This book is an undergraduate introduction to real analysis. Teachers can use it as a textbook for an innovative course, or as a resource for a traditional course. Students who have been through a traditional course, but do not understand what real analysis is about and why it was created, will find answers to many of their questions in this book. Although this is not a history of analysis, the author returns to the roots of the subject to make it more comprehensible. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early nineteenth century. Cauchy's attempts to establish a firm foundation for calculus follow, and the author considers his failures and his successes. The book culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof. Mathematica ® commands and programs are included in the exercises. However, the reader may use any mathematical tool that has graphing capabilities, including the graphing calculator.
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This book is an undergraduate introduction to real analysis. Teachers can use it as a textbook for an innovative course, or as a resource for a traditional course. Students who have been through a traditional course, but do not understand what real analysis is about and why it was created, will find answers to many of their questions in this book.About the Author:
David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College. He served in the Peace Corps, teaching math and science at the Clare Hall School in Antigua, West Indies before studying with Emil Grosswald at Temple and then teaching at Penn State for 17 years, eight of them as full professor. He chaired the Mathematics Department at Macalester from 1995 until 2005. He has held visiting positions at the Institute for Advanced Study, the University of Wisconsin-Madison, the University of Minnesota, Universite Louis Pasteur (Strasbourg, France), and the State College Area High School. He has received the MAA Distinguished Teaching Award (Allegheny Mountain Section), the MAA Beckenback Book Award for Proofs and Confirmations, and has been a Polya Lecturer for the MAA. His is a recipient of Macalester s Jefferson Award. He has published over fifty research articles in number theory, combinatorics, and special functions. Other books include Factorization and Primality Testing, Second Year Calculus from Celestial mechanics to Special Relativity, the first and second editions of A Radical Approach to Real Analysis, and, with Stan Wagon, A Course in Computational Number Theory. David Bressoud chairs the MAA Committee on the Undergraduate Program in Mathematics. He has chaired the AP Calculus Development Committee and has served as Director of the FIPSE-supported program Quantitative Methods for Public Policy. He has been active in the activities and programs of both the Mathematical Association of America and the American Mathematical Society.
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Descrizione libro The Mathematical Association o, 1994. Paperback. Condizione libro: New. Never used!. Codice libro della libreria P110883857014
Descrizione libro The Mathematical Association of America, 1994. Paperback. Condizione libro: New. Codice libro della libreria DADAX0883857014