The Fundamentals of Analysis for Talented Freshmen

The Fundamentals of Analysis for Talented Freshmen

Peter M. Luthy, Guido L. Weiss, Steven S. Xiao
ISBN: 9781627054577 | PDF ISBN: 9781627059510
Copyright © 2016 | 98 Pages | Publication Date: August, 2016

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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.

This book is based on a set of notes for a course developed over many years and taught by Guido Weiss to a class of talented freshmen at Washington University in St. Louis. This course was attended each fall semester by approximately twenty incoming students, most of whom became mathematics majors, and, subsequently, mathematicians. The course was designed for students with strong mathematical ability to develop their understanding of more advanced mathematics.

Table of Contents

List of Figures
Limits, Continuity, and Compactness
Differentiation on R
One and Several Dimensional Integral Calculus
Authors' Biographies

About the Author(s)

Peter M. Luthy, College of Mount Saint Vincent
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.

Guido L. Weiss, Washington University in St. Louis
Professor Guido L. Weiss has had a very wide and interesting career. If one enters "Guido Weiss" in Google, several rather long articles about him will appear. We shall describe them in relatively few words that will give an idea of what he has done mathematically. His CV is very broad. All his university degrees are from the University of Chicago. After graduating with a Ph.D., he was on the faculty of DePaul University from 1956 to 1960. After this, from 1960 to 2015 his positions were all at Washington University in St. Louis. During his fifty-five years period he was very active as a mathematician and performed a considerable amount of research and occupied several academic positions. The list of publications (from 1955 to 2012) contains 121 papers (in one of the Google articles) and has published nineteen more articles and is now cooking two more. His professional experience and honors are considerable. He received honorary professorships from the University of Milano (Bicocca), in Italy, the University of Barcelona, Spain, the Beijing Normal University, in China; the Chauvenent Prize and other similar prizes. He has been invited to many lectureships all over the world. In particular he has traveled to China many times since 1980 and has “replaced” many Soviet mathematicians as a professor (nine of his forty-eight Ph.D. students are from China).

Steven S. Xiao, Washington University in St. Louis
Steven S. Xiao earned a Ph.D. in Mathematics from the Institute of Mathematics, Chinese Academy of Sciences, Beijing, China. He once was one of Professor Weiss’s post-docs and now takes care of all the computing in the department. He also teaches mathematics courses and computer programming courses in the university college.


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