References for "Proving Things: Analysis"

These are classics — probably available in your local library. They are very different from each other.
George Polya, How to Solve It, Princeton University Press (paperback)
George Polya, Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics   and   Volume 2: Patterns of Plausible Inference, Princeton University Press (paperback)
Richard Courant & Herbert Robbins, What Is Mathematics?, Oxford University Press (paperback)
G. H. Hardy, A Course of Pure Mathematics, Cambridge University Press (paperback).