The Process of Learning Mathematics
University modules go much faster than A-level teaching, therefore beginning a Mathematics degree can often come as a shock. We ease the transition for you by taking the first year gently, but it's still easy at any stage to fall into the trap of doing too little work.
With that in mind, these tips might help...
Work at those exercises! It is essential to back up every hour of lecture time with at least one hour of private study on the same topic. When you get an example sheet, the ideal is to do all the exercises within a week, by your own effort. Only the best students will manage this all the time. Often there are three sections - A, B, and C - on an example sheet. Section A is the most straightforward, Section B is slightly harder, and contains the exercises for handing in, while Section C contains exercises that go a little further afield. Some of these are quite hard, while others touch on topics that stray from the syllabus, but that the lecturer couldn't bear to leave out. You should attempt all the questions which you are asked to hand in. (Marks on written assignments tend to average around 70%: be aware that examination questions may be rather harder.) Discuss with the people in your supervision group, or with friends from lectures, those questions which you (or they) can't do. If you are really stumped by a large proportion of the exercises, talk about it to your tutor, who may well be able to help.
Solving is winning. "Each time you succeed with a problem, you have won a small victory over the mathematics." It boosts you psychologically, and your mind stores the mathematical ideas involved.
Mathematics is not a spectator sport. It's tempting to ask your supervisor to show you how to work out the problems. But that isn't the same as trying it out for yourself. If, before hearing how to do a problem, you work on it by yourself or with a friend, you'll be much more likely to take it in.
Mathematics takes time to absorb. The absorption takes place as you do your written work. So keep up with it!
Files and ring-binders are hopeless at learning mathematics. Don't collect lecture notes and store them away in a file or folder on your computer. Air them, read them, discuss them with your friends, your supervisor, your tutor. Ask the lecturer questions too: they wants to share their enthusiasm with you. Talking about mathematics makes it live. Then read your notes again and see how any remaining problems have become more transparent.
Personal Organisation and Work
Your most important resource, which to get a good degree you need to draw heavily on, is your own effort and determination. Try to be organised and systematic. Try to keep on top of your work. You are responsible for organising most of your time while at university. Many maths students found it possible to revise for A-level modules in the few days before the exam, but this is usually a disastrous strategy for university modules. Modules cannot be learnt in a week. You need time to think about the theory and practice on examples.
If you have problems understanding things, ask people: other students (in your own or higher years), your supervisor, your tutor, the lecturer.
Study Skills
New students (and some experienced ones too!) may need to build up their study skills to get the best out of the effort they put in to their work. The university library keeps books on study skills under LB1049 or LB2395; you are encouraged to spend some time looking at these. We recommend books by W. Cassie, R. Freeman, A. Howe, L. Marshall and A. Northedge, and the pamphlet, D. Burkhardt (Ed.), Study Skills in Mathematics. This last contains some good hints on problem solving, and you will get more from G. Pólya, How to Solve it.
Preparing for Exams
When starting a module, your first target is to absorb the lectured material and the lecturer's problem sheets. Later in the term, and in the run-up to the exam, test yourself out on past exam papers, which give a good indication of the standard expected.
In the third term, many lecturers give a revision lecture on their module, which should help you see its overall structure.
There's no point in trying to guess what will be on the exam paper. Rather than worrying about what will be on the paper, you're better off thinking through the material of the module, and making sure you know what the theory means in practical problems such as those on the example sheets. Even if you don't have much time, there's just no point in trying to memorise your notes; aim to analyse a corner of the theory, and work it all out in a case you can understand.
The University Library
Find out more details in the textbooks section of this handbook.
The Mathematics Society: WMS
The Maths Society (WMS) offers opportunities for involvement in both academic and social activities. Although officially a society of the Students Union it also has close links to the department.
They publish guides to the more difficult and important modules for the benefit of first year students. They also arrange extra informal tuition by second and third year students, in addition to official supervisions. They also hope to provide an introductory course and guide to LaTeX, the popular computer typesetting package for maths, which is invaluable for writing essays and projects.