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Here is a list of some of my favorite books that are appropriate reading for undergraduates interested in finding out more about math. The required level of expertise is not uniform: some items are written at the precalculus level, while others are aimed at the senior mathematics major/beginning graduate mathematics level. Some items are double listed and there is no pre-designed order within a category.
Geometry
- Geometry and the Imagination, by D. Hilbert and S. Cohn-Vossen, Chelsea, 1952.
- Introduction to Geometry, by H.S.M. Coxeter, John Wiley, 1961.
Problem Books
- Mathematical Discovery, vol. 1-2, by G. Polya, Princeton University Press, 1962.
- Problems and Propositions in Analysis, by G. Klambauer, Marcel Dekker, 1979.
- Problems and Theorems in Analysis, vol. 1-2, by G. Polya and G. Szego, Springer-Verlag, 1972.
- The Art and Craft of Problem Solving, by P. Zeitz, John Wiley and Sons, 1999.