The Princeton Companion to Mathematics, Timothy Gowers

Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter

A Mathematician's Apology, G.H. Hardy

The William Lowell Putnam Mathematical Competition: Problems and Solutions 1965-1984, Gerald L. Alexanderson

The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary, Kiran S. Kedlaya

Problem-Solving Through Problems, Loren C. Larson

The Red Book of Mathematical Problems, Kenneth S. Williams

Putnam and Beyond, Răzvan Gelca and Titu Andreescu