- M R Spiegel, Vector Analysis and an Introduction to Tensor Analysis, Schaum – Chapters 1 to 4 are essential (except for the parts marked as “hard”) but read as much as you can.
- R P Feyman, Lectures in Physics – Volume 1 Addison-Wesley, Chapters 1 – 17 and 21 – 25. This is an excellent introduction to the physics side in mathematics. It is especially important if you have not studied physics at school. (Volume II chapters 1 – 8, 12 – 18 and 20 are also interesting and useful).
- M Spivak, Calculus, Benjaminc – A good introduction which is aimed slightly above A level and concentrates on techniques.
- R P Burn: Numbers and Functionsc, Cambridge University Press – An alternative which concentrates on ideas.
- D Smart, Linear Algebra and Geometryc, Cambridge University Press – Provides a good introduction to the algebra and geometry course as well as later material.
- T W Körner, The Pleasures of Counting, Cambridge University Press – This gives an excellent but relaxed approach to rigorous mathematics.