Study Skills for Mathematics

In compiling this document we have received help from many sources. In particular we have drawn on some of the Study Skills leaflets produced by the Student Advice & Information Centre in the Students' Union, material produced by the Chemistry Department and a booklet produced by the University Mathematics Teaching Conference at Nottingham in 1981. In addition we have had valuable input from a number of staff and students.

Each section of the booklet consists of a discussion of the issues, and includes a short set of questions for you to ask yourself. If the answers to these questions indicate problems, you should do something about it - either yourself or by asking someone else, for example your tutor or a friend.

Like much of the information produced for you by the School, this is not a document to be read from cover to cover and then put away. Use it as a reference from time to time when you need to, for example at examination time or when you are having study problems during your course.

Remember that studying is an individual thing, but that the ideas and suggestions in this booklet have been found helpful by many students in the past.

We would value feedback on this document. Please tell us if you find any of it helpful, or if there are any additional matters relating to Study Skills that we should include.

The University has a Study Skills Website which you might also find helpful.

A useful recent book giving general advice is: Phil Race, How to Get a Good Degree, Open University Press (1999)

Contents

1 Getting Organised - Managing Your Time

2 Your Working Environment

3 Information - Where and How to Find it

4 Getting the most out of Lectures

5 Getting the most out of Tutorials

6 Problem Solving - Skills and Strategies

7 Textbooks - Reading and Understanding

8 Getting Help - When and from Whom

9 Coursework - Planning and Execution

10 Examinations - Preparation and Revision

1. Getting Organised - Managing Your Time

Questions to ask yourself:

  • Am I spending enough time studying - or too much?
  • Have I reasonably planned the use of my time each week?
  • Is my private study time being used effectively?
  • Does my concentration wander too much when I am studying?
  • Do I often put off studying and do other things instead?

At university you are moving into a new learning environment. You will need to make an early start on organising your time. You will have a number of things competing for your time: study (attending classes, doing coursework, private study...), domestic needs (eating, phoning home, sleeping...), leisure activities (choral society, visiting Winchester, relaxing with friends...).

As soon as you can (during the first couple of weeks) draw up a timetable for a normal week in term-time. This will include lecture times, tutorials, computer labs and private study time. It may include social commitments (e.g. meetings at the Chaplaincy or hockey training). Some times will be fixed and mandatory, like lectures or orchestral rehearsals. Others may be more flexible, like private study and going out with friends.

Plan your periods of study time when you feel at your best and able to concentrate. This may depend on the vagaries of your biological clock! Some people are awake and raring to go at the crack of dawn. Others are at their best in the late evening when (and if) things are quiet. Remember to schedule routine things like reviewing lecture notes as well as meeting requirements like coursework deadlines.

As well as times for individual activities you should plan for the total amount of study time each week. The question of how much this should be is not an easy one. The important thing is that your study time should be used effectively. In mathematics you study four units per semester. As a rough guide you might expect to spend 10 hours per week on each unit (i.e. a 40 hour working week). Of those, three will be lectures and one a tutorial, giving roughly two hours of private study for each lecture. Sometimes you will spend more time, for example during revision or when a coursework deadline is looming. Sometimes you may spend less, for example when studying outside term-time.

Some employees in industry work a 35 or 40 hour week, but those in the professions work rather longer hours. Think of people you know: hospital doctors, school teachers, barristers, police officers, people working in business, and consider what long hours some of them work. A survey of university academic staff conducted a couple of years ago revealed that most were working 50-60 hours per week on average.

As well as the total time spent studying, its distribution is important. Research has shown that periods of about an hour are ideal. Much shorter and little will be achieved. Much longer, and concentration drops. Short breaks enable concentration to become re-established. Periods of an hour during the day when you do not have consecutive classes are therefore useful in this respect, and you are likely then to be within easy reach of help, for example your colleagues on the course. Studying regularly through the year, during vacations and term-time, perhaps peaking near examinations, is also more effective than trying to cram everything into a short period, for example during the Easter Vacation.

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2. Your Working Environment

Questions to ask yourself:

  • Is there too much noise where I work?
  • Are there too many distractions or interruptions where I work?
  • Is the place where I work uncomfortable?
  • Does my concentration wander too much where I am studying?
  • Do I have everything I need at my place of work?

As well as time management you need to consider the environment where you work. It may sound obvious, but most of us work better if we have somewhere which is reasonably comfortable (but not soporifically so) and adequately heated, lighted and ventilated. You also need to be free of things which might distract you. This will vary between individuals: some prefer to work alone and others in groups. Some prefer to work in silence and others with some quiet background music. You should experiment to find which suits you best. If you are living with others in hall or in a house it is often useful to have a friendly discussion to reach agreements about one anotherÍs work needs in terms of noise and interruption. You may find that you work best in the library where you will not be disturbed (find a place in the deep recesses of the Arts section for example, where nobody will find you).

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3. Information - Where and How to Find it

Questions to ask yourself:

  • Do I know where I have put the Faculty Handbooks?
  • Where can I find out officially what I need to know?
  • Who can I ask who will know the answers to my questions?
  • Do I have to pass each unit to progress to the following year?
  • What will happen if I miss a coursework deadline by a couple of days?
  • Which parts of the course are considered more important than others?

Sometimes when you are studying there may be occasions when you are not sure what the requirements are. The important thing is to find the answers to questions which are concerning you as soon as you can, and from a reliable source. Do not rely on what your friends tell you. Tutors are often faced with students who tell them "my friends say that X is true..." when in fact X is completely false. You will have a wealth of written information issued by the School: the Student Information Handbook, particularly the section dealing with examinations, and the Student Programme Regulations. If you haven't already done so, spend a few minutes familiarising yourself with the contents of these documents. You will find authoritative answers to many of your questions in these sources. Other matters appear on notice-boards from time to time, for example at examination time the draft timetables and rubrics appear. It is important to look at the noticeboards regularly to see if anything relevant to you has been posted. A lot of information is now on the University and Departmental Web sites. If you cannot find the answer to the question that is worrying you then ask your tutor, or the course lecturer, or the Director of Undergraduate Studies, or the School Office. If they don't know the answer they will know someone who does!

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4. Getting the most out of Lectures

Questions to ask yourself:

  • Can I hear and see clearly in the lectures?
  • Do I find that the lecture has sometimes started when I get there?
  • Do I find that I have forgotten to bring something important to the lecture?
  • Do I sometimes feel "I wish I had asked ƒ"?
  • Can I understand what is in my notes when I look back at them?
  • Do my copies of printed notes and handouts have my annotations on them?
  • Can I relate my lecture notes to the textbook?

Taking notes is a skill that you need to think carefully about. What follows contains some suggestions, but your task is to develop your own procedures and style so that your notes are as useful as possible to you. You may find that it takes a bit of time and effort for you to find a style you are comfortable with, but the effort will be worth the rewards. You will meet a variety of styles of lecturing during your course and some of them are discussed below.

Continuous Written Presentation
The lecturer develops a detailed calculation or proof, writing it all carefully on the board or overhead projector (OHP). You will need an accurate record of this for later study. This means that if you spot what you think is an error you should ask about it -don't hesitate, even in a large group. The lecturer and your friends will be grateful for your intervention. If you feel that a lecturer is writing unreasonably fast see whether your colleagues in the class agree. If not you may need to work at speeding up your note taking. If they do agree then you should approach the lecturer individually or as a group and explain (in the nicest possible way) the difficulty in keeping up.

Even with continuous written presentation there may be additional spoken explanation taking you from one step to the next. For example "multiplying out the brackets gives...". Try to jot this down in your notes, perhaps having quite a large margin for such purposes.

Spoken Discussion
Here the lecturer may be writing calculations on the board, and then may pause to try to explain some aspects verbally. For example if there is a diagram the discussion may involve the lecturer pointing to various parts of it and explaining the relationship between the parts. Sometimes the lecturer may discuss some real world problems which give rise to the equations whose solution forms part of the lecture. Sometimes the lecturer may offer some analogy to try to help you appreciate the meaning of a new abstract idea. It is important that you make some notes as this is happening. You may not be able to take down verbatim what the lecturer says, so you will need to cultivate an abbreviated form of taking such notes, using keywords, or key phrases. In particularly difficult cases the lecturer will usually be happy to explain the idea again if necessary. However, we are not mindreaders, so you have to ask! Do not feel embarrassed! If you are finding something difficult then so are a good number of your colleagues. You will earn their undying gratitude, and perhaps more surprisingly that of the lecturer, with appropriate questions during lectures. If you find it difficult to ask questions during a lecture, approach the lecturer as soon as the lecture has ended.

Lectures based on a textbook
Here there is likely to be much less detail by way of calculation on the board or OHP. The lecturer may go through principles underlying a calculation or proof without giving all the steps. Make sure that you have an accurate record, perhaps leaving plenty of space so that you can fill in the details when you work though the appropriate section in the textbook. Note down carefully page references which the lecturer gives.

Lectures based on printed notes
Sometimes a lecturer will provide printed notes for all or part of a course. There may be handouts, for example when there are detailed calculations which you need to understand but for which it would be an inappropriate use of time simply to copy down. You should expect to annotate these handouts during the lecture, as the spoken discussion will often be explaining the principles underlying what appears in print.

One or two lecturers use skeletal notes that have gaps to be filled in during the lecture. The aim here is to engage the audience in some kind of active involvement rather than just passive listening.

Preparing for Lectures
Make sure you arrive before the lecture starts and that you have all that you need with you. This includes, as well as the obvious things like something to write with and on, previous lecture notes, which may well be referred to, the textbook if one is being used, and printed notes or other material such as statistical tables where appropriate. Sit where you can see the board or OHP most clearly, and where you can hear best.

Mathematics is a progressive subject, so you will understand a lecture better if you have done some work in relation to previous lectures.

Your Notes
You will need to review your notes after lectures. There is well-documented research which shows that if you go to lectures and then do nothing with the notes, the most you will retain will be about 10%. This can be doubled or trebled if you review the material within 24 hours, and this will considerably increase the effectiveness of your work, especially when it comes to revision time.

By the time you get to the end of a course unit you should have a set of notes for which the pages are numbered, headings and important definitions and results underlined or highlighted, and for which you have an index or a list of contents. You need to be able to find your way through a set of notes, which will often contain some quite complicated ideas. Dating your notes can also help to find things.

When you get to the end of a particular section of the work (for example when you finish applications of integration in the calculus course) make a summary containing the important definitions and an outline of the methods used. This will be useful revision and an aid for later use before examinations.

Think about mundane things like stationery. Loose-leaf files are convenient for lectures as you will want to review and rearrange your notes afterwards, but for your consolidated set of notes you might find a hard-backed notebook better. Think about the use of colour and highlighting to emphasising important results and formulae.

The overall aim is to put together a set of notes which you can use effectively.

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5. Getting the most out of Tutorials

Questions to ask yourself:

  • Am I missing tutorials? If so why?
  • Do I hand in the set work in time to get it marked and returned?
  • Do I get the help I need in tutorials?
  • Do I prepare properly for tutorials?
  • Am I made to feel stupid? What can I do about it?
  • Do I contribute as much as I should in tutorials?
  • Do I get a chance to show what I know and can do?
  • Do I get feedback on the homework?

Preparing for Tutorials
Unlike lectures where the lecturer is usually solely responsible for the organisation of what goes on, in tutorials the responsibility is often shared with the class. Tutorials are occasions where you can receive individual help. It is not a good use of tutorial time simply to turn up unprepared and expect it to be like another lecture. You should decide beforehand what you would like particular help with.æ If it is a section of your lecture notes or the textbook make sure you know which page it is on, and try to write down beforehand what your difficulty is, to help you remember when the time comes.

You should have tried the problems assigned before the tutorial, especially where they are collected in for marking. If you are having trouble with a problem or an exercise make sure you have your attempts with you so that the tutor can try to understand how you have been thinking.

Styles of Tutorial
The tutorials may be staffed by a member of academic staff, or a graduate student, sometimes working alongside a lecturer. The person taking the tutorial will usually have marked the homework, and will have been briefed by the lecturer. Like lectures, tutorial styles vary. There may be a class explanation where the tutor is aware from the homework that most of the class had difficulty with a particular problem. Sometimes the tutor will try to get the class to work through a problem orally, making suggestions and responding to questions. It is very important to develop the skill of discussing mathematics, as this is likely to be called upon in later study or employment. In the hands of a sympathetic tutor (aren't we all?) such activities can help to build up confidence and increase the propensity to ask for help when it is needed.

Getting Help in Tutorials
When you ask or respond to a question you should expect it to be dealt with seriously. If you think that you are being made to feel stupid find out from your friends whether this is a general feeling. If so you can talk to the tutor as a group, or to someone else, for example the course lecturer, or your personal tutor, or the Director of Undergraduate Studies. If no-one else feels the same, try to convince yourself that the tutor does need to be able to probe what you do not know in order to help you to learn.

Do discuss your worries with him or her.

If you find that there is no opportunity in the tutorial to get the help you need discuss the matter with the tutor or the course lecturer. Help us to help you!

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6. Problem Solving - Skills and Strategies

Questions to ask yourself:

  • Am I persistent when trying to solve problems?
  • Do I give up too easily? If so what can I do about it?
  • Am I good at planning my approach to problems? How can I improve?
  • Am I good at planning in general?
  • Do I make an effort to learn?
  • Do I get a buzz when I produce a neat solution to a problem?
  • Do I find it hard to accept defeat sometimes?
  • Am I sufficiently flexible in approaching problems?
  • Am I good at analysing complex information? How can I improve?

The core of all intellectual activity consists of solving problems, in whatever subject. For example devising an experiment to detect gravitational waves, translating into Mandarin Chinese the proverb "virtue is its own reward", disposing of radioactive waste safely, evaluating a complicated integral. Problem solving is a mixture of frustration and deep satisfaction. Anyone involved in mathematical research will tell you of the long periods of frustration when problems cannot be solved.

So what do we do about it? Most importantly we talk to one another. Mathematicians are constantly discussing their work together, to try to gain ideas by getting someone elseÍs point of view, to see whether a colleague can offer an unexpected insight. Mathematicians will also tell you of the immense satisfaction that comes from finally unravelling the solution of a problem which has been nagging at them for a long time. Mathematics is a social activity both in the informal discussion of problems and in the evaluation of the correctness or otherwise of proposed solutions.

So much for the sermon. How can we become better problem solvers? If there were an easy answer to that question we would all be out of business - in fact there would be no problems.

The problems which form part of undergraduate mathematics are often exercises through which you practice and understand techniques and methods, for example for solving differential equations. Sometimes however you will encounter problems where you are unsure at the outset what methods will be applicable, or indeed precisely what the problem is asking. Some of the situations in applications of mathematics have this characteristic, where the uncertainty lies in the transition from the problem itself (forecasting the weather, predicting the growth of crystals, evaluating the efficacy of a new drug) to a useful mathematical description of the problem (i.e. the problem of abstraction).

Various authors have tried to analyse the activity of problem solving. A classic in the field is How to Solve it by George Polya, first published in 1945. A more recent text (1985) is Mathematical Problem Solving by Alan Schoenfeld, which is a scholarly account of research in the area rather than a book of hints and tips. Each has some useful ideas to offer, but both emphasise that by and large we become better problem solvers by working on lots of problems, gaining and reflecting on experience, and this everyone has to develop through their own activities. There is no real secret - we become better problem solvers by practice.

Polya breaks down problem solving activity into four phases:

1. Understanding the Problem

  • Read the problem carefully.
  • Make sure you understand any definitions, symbols and technical terms used.
  • Look them up in your notes or textbook if you need to and write them down.
  • Make sure you are clear what information you are being given.
  • Make a list of the individual bits of information or assumptions given.
  • Make sure you understand what you are being asked to find or prove.

2. Devising a Plan

  • Draw a diagram if you can.
  • Think carefully about the notation that you may need to use.
  • Have you seen a similar problem?
  • Can you solve a simpler problem and then generalise the solution?
  • Is there anything in your notes or textbook which will help?
  • Will trying some numerical examples help you to see a general method or pattern?
  • Can you rearrange the problem to give an alternative point of view?
  • Can you break it down into sections - each of which you might be able to solve?
  • Do you know the mathematical procedures needed to solve the problem sufficiently well?
  • Can you write down an outline of the steps you think you will have to follow to produce a solution?

3. Implementing the Plan.

  • In carrying out the plan it is important to check each step.
  • Have you done the algebra and arithmetic accurately?
  • Is the diagram a correct representation of what the problem says?
  • It is important to monitor your mathematical activity, asking yourself why you have embarked on a particular approach, and why you think it is likely to lead to a solution.

4. Looking Back

  • Can you check the solution?
  • Does it look as you expected?
  • Can you verify it with special values for which you know the answer?
  • Can you do part or all of the problem another way to give an independent check?
  • Is the method applicable to other problems?
  • Time spent checking pays dividends.

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7. Textbooks - Reading and Understanding

Questions to ask yourself:

  • Do I really understand what I have just read?
  • Have I been actively involved with the mathematics in the book?
  • Can I find an example like the one I am having problems with?

When using a book on a particular occasion you need to decide what your purpose is.

  • Are you looking for an explanation of an idea which you have not completely understood from lectures, and where a different point of view may help?
  • Are you looking for a particularly well constructed diagram?
  • Are you looking for a worked example similar to one in the lectures, but where the details are different so that you can better understand the underlying method?
  • Are you trying to find a worked example to help with a homework problem?
  • Are you studying a section in advance of a lecture in order that you will understand the lecture better when it comes (yes that is allowed!)?
  • Have you been set a section to study by yourself?

Mathematics textbooks are not like novels or the Sunday papers. In most cases a superficial read will not achieve a great deal, except perhaps to give an overview of what the subject consists of. It is the details which are important, and so the part of the textbook which you are studying at any given time needs to be read actively. This is a key concept in using mathematics textbooks. You should be working through the material, making notes, rather than just passively reading the symbols on the page. Where there are calculations you should try to work them through yourself and then check them with the book, to give you confidence.

The advantage in using a textbook is that your learning is not dictated by the pace of the lecturer. You are free to vary the pace at which you progress. With a really difficult idea you may spend a good deal of time over a single paragraph, reading and re-reading the explanation, working through examples and exercises to help reinforce the idea, asking your friends or your tutor and then coming back to it later. Calculations in worked examples which you feel confident about can be skipped over if your aim is to form a broader picture of a particular part of the topic.

Remember that books sometimes have mistakes, and so if you and your friends think there is an error ask your lecturer or tutor. If the copy of the book is your own do not be afraid to annotate it just as you would your lecture notes.

Answers in the back of the book are there to help you check your work. They are not there as a substitute for trying problems yourself. Simply reading through a worked example or a printed solution to a problem will not achieve nearly as much as your constructing a solution for yourself, albeit with some assistance.

There will often be more material in a textbook than is in the syllabus for a course. This enables you to get some idea about how the subject progresses further, or perhaps to give you ideas for projects you may want to undertake later in your course.

First year textbooks are often useful in later courses, where lecturers expect you to know material which you may have forgotten, but which you can revise from the book.

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8. Getting Help - When and from Whom

Questions to ask yourself:

  • Have I been to see my tutor recently? If not why not?
  • Am I coming away from tutorial sessions feeling little benefit? If so why is this?
  • What can I do to make more of the help I am given?
  • Am I learning from my friends?
  • Are my friends learning from me?
  • Are there things I am afraid to ask for help with? What should I do about it?
  • Do I feel encouraged by the help I get?
  • Do I feel confident about asking for help?
  • Do I plan how to use sessions with tutors?

There are many sources of help available for your work, apart from the timetabled classes themselves. One of the best sources of help is fellow students. Experience in computer laboratories confirms that a great deal of mutual teaching goes on in that context, and it can happen throughout your learning. Working as part of a small group on a regular basis, provided everyone is contributing, is an excellent source of learning. This is particularly useful when a group of you is unable to sort something out as it is a more efficient use of a tutor's time to deal with a group together.

The university library contains books other than course textbooks and sometimes you will find what you want there. The course lecturer or one of the other tutors on the course can be approached for help. If they are busy they will fix an appointment for you.

If graduate students are assisting with the course, you can arrange to see them. They generally share offices in the department so there is somewhere you can meet. Your personal tutor can sometimes help with first year material and with some of the later course units depending on the subject.

A few students work best on their own all the time, but generally they are in the minority, and you would be well advised to arrange your private study time so as to meet regularly for part of that time with a group of friends studying the same subjects. You will often find friends in Hall or in the same tutorial group for whom this will be a congenial way of working.

You should seek help from tutors when you feel you are really stuck. If you canÍt do a problem at first you need to wrestle with it for a while before giving up. The intellectual struggle is perhaps the most important part of the learning process. Accounts written by professional mathematicians give testimony to the benefits of returning to a problem, after some subconscious processing has occurred. We all sometimes find ideas popping into our heads unexpectedly, so it is a good idea to keep a notebook handy to jot them down to work on later. There are a few accounts of people dreaming solutions, but this happens all too rarely unfortunately!

Do remember that as well as getting help from tutors on your academic work, they are also there to help with other problems, which may in turn be affecting your studying.

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9. Coursework - Planning and Execution

Questions to ask yourself:

  • Do I do better at coursework than in examinations?
  • Am I taking on too much coursework? Or not enough?
  • Am I clear when the deadlines are for my assignments?
  • Do I plan my time well in relation to deadlines?
  • Is everything always a great rush? What can I do about that?
  • Am I quite clear about what the coursework requirements are?
  • Am I clear where the limits of collaborative work lie in relation to coursework?
  • Do I need to improve my standard of presentation? What should I do about it?
  • Am I writing good English?
  • Is my handwriting legible?
  • Do I learn from doing coursework assignments?
  • Do I feel a sense of achievement when finishing a substantial assignment?
  • Do I need help to improve my word-processing skills?

Coursework will be of many different kinds: essays, sets of problems, self-study projects, statistical reports, computer programs, etc. When you choose a course unit you should find in the course description published by the Faculty a brief note of the type of coursework and the percentage it contributes to the unit.

During the course the lecturer should give you a written handout specifying the requirements of the coursework, the deadline for handing it in and what the penalties are for late submission. It is your responsibility to make sure that you have this, which will usually be handed out in a lecture. Study the coursework specification straight away, and if you are not clear about what is required ask the lecturer.

If for any reason you think that you may not be able to meet a deadline you should discuss it with the lecturer at the earliest opportunity - certainly before the deadline.

Doing your best on coursework assignments requires that you plan your time effectively. You need to know fairly near the beginning of the semester when the various deadlines are, especially if you are taking more than one unit with coursework. Plan your time so that you are not feverishly writing right up to the last minute. Under those circumstances the work will often be less than your best. Many people find that doing an early draft and then thinking about it for a few days helps to improve the final piece of work, but you need to plan your time to make that possible.

Take care over your presentation of the work. Because it is not being done under tight time constraints as in an examination the standard of presentation is important. In some cases it will be an explicit part of the assessment criteria, but in all cases a well presented piece of work creates a more favourable impression than a scrappy offering, with lots of crossings out and clear signs of sloppy and hurried work. If you are unsure as to whether word-processing is a requirement ask as early as possible. Make sure however that you do not spend more time than is necessary on the presentational aspects, as this can limit the time you have to spend on the actual mathematical content.

Some lecturers will specify assessment criteria with the details of the coursework assignment. If you are not sure about what is being assessed you must ask the lecturer.

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10. Examinations - Preparation and Revision

Questions to ask yourself:

  • Do I feel reasonably confident about exams?
  • Am I revising systematically and in good time?
  • Do I know what the exam requirements are?
  • When I read the exam paper is it usually roughly what I expect?
  • Do I plan the use of my time in exams?
  • Do I often feel I could have done a lot better?
  • Do I usually feel that I have performed somewhere near my best?
  • Do I panic a lot in exams?
  • Do I feel overwhelmed with stress and worry before exams?
  • Am I managing stress OK?
  • Am I a bit too laid back about it all?
  • Can I usually predict roughly how well I have done?
  • Am I clear what will be done with the results of the exams?

Planning Revision
Planning revision is important. It is not something you can do at the last minute. You should be revising during the course, for example during part of the Easter vacation. This will help not only with preparation for examinations but also with later parts of the course. During the latter half of each semester you should draw up a revision timetable. Plan to finish well before the examinations. This will give you flexibility in case something unforeseen such as illness or a bereavement disrupts your revision. It will also give extra time for additional work on things which have caused you particular problems during your revision.

Revision Techniques
It is not good enough simply to read and re-read your notes. You must be actively involved in doing mathematics. Re-work some problems which you have tackled earlier in the course, to give yourself some confidence. Try additional exercises from textbooks. Make sure you work through past exam questions. Past papers are sometimes distributed in lectures, or they may be available in the library.

Make written summaries as you revise your lecture notes. This will help to organise your memory. Trying to learn detailed calculations or proofs is not generally a good idea. Learn the underlying structure or method and then try to reconstruct the details yourself. You should be able to re-create detailed solutions in the examination provided you have a thorough knowledge of the main procedures of the particular method being used.

Test yourself frequently. Can you write down from memory important definitions, results and formulae? The act of trying this will improve your factual recall.

When you get stuck on a problem or past exam question, this is the time to study detailed parts of your notes or textbook.

Write down really important things on cards. Carry them with you and look at them in odd moments.

Make sure you have periods of relaxation, and sufficient sleep. You need to be in good physical as well as mental condition to be able to concentrate and do your best.

Finally bear in mind that efficient learning is an individual thing, but that the ideas above have been found helpful by many students in the past.

Getting Help
If you really get stuck ask friends. In fact doing part of your revision as a group can help you to learn and can give you a feeling of confidence. Lecturers and tutors are glad to help, but you must have specific points to ask them about and you must do it in plenty of time. Tutors occasionally get students appearing at their office on the morning of an exam saying "I don't understand my notes", sitting down and opening them at page 1. We know that they are unlikely to do very well in the exam that afternoon! On the other hand a student coming a week beforehand asking for help on a specific method or a particular part of a proof is likely to be well prepared.

Coping with Stress
Nobody can go through life without meeting stressful situations. Even a hermit must feel stress sometimes! A healthy amount of stress associated with important occasions can motivate you and increase your concentration so that you perform well - ask any athlete. Continuous stress over long periods however is counterproductive, and needs to be dealt with. When preparing for examinations you will be under a certain amount of stress - they are after all important occasions. This is why relaxation is so important, as a way of giving you stress-free periods. So donÍt give up going to orchestra practice, or your regular voluntary work, or church on a Sunday, or whatever you normally do outside your academic work. Your revision plan must include periods free of work.

For a few people the feeling of stress can be such that it seriously inhibits their ability to work effectively during revision or examinations. If that is the case then it is important to recognise these symptoms and seek professional advice from the Health Centre or the Student Counselling Service. There is no stigma about needing to do this for a short time - we all need help from professionals on occasion.

Before the Exam
Make sure that you collect your exam timetable in good time, and that you are quite clear where and when your examinations are. This and the other things in this section all sound very obvious, but one does encounter the occasional student who turns up at the wrong time or in the wrong place. Unbelievable but true!

Make sure you get there in plenty of time. Allow more time than usual - the traffic may be heavy, your bicycle tyre may puncture. If you are very early you can always go somewhere and relax. Get a good nightÍs sleep.

Take more than one pen with you! Make sure you know whether or not you are allowed to use your calculator, and that it is working properly. In the winter make sure you will be warm enough, as you will be sitting still in the exam room for some time.

Make sure well before the exam that you are clear about the format of the paper. The rubrics for each examination are posted on a noticeboard in good time. They tell you how many questions you will have to do, and remind you about items which you may be able to take into the examination. If you are still not sure ask the lecturer.

During the Exam
DON'T PANIC. Easier said than done sometimes! Seriously though, we want you to do your best, and show us what you know and can do. You have all taken examinations successfully before so use that experience to think beforehand what is the best course of action for you if you get stuck on a question, or if a calculation refuses to come out.

Take things calmly. Examinations are not designed to be speed tests, and a couple of minutes here and there to think, take stock and plan what to do next will often pay dividends, rather than simply rushing on writing furiously whether it is right or wrong. Do not leave the exam early in desperation! If you have been working properly during the course and during your revision it is likely that you will be able to answer further questions. Take a short time to compose yourself and then begin again.

Formulate a rough plan beforehand about how you might best use your time in the exam. You know what has worked successfully for you in the past. It is much better to think of contingency plans beforehand than to be forced into taking unprepared emergency action during an examination.

Remember the advice about problem solving. Make sure that you take time to check steps as you go along. When you read a question decide the overall strategy - maybe even jot it down in your rough work.

If you do run out of time part way through a question spend the last couple of minutes writing down what you would have done if you had more time. This can show that you knew how to do the question and may get some credit.

Finally remember that we really do want you to do your very best.

After the Exam
Forget about it and think about the next one, or breathe a sigh of relief that they are over! If you feel that you did not do your best, or that you panicked unnecessarily, think how you might improve your examination behaviour for the next paper.