Help with starting maths problems

Here's some advice which might help you.

• Don't be afraid to try things out!
  Always be prepared to think about a problem and have a go at it.
  Students very often underrate what they do themselves so that if something doesn't work out, they tend to think that their effort was wasted. This is not true!
  Thinking about questions for yourself is how you learn and understand what you are doing, so that you will be able to apply this knowledge whenever you need it in later work.
  
• Use all the resources you have.
  Use your notes from your classes.
  Talk with friends who are trying the same problem, or who already know how to solve it.
  Doing this is also helpful to the person you ask. Explaining something to somebody else is the best way of being sure that it has been really learnt and understood.
  Take advantage of tutorial time with your teacher.
• You could also get help from books.
  You may already have bought a particular book which is recommended for your course. If you want to use an extra book, go and look at some in your library or bookshop. See if you can find the thing that you are stuck on in the index. (If not, be cautious! A bad (or no) index is a great disadvantage in a book.)
  Once you've found it, is it explained in a way that you think will help you? Don't just buy the first book that you come across in the hope that you will somehow mysteriously absorb its contents just by owning it - would that it were so easy! You and it will have to work together.
• You could use the increasing resources on the web.
  You can find external links to various sources of help at the end of my Where next? page.
• Have a pencil and paper handy when you study.
  When you are working through your notes or using a book, it is a very good idea to have a pencil and paper handy so that you can write down your own thoughts and working out as you go along. This will turn the maths into part of your own thinking.

• Never under-estimate what you do yourself!

If someone else starts you off on a solution don't let them do the whole thing for you.
For example, if you are using my book, you will find that I've given full solutions to all the problems so that you can work from it on your own. If you do get stuck, look in the back but only go as far as you need to in order to get unstuck. Then try to finish the problem yourself.
• Don't try to learn large amounts of maths in a hurry.
  Most people need absorbtion time and practice so that they can connect new concepts into their own mathematical understanding. Without this, they risk finishing up with a lot of isolated half-understood bits. Because these bits aren't linked together, they can't be applied in unfamiliar situations and they get forgotten.

• Don't get discouraged if you find that your method was slow.
  When you've got through to the end of a problem, you may find that there was a faster way to do it. For example, you might find that if you had noticed a factorisation, or used some results that you already had, you could have got to the answer twice as quickly.
  Don't be discouraged if this happens. The next time that you are in a similar situation, it will be very satisfying to be able to do that short-cut.
• Make every effort to do each work assignment that you are set.
  This is the most important single piece of advice that I can give you.
  It is enormously different from watching a lecturer working through a demonstration problem when you actually come to do a similar one yourself. Instead of gently nodding agreement, you will think `Um ... what next?'
  Thinking about and answering these 'what nexts' for yourself is what makes you understand the maths so that you can apply it in your chosen field.
  This is also why it's very important that you don't just copy work from someone else, deeply tempting though this may seem at times.
• What matters is for you to feel just a bit more in control of what you do.
  Even if this time you don't quite make it all the way through, you'll feel more confident next time! Good luck!