Real Analysis and Infinity

Description

Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts.

• The proofs of the vast majority of theorems are presented whilst pedagogical considerations are given priority
• Preliminary discussion of each major topic via examples and diagrams helps ease the reader into the appropriate context for the topic
• Examples follow most major results to improve comprehension and chapter-end exercises help with the refinement of proof and calculation skills

About the Author(s)

Hassan Sedaghat, Professor Emeritus of Mathematics, Virginia Commonwealth University, USA

Hassan Sedaghat is Professor Emeritus of Mathematics at Virginia Commonwealth University, USA. He has over 35 years of teaching experience in college mathematics, from freshman to the postgraduate level. He is the author of three books and over 60 research papers in the areas of analysis and nonlinear difference equations. He has collaborated with many researchers throughout the world on work in many joint publications and has given numerous invited talks in local and international venues.

Table of Contents

Preface
1:Manifestations of Infinity: An Overview
2:Sets, Functions, Logic and Countability
3:Sequences and Limits
4:The Real Numbers
5:Infinite Series of Constants
6:Differentiation and Continuity
7:Integration
8:Infinite Sequences and Series of Functions
Appendix: Cantor's Construction: Additional Detail
Appendix: Discontinuity in a Space of Functions
References and Further Reading

Reviews

"Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts." - MathSciNet

"This is a thorough introduction to the subject for undergraduates. There are very few prerequisites (less than in most similar textbooks) because topics such as infinity, countable and uncountable sets, and even the principle of mathematical induction are discussed in an early chapter. [...] The main advantage this book offers is its reader-friendly style." - Miklós Bóna, University of Florida, Department of Mathematics

"Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts." - zb Math Open