What a maths degree is really like
School maths is mostly about getting the right answer. University maths is mostly about showing why the answer is right.
The big jump: proof
At A Level you learn methods and apply them. In the first year of a maths degree you go back to things you thought you knew, like numbers, functions and limits, and build them up again from definitions. Almost every question asks you to prove something.
Many students find this the hardest part of the first year. It's not that the maths is harder to calculate. It's that the way of thinking is new. The good news is that it's a skill, and it gets easier with practice.
Typical first-year modules
- Analysis - limits, sequences, series and continuity, done carefully with proofs.
- Linear algebra - vectors, matrices and the spaces they live in.
- Calculus and methods - differential equations and techniques you'll use everywhere.
- Probability and statistics - the maths behind data and uncertainty.
- Groups or number theory - your first taste of abstract algebra.
- Mechanics or modelling - using maths to describe how things move and change.
After the first year
From the second year you usually get more choice. Most courses let you lean towards one of these areas:
- Pure maths - algebra, analysis, geometry and topology, for the love of the ideas themselves.
- Applied maths - fluids, waves, climate, biology and finance, using maths to model the world.
- Statistics and data science - very popular with employers.
- Computing - many courses include programming in Python or similar.
How teaching works
Expect lectures, smaller tutorials or problem classes, and weekly problem sheets. The problem sheets are where most of the learning happens. You'll spend a lot of time stuck on a question, and that's normal.
Is it for you?
You'll probably enjoy a maths degree if you like the "aha" moment of seeing why something works, you don't give up after the first try, and you enjoy the hardest questions on a paper more than the easy ones. Trying a few NRICH problems or a past STEP or MAT question is a good test.
Not sure yet? Lots of degrees use plenty of maths: physics, engineering, economics, computer science and natural sciences. You can compare courses on UCAS.
Last updated October 2026.