Here is some advice on the MAS114 exam: or, at least, on the first half of it, which relates to Semester 1.

The exam consists of two hours to answer six questions, and you should attempt them all. Broadly speaking, the first three are relevant to Semester 1, and the second three are relevant to Semester 2.

80% of the course credit is from the exam; the other 20% from online tests over the course of the year.

I have prepared some revision notes for you to use. Note that they do not contain everything you need to know, but you do need to know everything that is on them.

Write English sentences

Write full English sentences explaining what you're trying to do occasionally. If you're trying to prove something by induction, say so (and also say explicitly what it is that you're trying to prove).

Even if your details are completely wrong, you can still get marks for having a basically correct idea, but only if the examiner can tell what your idea is!

Learn the ideas

While you don't need to know the tougher proofs to do the exam, it may be helpful to read them when revising, all the same:

• One good way (not the only way) of understanding a definition is to see it used, and proofs are good uses of definitions.
• Proofs often contain hints about how to do things in practice, and the exam will ask you to put some of your knowledge into practice.

Learn the definitions both formally and informally

It will be vital in the exam to know (for example) what a convergent sequence is, and what a Cauchy sequence is.

This means you need to memorise the formal definitions, but you also need to keep in mind some informal picture of what they mean. You also need to understand how the formal definition relates to the informal picture you have in mind.

You will need to be able to do easy examples of proofs that various series are convergent, or that they are Cauchy. For example, it would be helpful to be able to prove directly that the sequences below are all convergent, and that they are all Cauchy:

an = 7;    bn = (n+1)/n;    cn = 3/2n.

Not only that, read the whole question carefully before starting. Take a few seconds to imagine how it might all work out, before you start writing anything. This helps avoid some serious blunders.