Reading in the summer before entry

If you are holding an offer here you may still be busy with examinations and you should certainly be spending your energy on these. However, once they are all over, it is a good thing to prepare yourself for your university mathematics course by doing some preliminary reading. University mathematics is rather different from A-Level mathematics, with much more emphasis on precision and on proofs. Definitions (even of relatively familiar terms like ‘limit’) are stated carefully in order to formulate concepts unambiguously and concisely. Beginning with a small number of basic definitions and assumptions (the axioms), everything else is rigorously proved. This rather abstract development leads to powerful methods for solving problems that are inaccessible by the more direct methods of A-Level mathematics, and makes it possible to learn about mathematical objects of which we can have no sensory experience - for example, objects in spaces of dimension greater than 3.

The following three books below can serve to introduce you to university mathematics.

1. The Foundations of Mathematics by Ian Stewart and David Tall (Oxford 2015; ISBN: 019870643X).
2. Guide to Analysis by Mary Hart (Macmillan 2001; ISBN: 0333794494).
3. Algebra and Geometry by Alan F. Beardon (Cambridge 2005; ISBN 0521890497).

The book by Hart is a recommended text for the first-year module “Analysis”. Browsing through any of them will give you a flavour of what mathematics at university will be like, and doing the exercises will prepare you for the kind of thing you will be asked to do once you are here. But there is no need to read them systematically before you arrive.

The books in the next list are not textbooks. You should be able to get hold of at least one of them through your school or public library. They are fun to read (at least in parts) but do not expect to read them as you would a novel. In particular, you may choose not to read them from cover to cover but to browse through the chapters and select sections which grab your attention. Do not be discouraged if you become confused during the first reading. Read on; new ideas are usually easier to assimilate at a second or third reading. Getting to grips with mathematical ideas requires many hours of careful reflection. Be patient, and persist until enlightenment dawns!

1. Mathematics: a Very Short Introduction by Timothy Gowers (Oxford Paperbacks, 2002; ISBN: 0192853619). Also very inexpensive.
2. What is Mathematics? by Richard Courant and Herbert Robbins, 2nd edition revised by Ian Stewart (Oxford University Press, 1996; ISBN: 0195105192). This is a classic; Courant and Stewart are both master expositors, from different epochs.
3. The Pleasures of Counting by Thomas W. Körner (Cambridge University Press, 1996; ISBN: 0521568234).
4. The Book of Numbers by John H. Conway and Richard G. Guy (Springer NY, 1998; ISBN: 038797993X).
5. Calculus Gems by George F. Simmons (McGraw Hill, 2007; ISBN: 978-0070575660). Small pieces of interesting mathematics, with historical background which, surprisingly, adds a lot to one's understanding.
6. Letters to a Young Mathematician by Ian Stewart (Basic Books, 2006; ISBN 978-0-46508-232-2).
7. Beautiful Mathematics by Martin Erickson (Mathematical Association of America; ISBN 978-0-88385-576-8). A potpourri of topics to browse through.
8. How to Study for a Mathematics Degree by Lara Alcock (OUP Oxford, 2012; ISBN 0199661324).

We will be contacting you again in September, after it is confirmed that you have gained a place on one of the Mathematics courses at Warwick, with further details on how you should prepare yourself for coming here.