Although we don’t have an official recommended reading list, I can certainly recommend some books that I personally enjoyed and think would be quite useful to Mathematics students due to start their first year in September.
Towards Higher Mathematics: A Companion by Richard Earl
This is a well-written book that covers a wide range of topics that bridge A-level mathematics with university mathematics.
How to Think Like a Mathematician by Kevin Houston
This book is less about teaching you specific topics and more about teaching you about how pure mathematics is done at university more generally. The focus of this book is on writing mathematics, logic and proofs – these are the things that first year mathematics students usually find most challenging so this is highly recommended.
Numbers and Proofs by Reg Allenby
The focus of this book is similar to the previous one in that it teaches you about how university mathematics is carried out. It is written in a slightly more technical fashion but it’s still very accessible and enjoyable (personally, I preferred this to the last one but both are good!).
The Pleasures of Counting Tom Körner
This book is not about preparing for university but it is a really enjoyable and non-technical book about mathematics so I thought I would include it. If you just want a fun read I would recommend it!