study your subject? I've always enjoyed maths and problem solving and not been too bad at it (I guess...) but I was actually set on chemistry or chemical engineering up until year 11 or so. I realised chemical engineering wasn't for me since it was too applied and that I actually enjoyed maths so much more once I got to study it at a higher level. I really enjoy solving problems and proving results, and there's a lot of that in university maths.

Why Cambridge? It's obviously one of the best universities I could possibly go to, and I'd already visited it several times to go to subject masterclasses and open days or talks, and the city is pretty nice as well so it was a fairly natural choice over Oxford. I also think the Cambridge maths course seems especially interesting considering the variety of topics studied.

Did any of your teachers inspire you? Or any other expert (TV presenter etc)? Not to a huge extent, but one of my maths teachers in years 12 and 13 would set lots of challenging problems and give us all something harder to do besides textbook work, so that helped develop my problem solving skills a lot.

Which resources did you use? Which books/journals did you read? Which did you like best, and why? What did they teach you? I read about some accessible maths topics (such as modular arithmetic) on the NRICH and Art of Problem Solving websites, which are good for introduction to new topics. I also worked through some books in the Theoretical Minimum physics series, which are very mathematical and approach physics from a much more abstract, mathematical standpoint. I learnt about some more new topics from those books, such as multivariable calculus and matrix eigenvalues and eigenvectors.

Did you attend any lectures, or take part in any competitions? If so, would you recommend them, and why? I went to the Cambridge Subject Masterclass for maths, which consisted of 2 taster lectures and the chance to ask questions about admissions. They were very interesting (the one I went to had a lecture about infinity and countable sets which was very interesting) and going to one of these could give you something to talk about in your PS (though I didn't manage to fit it into mine). I did the UKMT Senior Maths Challenge in year 12 and got a silver, so I didn't get to any follow-on olympiads. I did the SMC again in year 13 and then did BMO1 (British Maths Olympiad round 1). UKMT competitions can be useful for developing your problem solving skills, but you do not have to have done olympiads to get an offer - I'm certainly proof of that! You may find that a lot of offer holders have done them, but this is more because people who are good at maths are more likely to do these competitions, than the converse.

Did you have any work experience? If so, how did you find it? I applied for maths which isn't a vocational subject, so no I didn't do any. You don't have to do work experience for any subject at Cambridge other than Medicine and Veterinary Medicine.

Did you have a specialist subject/EPQ? What was it? How did you go about your research? No - I didn't do an EPQ.

What did you mention in your personal statement and why? I talked about how I was interested in proofs as a kind of exposition on why I was interested in maths. I wrote about the Theoretical Minimum books I read, and what maths I learnt from them. I also mentioned a combinatorics paper I wrote about counting isomers in chemistry, as well as an RSA encryption program I wrote in Python. I mentioned my UKMT competitions and put a short paragraph at the end about non-academic extracurriculars which undoubtedly wasn't very important. The main thing you need to do is talk about subject-related activities that you've done, and what you learnt from them. I hear Cambridge doesn't place that much importance on the PS for maths but it's still important to make it good for other universities.

Which techniques did you use for the entrance test? Cambridge maths is different to most other subjects since there is no admissions test for maths taken in October. Instead, the interview is the main deciding factor in whether or not you get an offer, and then your offer contains a STEP condition as well as A levels. STEP is a series of three-hour maths exams taken in June at the same time as A levels. There are three STEP papers - STEP 1, STEP 2 and STEP 3 (Cambridge gives offers based on 2 and 3 only). The papers have 12 questions that take about 30-45 minutes each to do and the standard offer is two grade 1s (see the Cambridge/STEP website for more information). STEP usually requires months of preparation, so I started working through STEP 1 questions at the end of year 12, then moved onto STEP 2 at the start of year 13 and then STEP 3 in January. I'm now doing questions every day and a timed paper each week (STEP will be online for my year due to the coronavirus situation). It's important to start preparing for STEP fairly early to get used to the question style.

How did you choose your college? Did you go to an open day and if so, did it help you to decide? I was pooled to Gonville and Caius, but I originally applied to Trinity. I chose it since Trinity has a long history of excellence in maths and takes about 40 maths students each year, so I liked the idea of being around more maths students. I liked it a lot when I visited it at the open day. Gonville and Caius is also very nice as well as being very central in Cambridge.

How did you find the interview process? Trinity has a one-hour test with 10 questions that you do immediately before your interview. You get the hour to do some questions and then you take your answers with you into the interview where you go over them and your interviewers help you through the questions you didn't complete. I actually ended up flopping my test because I panicked and kept jumping between questions rather than concentrating on a smaller number. Generally completing three or more full solutions is strong, but I ended up with only 2 full solutions (one of which had a small mistake) and a number of partials so I'm not that surprised I got pooled. In the actual interview, my interviewers asked me to talk through the questions I did and then I completed another 3 questions in the interview with some hints. They usually ask you to justify your steps completely and want to see how you think. Overall it was a pretty good experience (I guess apart from the fact I had a bit of a freak out after what happened with the test).

Any interview tips? If you're applying to Trinity or another college that has an at-interview test, try not to panic (easier said than done) and try to focus on completing a smaller number of questions rather than jumping all over the place. Trinity also has three specimen tests on their website, which you can use to practice. Also in your interview, try not to be too afraid of being wrong - they can tell the difference between someone who has a good understanding but makes a mistake, and someone who has a poor grasp of the subject material.

Did you socialise during interview week? If so, what did you do? I'm not entirely sure what this question is referring to, but I'm not a massively social person anyway. I did quite a lot of preparation the week leading up to my interview though.

How did you feel after the interviews? I thought I'd blown my chances completely after I did so few questions in the test, but I thought my interview itself wasn't too bad as I managed to pick up on hints fairly well.

Where were you when you got your offer? How did you react? I was in the foyer outside my sixth form common room putting my stuff back in my bag and saw the email. I actually locked myself in a toilet stall for a few minutes to process it but I was really happy that I'd managed to get an offer.

Are you looking forward to coming up to Cambridge? I still have STEP to do in June so I'm not guaranteed a place yet or anything, but I know I'd love to study there so definitely!

I'll be happy to answer any questions that you have about the Cambridge admissions process, preparing for STEP, or just applying to maths at university in general.

Really enjoyed reading this! Best of luck with STEP and congratulations on your offer! Maths is such an awesome subject

Hi GreenCub

Thank you for your great chapter!

So what were the salient points, here?

You enjoy problem solving and proving results. This is exactly what your opposite number on the Oxford thread said!

I once met a Trinity (Cambridge) maths student. She told me that many people apply because they are very quick at sums (like a human calculator) but these people don't get in, because it is more about problem solving.

You preferred the topics you will study at Cambridge, over Oxford. To those candidates who have yet to decide between the two unis, what are these topics?

You fell in love with Cambridge when you visited several times. This year, obviously this isn't possible, because of Covid-19, but in future years it will hopefully be different.

Please find the link below for the Cambridge subject masterclasses

https://www.undergraduate.study.cam..../masterclasses

and the talks

https://www.maths.cam.ac.uk/undergra...ssions/openday

Despite lockdown, there are other things you can be looking at online

https://nrich.maths.org/

Art of Problem Solving books

https://www.amazon.co.uk/s?k=Art+of+...f=nb_sb_noss_2

https://www.amazon.co.uk/s?k=Theoret...f=nb_sb_noss_2

Also competitions:

UKMT senior maths challenge

https://www.ukmt.org.uk/competitions...ical-challenge

BM01

https://bmos.ukmt.org.uk/home/bmo.shtml

Also you don't have to get the questions right in the test, as OP said. One Oxford applicant was given a problem to solve. She got home and looked up the answers. She found out that all the answers she had given were incorrect. Sure that she had been rejected, she forgot about Oxford.

Not only did she get in, in her first year she got the top results in the entire college, and got first pick of her second year accommodation (she chose Bill Clinton's old room).

Another stand out was the writing of the combinatorics paper and the RSA encryption program in Python. This was, I assume, done outside of school time, and on your own initiative. You did it because you were simply intellectually curious. This is the kind of initiative Cambridge loves, and it will have made you stand out on your personal statement.

This going above and beyond features in every single offer holder chapter, across both Oxford and Cambridge.

More resources:

Maths sample interview questions

https://sites.google.com/site/oxbrid...ns/mathematics

https://www.cambridgeinterviewquesti...s/mathematics/

(plus recommended reading)

Cambridge maths interview youtube

https://www.youtube.com/watch?v=16WOfGaVfM0

https://www.youtube.com/watch?v=6qYur0ttvzo

https://www.youtube.com/watch?v=fljnOAggS7Y

https://www.youtube.com/watch?v=voCDbss-wOs

https://www.youtube.com/watch?v=1VLr1FGlxHM

https://www.youtube.com/watch?v=hZYlp0qo4R8

Yeah that's true - lots of people think maths is about doing arithmetic and adding and multiplying numbers very quickly, but it certainly isn't about that and many good mathematicians won't even be very good at arithmetic. For those of you who watch Countdown an analogy I like to use is that doing the Countdown numbers game is arithmetic and proving when it is impossible to get the given number is maths.

As for the topics, Cambridge has a huge variety but I particularly liked how there was a breadth of topics in the first year (the 8 topics are Numbers and Sets, Groups, Vectors and Matrices, Probability, Analysis, Differential Equations, Dynamics and Relativity, and Vector Calculus iirc). Cambridge maths also has a large theoretical physics component which I also find interesting - I'm liking what I see of theoretical physics after working through the books I mentioned in my post.

Thank you, Greencub! I am certain you are going to love your Cambridge course.

It's a very well known fact that nobody likes Dynamics and Relativity...

Please do tell me more. I'm intrigued.

Thanks! I'm still pretty stressed because we haven't been told how STEP is going to work or how they're going to prevent online cheating, and I'm still not 100% confident about it yet.

Some people say it's the worst course on the whole degree (e.g. my Director of Studies), but if you're a physics fan you'll be all right to be honest.. And the last part on Special Relativity is interesting.

More kids need to learn about the Art of Problem solving. I'm not a math guy, but I find it incredibly useful! The books are a must have collection in your libraries!!

I am so delighted to hear you got into Cambridge! Any update is great to see, as I am wondering how all the Oxbridge Demystified chapter writers got on. So far, everyone was successful.

Just so you know, right now you are helping a prospective maths applicant decide, with this very chapter, whether to apply to Oxford or Cambridge for maths.

This is why I am so very grateful to you, and to others like you.

I thought I'd bump this in case it's useful for anyone around this time of year.

How have you found the beast that is a Cambridge Maths degree so far? I presume you’ve started this year?

Well done meeting the dreaded STEP requirement. I'm applying to Oxford Maths and Stats. Any tips for the interview?

Yeah it's been going fairly well so far, I think. The course is interesting (though I still can't stand the differential equations sheets which are a drag) and the content is delivered at a pretty fast pace but it's definitely manageable if you stay on top of everything - I definitely haven't been properly "stressed" at any point. I generally prefer the pure courses, which are harder than the applied but much more interesting. I think I'm doing all right in the sense of being able to do most of the questions on most sheets without getting hints, though I've been trying not to compare myself to others too much and there are some really good people here. My supervisors are all very good.

Thanks! In terms of the interview, much of this advice is probably a bit generic but the best thing to do is just practice as much maths as you can before the interview (as they probably won't ask you about your PS or anything like that) and practice explaining your thought process while solving a problem. Just be sure to explain what you're thinking even when you get stuck - having a few pauses is fine as they aren't trying to "catch you out" by intentionally looking to see how much you pause. This isn't to scare you off or anything, but I knew a couple of people who applied to Oxford who ended up being rejected despite being strong mathematically because the interviewers thought they wouldn't do well in the tutorial system. So the important thing is just try to communicate what you're thinking and take hints on board.

Thank you so much! All of what you've said has been so useful. Which was your favourite Theoretical Minimum book / which ones did you read?

(I'm not a Maths applicant though - I'm a hopefully future NatSci).

I've finished the first 2 - Classical Mechanics and Quantum Mechanics and have had a look at the third (Special Relativity and Classical Field Theory) but haven't had time to do much of it yet. Quantum Mechanics was probably the best so far.

Good luck for your natsci application!

Thanks for the recommendations! I still haven't heard anything back from Cambridge (even Imperial has contacted me and they're notoriously slow), so I'm starting to wonder if anything will ever arrive.