The Masters Course is a four-year ‘integrated masters’ course in which the first three years are equivalent to a typical mathematics bachelor’s degree, and the final year involves research in a specialist area of mathematics.

Studying maths at university teaches you not only to think abstractly but aptly demonstrates that it is indeed a *creative* subject. Maths is not simply about crunching numbers or solving equations: one critical difference between school-level maths and university maths is the concept of *proof*. A proof is a sequence of logical steps that lead you to something you want to *prove*, and if what you’re trying to prove is an especially important result, it’s often called a ‘theorem’. As such, definitions, theorems and proofs are the buildings blocks of mathematics. At school, we’re often presented with various facts and examples and then taught to apply those results in a particular way. At university, we take a closer examination at *how* these results came about.

Maths at university can be loosely divided into two strands: ‘pure maths’ and ‘applied maths’. Pure maths typically involves studying maths (and mathematical problems) for their own sake, whilst applied maths typically focuses on the application of maths to real-world problems. Pure maths can itself be split into two broad categories, namely, ‘analysis’ and ‘algebra’. However, the lines between these strands are very often blurred.

At UCL, the first year and a half consists of compulsory modules only, so that every maths student is given the same treatment of pure and applied maths. Other universities offer more flexibility in this regard. However, I don’t think having these compulsory modules is necessarily a bad thing: it is easy to fall into the trap of prematurely writing off some parts of maths if you have not yet been exposed to the full depth of those fields. For example, a typical introductory course about group theory (which, if you like, is the study of ‘symmetry’) might focus mainly on what a group is and some ways of classifying them, but only more advanced courses truly exhibit the beautiful interplay between geometry and groups. Lectures normally last around 2 hours, and some courses offer ‘problem classes’ in which problems similar to those found in your homework (called ‘problem sheets’) are discussed. We typically got around 4 problem sheets per week.

My area of specialism for my masters thesis was about the intersection of spectral theory and analytic number theory, which are two very active areas of research. The fourth year is a good chance to get your hands dirty in a field of your choice, some of which involve working on novel research problems which have not yet been worked on. The contents of masters projects vary considerably, with some involving detailed expositions of specialist areas of pure maths, and others involving lots of opportunities to use programming to generate real data. In some cases, students have ended up publishing a paper out of the results they found, which can happen if your thesis contains plenty of original mathematics.

The project offers a great insight into how mathematicians work: contrary to popular belief, mathematics at the highest level is done by intuition, by *instinct*: ‘this is how I *think* it should be, and I must prove that it is so.’ You might even be trying to prove something which may not actually be true! This is how new mathematics is born: we take an idea from the field, combine it with an idea from another, and use it to produce something new. Something *original*. Something which has *never been done before*.

Employers place a high value on the skills a maths graduate has. They typically aren’t necessarily interested in what exactly you studied during your maths degree, but rather your capacity to think abstractly, analytically and problem-solve. Some industries (e.g. quantitative finance) may be interested in hearing about which modules you have studied if they are relevant to the job, such as financial, statistics or programming modules. A maths degree offers a wealth of career opportunities in many fields, with many graduates working in a field they’d previously never imagined themselves working in.

Students often pursue a maths degree for various reasons. Some students study maths with the intention of pursuing a particular career, or going into academia. I studied it simply because it was *fun*, which is certainly a good enough reason for studying mathematics!

So, what are you waiting for? Learn more about where you can study a Mathematics degree on the UCAS website here!