A Guide to Studying Mathematics at University

One of the first things that a Mathematics undergraduate will tell a prospective student is that maths at university is entirely different to what you studied at school. Below we’ve outlined some of the key features of a maths degree and some tips on how you can prepare.

Typically students studying maths in high school are taught the method for a particular question which they then apply to practice questions until they get it right most, if not, all the time. They repeat this as they cycle through different modules within the field of mathematics, gradually increasing the bank of methods that they can apply to a fixed question so that they can answer every question type that might appear on their exam paper. Your teacher will grade your paper with a tick or a cross with additional marks for showing your working. It’s all very methodical, predictable and the perfect accompaniment to the old adage that ‘practice makes perfect’.
Maths at university level is not like this. Even the content of the modules is different; what you consider to be ‘pure’ maths, for example, prime numbers, may be included in an entirely separate module (prime numbers are commonly used in cryptography so may be included in a related module). To complicate things even further, each university has its own system of compulsory and optional modules, and different class sizes and styles. However, lectures and seminars (sometimes known as tutorials) are usually present in all university courses.

Lectures are generally not interactive and the element of a course that students are likely to skip (which is a big mistake). A lecture theatre may have up to 300 students all listening to a lecturer who will explain some theory and then usually a couple of worked examples as part of a presentation. Students are expected to take notes. At this point, a lot of students put their notes in a “safe place” and panic that they can’t find them the day before exams. Avoid this stress! Take detailed notes during the lecture (it helps you pay attention if you’re struggling to stay focused) and as soon as possible afterwards, sit down and work through your own practice questions. Independence of learning is the major difference between secondary and tertiary education and usually disarms first years. It’s also a significant source of irritation for university lecturers who find themselves repeating their lectures to young students who are used to being spoon-fed. It’s not the best way to make a good impression on someone who may very well be writing a reference for you at some point in the future. Practicing now will also reduce the amount of work you have to do in exam season and make any follow up tutorials that much easier. It is your responsibility to make sure you’ve understood the theory and how that works in practice – your tutor will only help you if you have clearly been working on understanding something for a while but not quite made it, in which case there is absolutely no shame in asking for help.

Seminars are much more of a collaborative process and while this naturally makes them more engaging, it also means that you have to contribute, so come prepared. Typically students will be using the theory they have learnt in lectures to creative proofs that the maths does in fact work. This is the key difference for maths students stepping up to university level maths. Rather than accepting that the method and theory are correct, undergraduates are required to explore the details of the theory and provide evidence that this is sound mathematics by using other mathematical principles. At this point you will also be taught what may seem like a new language: notation. You will likely have encountered notation before, so it shouldn’t be too alien. However, at university level, your notation (that is, symbols and lettering that represents your mathematical working) is more likely to come under criticism than your actual mathematical thinking. This is where the earlier point about practicing the maths taught in lectures comes in. By following, revising and then applying the mathematics and notation that was covered in the lecture you will be able to follow the seminar much more easily and your notation will naturally improve quickly, keeping you on the good side of your lecturers. Seminars are a time to get stuck in, make mistakes and then be guided to a solution, either by your peers or your lecturer. It’s important to really engage in these sessions so try to push beyond the awkward silence that might punctuate the first couple of weeks.

Further reading and learning beyond the core curriculum is exactly what top universities want to see

So, now that you have a very general understanding of what to expect, how can you best prepare? It’s impossible to provide one hard and fast rule that will work for all students. One of the first things you come to learn at university is that every person is unique and learns in their own way. Having said that, admissions exams provide great insight into university level maths while also helping you study for your high school exams! Most of the top universities in the UK have an admissions exam that applicants are required to take before they apply to the university. There are STEPs, MATs, TMUAs and AEAs. Largely these are all the same in that they call on your ability to apply maths and logic to a series of questions. However, they are also a good bridge between secondary- and tertiary-level mathematics and you’ll find they are harder than most of your high school studies. There are plenty of free online resources for each of these exams so download them and start practicing. Anyone applying to a top university will need to prepare for at least one of these exams anyway but the sooner you start practising the better. If you hate every second of the preparation for these exams, you certainly are not alone but it may also indicate that maths at university is not for you. It’s much better to figure this out before you apply!

All this preparation will work to your advantage, no matter what university you want to apply to. The practice will allow you to explore university undergraduate degrees with a greater understanding of what each module will actually entail, therefore enabling you to make a more informed decision about which university course you want to study. Beyond this, the ability to discuss your interests in a more scholarly manner, and reference advanced mathematics that you wouldn’t encounter before university will significantly enhance your personal statement and show just how passionate you are about your subject. Further reading and learning beyond the core curriculum is exactly what top universities want to see.

 

Immerse Education also offers insight into what Mathematics is like at university. Find out more about the unique academic residential programmes that Immerse runs for 16-18 year olds by visiting their Maths page.

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