I suspect that we could reorder some class offerings to improve the "throughput" of a math program. I can divide my math education career into before and after the semester I took the course based on Smith/Eggen/St. Andre's "A transition To Advanced Mathematics." Mathematics is proofs, and knowing how to speak them is completely critical. After that course, I could do mathematics much more easily than before. I feel that this book is fundamental to learning mathematics. And the majority of that is being blooded in the art of proof by contradiction and proof by induction.