Studying Maths at Warwick will be a big step up from A Level, but there are several ways you can prepare yourself before you arrive to make the transition as seamless as possible.
This is a fast-paced degree, where you will be expected to already have a strong mathematical foundation. Therefore, the most important preparation you can make is ensuring you are 100% comfortable with fundamental topics such as algebraic manipulation, differentiation and integration. Additionally, there are some topics which you are expected to know but are not taught in certain A Level syllabi. The most common of these appear to be: vectors (including the dot and cross products), integration by parts, and hyperbolic functions.
A large focus of first year (and university mathematics in general) is learning to methodically and concretely prove statements and theorems. You should be aware of, and practice, the most common methods of proof such as induction, contradiction, and contraposition. There are many online resources containing examples and exercises to help with this.
The most important preparation you can make is ensuring you are 100% comfortable with fundamental topics such as algebraic manipulation, differentiation and integration
It would be a huge benefit to become familiar with the standard notation used in university mathematics. In particular, set notation, logical symbols and the use of quantifiers are integral to understanding definitions and writing proofs; learning these will help you hit the ground running with your mathematical writing.
There are a plethora of books targeted towards students making the transition to undergraduate mathematics. I would personally recommend Lara Alcock’s How to Study for a Mathematics Degree, in which she provides very helpful advice on not only mathematical study such as proof technique, important definitions, and writing mathematics but also on more general topics such as time management and study skills. It is certainly not necessary to learn any of the course before you get here, but those looking to get a head start may wish to read the introductory sections to Mary Hart’s Guide to Analysis, which serves as a comprehensive textbook for first year’s largest module in Maths.
Set notation, logical symbols and the use of quantifiers are integral to understanding definitions and writing proofs; learning these will help you hit the ground running with your mathematical writing
Finally, the online Warwick Maths Undergraduate Handbook provides detailed summaries of all modules, and I would recommend reading through these briefly to get an idea of what to expect in your first year. This will also allow you to begin considering which optional modules you would like to take. Furthermore, the handbook provides information on course regulations and degree structure, so if you have any questions about the course this is the first place to look.