The Fundamentals of Analysis for Talented Freshmen


Synthesis Lectures on Mathematics and Statistics


August 2016, 98 pages, (doi:10.2200/S00725ED1V01Y201608MAS017)
Peter M. Luthy

College of Mount Saint Vincent 

Guido L. Weiss

Washington University in St. Louis 

Steven S. Xiao

Washington University in St. Louis 


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.

Table of Contents: List of Figures / Preface / Limits, Continuity, and Compactness / Differentiation on R / One and Several Dimensional Integral Calculus / Authors’ Biographies / Index

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