A Basic Course in Real Analysis / Edition 1

by Ajit Kumar, S. Kumaresan

Overview

Based on the authors’ combined 35 years of experience in teaching, A Basic Course in Real Analysis introduces students to the aspects of real analysis in a friendly way. The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand the underlying principles, and coming up with guesses or conjectures and then proving them rigorously based on his or her explorations.

With more than 100 pictures, the book creates interest in real analysis by encouraging students to think geometrically. Each difficult proof is prefaced by a strategy and explanation of how the strategy is translated into rigorous and precise proofs. The authors then explain the mystery and role of inequalities in analysis to train students to arrive at estimates that will be useful for proofs. They highlight the role of the least upper bound property of real numbers, which underlies all crucial results in real analysis. In addition, the book demonstrates analysis as a qualitative as well as quantitative study of functions, exposing students to arguments that fall under hard analysis.

Although there are many books available on this subject, students often find it difficult to learn the essence of analysis on their own or after going through a course on real analysis. Written in a conversational tone, this book explains the hows and whys of real analysis and provides guidance that makes readers think at every stage.

Product Details

ISBN-13:	9781482216370
Publisher:	Taylor & Francis
Publication date:	01/10/2014
Pages:	250
Product dimensions:	6.20(w) x 9.30(h) x 0.80(d)

About the Author

Dr. Ajit Kumar is a faculty member at the Institute of Chemical Technology, Mumbai, India. His main interests are differential geometry, optimization and the use of technology in teaching mathematics. He received his Ph.D. from University of Mumbai. He has initiated a lot of mathematicians into the use of open source mathematics software. Dr. S Kumaresan is currently a professor at University of Hyderabad. His initial training was at Tata Institute of Fundamental Research, Mumbai where he earned his Ph.D. He then served as a professor at University of Mumbai. His main interests are harmonic analysis, differential geometry, analytical problems in geometry, and pedagogy. He has authored five books, ranging from undergraduate level to graduate level.

Table of Contents

Preface 1 Real Number System 2 Sequences and Their Convergence 3 Continuity 4 Differentiation 5 Infinite Series 6 Riemann Integration 7 Sequences and Series of Functions

Editorial Reviews

"… there are some unique features that put this book aside. … a welcome addition to the library of teachers and student alike."
—Zentralblatt MATH 1308

"… this book describes the basic results of analysis in an extremely clear, straightforward, and well-motivated way. … if you’re looking for a text on the easy end of the spectrum for a course in real analysis, then this book is certainly worth a serious look …"
—MAA Reviews, October 2014

From the Publisher