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Reading List - Mathematics Undergraduate Admissions

Reading before arrival

Preparing for a Mathematics course

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.

Difference from A-Level Mathematics

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.

It 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.

Suggested Reading

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

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.


Image cover of Foundation of Mathematics book
The Foundations of Mathematics by Ian Stewart and David Tall (Oxford 2015; ISBN: 019870643X).
Cover image of guide to analysis book
Guide to Analysis

by Mary Hart

(Macmillan 2001; ISBN: 0333794494).

This book by Hart is a recommended text for the first-year module “Analysis”.

Cover image of algebra and geometry book
Algebra and Geometry

by Alan F. Beardon

(Cambridge 2005; ISBN 0521890497).

Exploring University Mathematics with Python book
Exploring University Mathematics with Python

by Siri Chongchitnan

(Springer 2023; ISBN 3031462696).

Optional Further Reading

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.

Cover image for mathematics a very short introduction book
Mathematics: a Very Short Introduction by Timothy Gowers (Oxford Paperbacks, 2002; ISBN: 0192853619). Also very inexpensive.
Cover image of what is mathematics book
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.
Cover image of the pleasures of counting book
The Pleasures of Counting by Thomas W. Körner (Cambridge University Press, 1996; ISBN: 0521568234).
Cover image of the book of numbers
The Book of Numbers by John H. Conway and Richard G. Guy (Springer NY, 1998; ISBN: 038797993X).
Cover image of calculus gems
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.
Cover image for letters to a young mathematician book
Letters to a Young Mathematician by Ian Stewart (Basic Books, 2006; ISBN 978-0-46508-232-2).
Cover image for beautiful mathematics book
Beautiful Mathematics by Martin Erickson (Mathematical Association of America; ISBN 978-0-88385-576-8). A potpourri of topics to browse through.
Cover image for how to study for a mathematics degree book
How to Study for a Mathematics Degree by Lara Alcock (OUP Oxford, 2012; ISBN 0199661324).


Approaching the reading

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!

Further preparation for studying with us

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.

Studying Mathematics at Warwick

Our Courses

You are free to do 100% maths, or if you prefer, we offer the opportunity to choose options from several other world-class departments at Warwick.

Our Teaching

Most of our teaching is through lectures. These are typically 3 hours per week for each module, and delivered by a member of academic staff.

The Library

Your Library is so much more than the physical spaces and books. We want you to be able to access everything you need - services, spaces or collections – and make the most of what we have to offer.

Entrance Exam

If you are applying to study any Undergraduate Mathematics course at the University of Warwick we ask many of our applicants to sit the MAT or STEP exams.