People study maths at university for many different reasons. For some, it's professional training for a future career as a mathematician in academia or industry, or as a teacher. For others, a maths degree opens the door to a large number of professions where quick-wittedness, clear thinking and an ability to work with numbers are called for. Many graduates go into the financial sector - as accountants, actuaries, investment bankers and financial analysts, for example - and another large group goes into IT and computing. Generally speaking, graduates who opt for one of these possibilities have to receive some training when they begin work, but the top companies compete for graduates with an upper-second or first-class degree, and pay them handsomely, even as trainees.

In the UK there are different types of maths degrees. Besides the three-year BSc (four years in Scotland), most leading universities offer a four-year degree called an MMath. Even though the first M stands for "Master", this is an undergraduate degree. The first two years are more or less the same as the BSc, but the final two years are more demanding, and take students closer to the frontiers of research.

Students entering university on one degree can transfer to the other if their interests change, and since the MMath is tougher than the BSc, students who do not maintain a good average grade in their first two years usually transfer to the BSc in their third year. Many of those who complete the MMath go on to higher degrees. Everyone who thinks they might want to do this should begin their studies on the MMath rather than the BSc, and change later if they find that the MMath does not suit them. Besides these two degrees, many universities offer joint BSc degrees such as maths and economics, maths with business studies, or maths with physics.

Studying maths at undergraduate level is rather different from studying maths at school. It is much more rich and interesting, but for many first-year students the overwhelming impression is that it is much harder. Of course you are expected to be more independent than you were at school, but the main difference is the emphasis on proof, and on solving new and unfamiliar problems. Proof, or rigorous, deductive thinking, is what mathematics is about. When you are studying the geometry of 11-dimensional space, or the factorisation of 1,000-digit numbers, there is very little else to guide you. But it's amazing where rigorous thought will take you, and how exhilarating its subtlety, power and versatility can be, and by the end of their first year, most students begin to feel this.

Of course, the level of difficulty varies from institution to institution. One of the things you have to decide is whether you want to be on a demanding course at a top university (typical entry requirement AAA, or AAB), or whether you might flourish more in a less demanding environment.

Besides the level of difficulty, one of the differences to look out for is the extent to which you can tailor your degree to suit your interests, whether in academia or the financial sector. Although you might see yourself as one or the other, your views may change. If you are ambitious, look for a university with strong research. The Higher Education Funding Council assesses each university department on the strength of its research, and gives it a rating from one (weak) to five (strong). Many departments advertise their rating on their websites.

Departments that actively research are more likely to have passionate and inspiring lecturers, though they will also have other concerns besides their teaching! A research-active maths department will have graduate students who provide additional small-group teaching, and provide a valuable bridge between undergraduates and lecturers.

David Mond is professor of mathematics at the University of Warwick,