# Study Guide

## The process of learning mathematics

University modules go much faster than A-level teaching. (They make the sixth form seem like a lazy idyll in lotus-land.) Therefore beginning a Mathematics degree is always a shock. We ease the transition for you by taking the first year gently, but it's still easy to fall *at any stage* into the trap of doing too little work.

**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. (Your social or sporting life is important too - nobody denies that - but if you don't limit those pleasant activities, expect only a third-class degree.) 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 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. But you can tell you're really falling behind if you don't even try to do all the questions in Section B! You should certainly do 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 without the pain of rote-learning.

**Mathematics is not a spectator sport.** It's tempting to ask your supervisor to show you how to work out the problems. But it only does a tenth of the good. "Oh, YES, now I see" - but have you really learned anything? Given the same type of problem two weeks later, you may well have forgotten. Some lecturers prepare solutions for posting on the web. Usually only the solutions to Section B are given. If, before hearing how to do a problem, you had worked on it by yourself or with a friend, you'd be much more likely to take it in. Working on a problem yourself helps to make nets for catching ideas with. If you haven't done the work, the ideas just fly right by you.

**"I [don't] understand" can be misleading.** How often have you said something like, ``I understood everything she said in that lecture''? Doubtless she's an excellent and popular teacher. But can you do the exercises she set you? If not, sorry, but you don't really yet understand what she said. On the other hand, if you *can* do the questions for some module, then you *are* understanding it (and so you needn't worry too much).

**Mathematics takes time to absorb.** The absorption takes place as you do your written work. So write early and write often.

**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: he wants to share his enthusiasm with you. Talking mathematics makes it live. Then read your notes again - and then see how any remaining problems have become more transparent.

## Personal organization 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 reasonably organised and systematic. Try to keep on top of your work. Most of your time is not scheduled by the university, but when exams loom you'll find you wish you had done more work earlier. 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. PĆ³lya, *How to Solve it*.

**Preparing for Exams.** On 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 - it may or may not be related to last year's paper, or to hints you think the lecturer dropped, and it's extremely unlikely to be related to the silly rumours that sometimes develop in the heat of Term 3. 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

Library Home Page | Searchable catalogues | Book suggestions

Many book, especially standard recommended text books for your modules, will be available through the library as e-books which you can read online, or often download as pdfs (be aware that sometimes there is a limit on the number of chapters you will be allowed to download).

In the main part of the physical University Library is an excellent wider collection of mathematics books. Get into the habit of browsing - books contain all sorts of interesting things! If you don't understand part of a module, try to find the material in a book. Learn how to track down books on a particular topic by browsing, using the library online catalogues and the review journals, guessing, and, when all else fails, searching physically through large numbers of books. You can't be a serious academic or scientist without detective work in libraries, and although resources available on the Internet are easier to locate there is still no substitute for browsing books.

During your first week at Warwick you should make yourself familiar with the Central Campus Library, there are excellent resources on their website to introduce you to the facilities available. If you need further help during your course, ask at the Enquiry Desk on Floor 1 during office hours, consult the printed guides and leaflets available on each floor or contact the Library's Science Team. Helen Ireland (email: H.Ireland@warwick.ac.uk) is the Subject Librarian for Mathematics and the departmental library representative is Sheetal Sharma. Contact either of them about any books which you feel ought to be in the Library, or if there are not enough copies of key texts. (Library matters can also be raised at SSLC meetings.)

You can also find books in the University bookshop as well as well-known online retailers! We do not expect you to buy your own copies of textbooks, but for some modules you may find it useful to do so, especially modules that you may find yourself struggling on. Standard maths textbooks will typically be around 40 pounds to buy from new, but cheaper copies can be found online second-hand (Amazon is good for this), or sometimes you can find students from higher years selling their old copies through the Student Union. Warwick has an arrangement with Blackwell's that includes a price match guarantee.

## 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.