By Aadi Mankodi, 1st Year Mathematics MSci
The transition from A-level maths to university-level maths is a significant leap, in terms of the style of teaching, and the mathematics itself. Here are some key changes:
From abstract algorithms to absolute precision
At A-level, maths often feels like being given a set of instructions.
You learn an algorithm that is seemingly plucked out of thin air. You apply it – and voilà, you attain the correct answer. For example, you use the formula for the inverse of a 3×3 matrix, or you assume that cubics always have 3 roots. Perhaps you were just told that integration yields the area under a graph, which to me at least, sounded pretty magical. However, at university, there are no assumptions or memorised formulae whatsoever.
At university, you will notice that every single concept is rigorously defined and derived from first principles. University mathematics does not allow for memorization; every theorem, every proof, and every technique is built from the ground up. You don’t just use maths—you understand why it works. This has taught me how to solve problems logically. Here’s an example:
Convergence of a sequence
Take the sequence un = 1/n which intuitively approaches 0 as n increases. But how do you know for sure? And what does convergence even mean? At university, you’ll learn the formal definition of convergence:
In other words, if a sequence converges, then no matter what positive number you pick (eg. 0.01 or 0.0001), you’ll find a point beyond which every term stays within that distance from the limit. We can make this number as small as we like. This is a more concise and clever definition, right?
This appears in my favourite first-year module, ‘sequences and series’, where you start with no knowledge of sequences, and then by the end, you’ll be able to prove convergence without even knowing the limit, and you’ll also prove facts like exponentials grow faster than polynomials.
Learn by doing – the tutorial system
University maths isn’t about passively absorbing information. It’s about struggling through problems, discussing ideas and sometimes being creative. One of the most distinctive features of university life is the tutorial system. Led by a PhD student, you will solve weekly problem sheets together, often in small groups of around 15 students, making the experience far more interactive than in lectures.
You are taught by the best
Your lectures are delivered by experts – professors who hold doctorates and many of whom are currently at the forefront of research. The benefit of this is that their explanations are crystal clear; the clarity and depth will amaze you. Beyond that, these professors are accessible. They hold dedicated office hours where you can turn up and ask them any queries, one-to-one.
Independence
At university, no one tells you when to start revising. You won’t have someone constantly chasing you to submit assignments. You are now in charge. On one hand, this lets you structure your day however you like. But with that freedom comes the challenge of discipline. The temptation to procrastinate is real, trust me, but fall behind for even a lecture, and the next lecture may be incomprehensible. The pace is quick, and material piles up fast. How to manage your time is up to you.
To sum it up, maths at university is proof-heavy and oftentimes challenging, but nothing beats the thrill of problem solving, or the sweet sense of reward after finally cracking a problem.
Leave a Reply