The Fundamentals of Analysis for Talented Freshmen (Synthesis Lectures on Mathematics and Statistics)

This book assumes the students know some of the basic facts about Calculus. We are very rigorous and expose them to the proofs and the ideas which produce them. In three chapters, this book covers these number systems and the material usually found in a junior-senior advanced Calculus course. It is designed to be a one-semester course for "talented" freshmen. Moreover, it presents a way of thinking about mathematics that will make it much easier to learn more of this subject and be a good preparation for more of the undergraduate curriculum.

Peter M. Luthy got his Ph.D. from Cornell University; immediately following that, he was a postdoc of Guido's at Washington University in St. Louis from 2012 to 2015. He is now the chair of the math department at the College of Mount Saint Vincent, a small college in New York City. When he was still in St. Louis, Guido and he talked many times about a course he taught at WashU, year after year, for good freshmen. It was during this time we decided we should write a book based on the course he had designed, and Steve Xiao joined us in the project.