- A Kee Dewdney, The (new) Turing Omnibus (Palgrave Macmillan, 2003)
You can have a quick look inside the book on the Amazon website if that helps, and some useful exercises are included at the end of chapters. Do try them!
As soon as you start reading about the Cambridge Computer Science course, you will notice that mathematics is a required subject to be studying at school (and Further Maths is recommended if you have the opportunity to take it). Fluency in maths is essential for computer scientists, not only for formal proofs, but also because maths is the language used to describe almost every aspect of the subject. A second good book is therefore:
- Kevin Houston, How to think like a mathematician (Cambridge University Press, 2009). There is a useful pdf introduction: 10 Ways To Think Like A Mathematician