(say)on hand-outs;some give out notes with gaps for diagrams or equations to be filled in by you.Some styles will suit you better than others,but it is very much a personal matter;do not assume that others will agree with you about what is best. Often,students especially first-year students who are used to A-level learning methods-want complete printed lecture notes, thinking that this is what they need to learn the material,as from a text book.That may be so,but the aim is to understand the material. which is a very different matter.For this,it may be much more useful to have a carefully distilled set of notes that brings out all the main ideas;the work you do in fleshing out the details will serve you far better in the long run than reading a complete set of printed notes. Supervisions There is apparently not much scope for heated discussion of topical issues in mathematics supervisions.In fact,any debate at all can be difficult (at least at first),since your opinion seems not to count for much when your supervisor knows all the right answers (having been told them by his or her supervisors when they did the course). Nevertheless,a supervision should not be a mini-lecture:if it turns into one,then that is a valuable opportunity wasted. Whereas lectures are to some extent interactive,this is very much the case with supervisions.A good part of the responsibility for mak- ing the supervision useful and interesting lies with you.Remember that most supervisors are human beings too:they like you to talk to them and show an interest (e.g.by asking questions)in what they are telling you. Generally,in a mathematics supervision,you sit at a desk with your supervisor who will write out solutions to exercises or explana- tions of pieces of mathematics on paper (not on a blackboard).You should not take notes yourself;leave your mind completely free to concentrate on understanding everything your supervisor says.At the end of the supervision,you take away what he or she has written and (best)use it to annotate,correct or complete your own super-
(say) on hand-outs; some give out notes with gaps for diagrams or equations to be filled in by you. Some styles will suit you better than others, but it is very much a personal matter; do not assume that others will agree with you about what is best. Often, students — especially first-year students who are used to A-level learning methods — want complete printed lecture notes, thinking that this is what they need to learn the material, as from a text book. That may be so, but the aim is to understand the material, which is a very different matter. For this, it may be much more useful to have a carefully distilled set of notes that brings out all the main ideas; the work you do in fleshing out the details will serve you far better in the long run than reading a complete set of printed notes. 4 Supervisions There is apparently not much scope for heated discussion of topical issues in mathematics supervisions. In fact, any debate at all can be difficult (at least at first), since your opinion seems not to count for much when your supervisor knows all the right answers (having been told them by his or her supervisors when they did the course). Nevertheless, a supervision should not be a mini-lecture; if it turns into one, then that is a valuable opportunity wasted. Whereas lectures are to some extent interactive, this is very much the case with supervisions. A good part of the responsibility for making the supervision useful and interesting lies with you. Remember that most supervisors are human beings too: they like you to talk to them and show an interest (e.g. by asking questions) in what they are telling you. Generally, in a mathematics supervision, you sit at a desk with your supervisor who will write out solutions to exercises or explanations of pieces of mathematics on paper (not on a blackboard). You should not take notes yourself; leave your mind completely free to concentrate on understanding everything your supervisor says. At the end of the supervision, you take away what he or she has written and (best) use it to annotate, correct or complete your own super- 5
vision work or lecture notes,or (second best)file it with your own work.Your supervision partner can use the notes after you,or save them digitally in some way. If you find that you come away from the supervision without adequate notes.you should discuss the matter with the supervisor either by e-mail or at the beginning of the next supervision.It is your supervision,so the supervisor should try to fit in with what you want. You must hand your work in well before the supervision,and certainly by the time specified by your supervisor. Your work should be neatly and clearly presented.If your work is scribbled and scruffy,then you should rewrite it.4 You will not regret time spent on this:clarity of presentation comes from and leads to clarity of mathematical thought It should be logically and carefully argued otherwise it is not mathematics.You may think you can do a problem before you even set pen to paper,but you don't know that you can do a problem until you write out all the details.Also,unless you are in the habit of writing careful solutions,you will come unstuck in the examinations when you do not have the opportunity to explain what you really meant. If you do not make good use of supervisions,then you will squan- der one of the most important(and expensive)assets that Cambridge has to offer.Experience has shown that to make best use of your su- pervisions,you should: bring your lecture notes to the supervision,having marked in the bits you don't follow; hand your work in on time,so that it can be marked thoroughly; mark your own work:make a note in the margin wherever there is a step you are not sure of,or which you have missed out.This 4Please read that sentence again.It is really disrespectful to hand in scruffy 6
vision work or lecture notes, or (second best) file it with your own work. Your supervision partner can use the notes after you, or save them digitally in some way. If you find that you come away from the supervision without adequate notes, you should discuss the matter with the supervisor either by e-mail or at the beginning of the next supervision. It is your supervision, so the supervisor should try to fit in with what you want. You must hand your work in well before the supervision, and certainly by the time specified by your supervisor. Your work should be neatly and clearly presented. If your work is scribbled and scruffy, then you should rewrite it.4 You will not regret time spent on this: clarity of presentation comes from and leads to clarity of mathematical thought. It should be logically and carefully argued otherwise it is not mathematics. You may think you can do a problem before you even set pen to paper, but you don’t know that you can do a problem until you write out all the details. Also, unless you are in the habit of writing careful solutions, you will come unstuck in the examinations when you do not have the opportunity to explain what you really meant. If you do not make good use of supervisions, then you will squander one of the most important (and expensive) assets that Cambridge has to offer. Experience has shown that to make best use of your supervisions, you should: • bring your lecture notes to the supervision, having marked in the bits you don’t follow; • hand your work in on time, so that it can be marked thoroughly; • mark your own work: make a note in the margin wherever there is a step you are not sure of, or which you have missed out. This 4Please read that sentence again. It is really disrespectful to hand in scruffy work; why expect the supervisor to spend time trying to make something of it when you can’t be bothered to present it nicely? 6
is not just to help your supervisors,though it will undoubtedly make their lives easier:a self-critical approach to your own work will prove invaluable when it comes to exam time; tell your supervisor (if appropriate and polite)exactly what you would like him or her to do-remember that sometimes your supervisor will have much less experience of supervisions than you,and will be glad of your advice; don't be afraid to say you don't understand something or couldn't do something -your supervisor is there to help you not to judge you,and this is your big chance to fill any gaps in under- standing and learn how to do the things you were stuck on; similarly,don't be afraid to hand in partial solutions to ques- tions you couldn't complete;your supervisor will then be able to see where the sticking point was; make sure your supervisor writes down enough on each example for you to reconstruct the solution afterwards; have an intelligent question ready in case the supervision is grinding to a halt with time to spare; review the supervision as soon as possible afterwards,while it is still fresh in your mind. Last of all,here is the most important tip:do not be lazy.It is very easy to let what the supervisor is saying just wash over you,perhaps hoping that all will become clear later.If you don't understand what the supervisor has done,say so. 7
is not just to help your supervisors, though it will undoubtedly make their lives easier: a self-critical approach to your own work will prove invaluable when it comes to exam time; • tell your supervisor (if appropriate and polite) exactly what you would like him or her to do — remember that sometimes your supervisor will have much less experience of supervisions than you, and will be glad of your advice; • don’t be afraid to say you don’t understand something or couldn’t do something — your supervisor is there to help you not to judge you, and this is your big chance to fill any gaps in understanding and learn how to do the things you were stuck on; • similarly, don’t be afraid to hand in partial solutions to questions you couldn’t complete; your supervisor will then be able to see where the sticking point was; • make sure your supervisor writes down enough on each example for you to reconstruct the solution afterwards; • have an intelligent question ready in case the supervision is grinding to a halt with time to spare; • review the supervision as soon as possible afterwards, while it is still fresh in your mind. Last of all, here is the most important tip: do not be lazy. It is very easy to let what the supervisor is saying just wash over you, perhaps hoping that all will become clear later. If you don’t understand what the supervisor has done, say so. 7