Throughout my university education, I tried incessantly to be a good student and I took pleasure in inflating my marks. Despite being one of the few students not having studied pure maths at A-Level, I almost exclusively achieved firsts (only once achieving a 2:1 in French, which I then improved the following year) and finished my undergraduate degree in Maths with awards for my high grades and requests from my teacher to continue my studies for the sake of science. Now that the memory of Bristol is becoming more and more distant, I want to tell you, reader, how I did that.
Before you’ve even started studying, imposter syndrome might set in. Don’t let the doubts about whether you deserve to be in your institution block your path. I remember thinking that everyone else had studied further maths; that maths was what the other students dedicated their lives to (while I just liked it enough); that my occasional lack of comprehension was proof that I got into this university on a whim and I was not as worthy as the other students. To those thoughts, I invite you to reply “Let’s see how far I can go with this.” If you really did get into an amazing university with students who are supposedly superior to you then let’s see how much you can take from this university: how many classes and mentally stimulating problem sheets, how many afternoons in your cherished campus until they realise that you’re not supposed to be there. Try your damndest to keep up and maybe you’ll surprise yourself and find that that drive is exactly what is going to keep you where you where you want to be. If you’re not supposed to be there: cash in.
Alternatively, maybe you got into a university which you think you’re too good for. Prove it. If you’re too good for this uni, then get a first and have them begging you to do a PHD. I dare you.
When starting university, you need to build skills as well as learn content. You know how to memorise the notions and how to apply the formulae – you’ve been using this kind of skill since GCSE – but building analytical skills or learning to write elegant proofs cannot be done in an evening or with a pack of flash cards. When learning to write proofs, I recommend to you to write out the teacher’s proofs and annotate the relevance or each sentence. I also used to break down big proofs into the function of each paragraph and then imitate it afterwards. You could also use this approach for applied maths: note the techniques used at each stage of a response at the side of the page and then try to do it yourself. Remember, though, that you a building a skill and this will take effort and repetition. If you’re not quite getting it on Tuesday, give it a good go (at least 20 minutes of actively trying to understand a method or a style) and then come back on Wednesday. You might not be used to having to leave something unfinished for the evening but Rome was not built in a day and your first year is essential for building a good foundation so use your time generously for your study.
PS. A small proof tip I have is to define any theorems you’re going to use in your introduction and then you won’t forget how you were planning to tackle the problem and you won’t need to define them later, which will improve your flow.
I didn’t consistently read the lecture notes before class started but when I did I felt rather proud of myself. I knew what was coming up in the lesson and therefore like I had an advantage over other students and if something didn’t click when I was reading, sometimes simply the teacher’s intonation would clarify all of it. A quick glance over the content (not necessarily absorbing any of it) is all it takes to feel smug and curious before the lesson even begins.
Conversely, consolidating content.
If you didn’t understand the lesson, the best thing you can do is actively review the lecture notes. Explain them aloud or write them out in a conversational tone as if you were explaining it to yourself. In maths in particular, this can render the abstract more intuitive and allow you to manipulate concepts more easily. Throw in an example or two if need be, to concretise your understanding.
Also, find some chums to discuss with after class. Even if you just complain about a homework problem, chatting with a friend can make topics more memorable. Don’t be shy about not getting something: your friend may rephrase the content and turn out to be a better teacher than the initial lecturer. So complain, rant, explain, or just make jokes about the lesson, and this might contribute to the community in your course simultaneously.
Taking this further, be present and helpful on your course group chat around exam season! You’ll find that other people may pose questions which highlight a gap in your knowledge or that explaining to another solidifies your own comprehension.
Even after your course ends, it could be nice to honour what you have learned using books and documentaries. I read Alex’s Adventures In Numberland after my maths degree just for the nostalgia and I ended up adding some niche trivia to my expensive education. Your knowledge should inspire you and stimulate you, not stress you out.
Be a teachers’ pet: you paid for it.
In first year, I frequented teachers’ office hours and I’m glad I did because receiving maths through verbal and illustrative demonstration helps me to surpass the abstract words on the page. If you have a quick query, don’t be afraid to send an email or chat with the teacher after the lesson. Put up your hand to ask or answer questions - sitting at the front might make this less scary since you can’t see all of the other students. These teachers are experts in their field so interact with them and enjoy their thought-provoking conversation – use it to nourish your own curiosity and to motivate yourself to make them proud. Many a time, teachers sent me extra articles or books after I had expressed a curiosity or lack of understanding to them and thus I have resources to further my study despite having graduated.
Better than knowing the content, know the teacher’s style.
I noticed when doing functional analysis past papers that there was always a question requiring a certain technique following a question requiring another technique: this knowledge was indispensable in the final exam! I almost wasted time trying the wrong technique until I remembered this and then recited a perfect answer, of which previous exam papers had assured me the correctness. Knowing the teacher’s style can give you a hint about the content of the exam (where to focus your revision) and helpful insight about strategies required. As well as this, they’re a booklet of fun problems which are tailored to your competences – what’s not to love?
The above advice is applicable only when you already have a study schedule and you do what is required to you to keep up with assignments and content, but how you do this depends on your learning style, your waking hours, your extra-curricular activities, etc. I can’t give you a study plan but I can give you the above flourishes to make a good routine even more effective and I can leave you with some final advice: don’t lie to yourself. Don’t tell yourself that something is good enough when you don’t think it will get you what you want. Sometimes you just don’t get things and you may need to take a jog or go to the bathroom to think about it with a clear mind or sometimes you don’t have the time to waste on a single problem when other assignments are urgent – that’s okay, but give yourself the best chance of getting it right by beginning it early and prioritising your study first and foremost. Don’t hope for a grade, work for it: effort is much more dependable than chance.
