Two books by David Bressoud:
- Bressoud, David M. Proofs and Confirmations. The story of the alternating sign matrix conjecture. MAA Spectrum. 1999
"My intention in this book is not just to describe this discovery of new mathematics, but to guide you into this land and to lead you up some of the recently scaled peaks. This is not an exhaustive account of all the marvels that have been uncovered, but rather a selected tour that will, I hope, encourage you to return and pursue your own explorations.''
There are conjectures; partial progress on the conjectures leads to new conjectures... students could learn something about the practice of mathematics by reading this book.
- Bressoud, David M. A radical approach to real analysis. Classroom Resource Materials Series, 2. MAA. 1994.
From Math Reviews:
This book "starts with infinite series, illustrating the great successes that led the early pioneers onward, as well as the obstacles that stymied even such luminaries as Euler and Lagrange''. Mistakes that were made are emphasized to highlight difficult concepts, and the student is led through some of the evolution of such concepts as uniform convergence as they arose in response to a need.