What degree to take at university is an important decision, and it can be a difficult one. Even if you know that you would like to do something related to maths, you still have to decide exactly what kind of degree it should be. Straight maths? Statistics? Or maybe a joint degree like maths and computing or maths and finance? To make an informed choice you need to know what is being taught in a typical maths degree and what it is used for. Below we look at the main subject areas within maths, and describe what they are about and what kind of careers make use of them.

Logic

Logic is the basis of mathematical arguments and proofs. If you don’t follow logical rules you can end up ‘proving’ nonsense like 1 = 2. The study of logic can sometimes stray into the realms of philosophy and metaphysics, and mathematicians have even used logic to prove there are some mathematical questions that can never be answered.

Calculus, analysis and dynamical systems

Dynamics is an extremely broad area of mathematics, and has many applications in the real world. Much of scientific modelling involves simplifying our complicated reality into a set of differential equations, then using computers to study the behaviour of the simulated system. Mathematicians also use dynamics to produce models of economic systems in the finance industry. These skills are always in demand and these links show how you can use analysis, calculus, and dynamical systems in your career.

Mathematical proof

Proof is the foundation of all mathematics. Beginning with a set of reasonable assumptions, a proof follows logical steps that demonstrate a result that must be true. Without this logical process, mathematicians could not build on the work of others and the whole of maths would come crumbling down.

Geometry

Geometry is one of the oldest branches of maths, used by ancient civilisations to in construct buildings and divide land. It’s also at the heart of cutting-edge science, where physicists use geometry to probe the fabric of the universe.

Topology

A topologist can’t tell the difference between a coffee cup and a donut, or so the saying goes. That’s because topology is the study of geometrical objects without considering things like length, angles, or shape.

Statistics

We hear about statistics daily in the news to describe everything from government spending to the latest football scores, but where do all these numbers come from? The answer, unsurprisingly, is statisticians. Statistics is such a broad area of maths that many universities offer it as a stand-alone course, and the work of statisticians can be quite different to that of other mathematicians.

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