Real Analysis and Infinity
Published on 31. March 2022
Book
Hardback
576 pages
978-0-19-289562-2 (ISBN)
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. After introducing sequences of numbers, it develops the set of real numbers in terms of Cauchy sequences of rational numbers, and uses this development to derive the important properties of real numbers like completeness. The book then develops the concepts of continuity, derivative, and integral, and presents the theory of infinite sequences and series of functions.
Topics discussed are wide-ranging and include the convergence of sequences, definition of limits and continuity via converging sequences, and the development of derivative. The proofs of the vast majority of theorems are presented and pedagogical considerations are given priority to help cement the reader's knowledge.
Preliminary discussion of each major topic is supplemented with examples and diagrams, and historical asides. Examples follow most major results to improve comprehension, and exercises at the end of each chapter help with the refinement of proof and calculation skills.
Topics discussed are wide-ranging and include the convergence of sequences, definition of limits and continuity via converging sequences, and the development of derivative. The proofs of the vast majority of theorems are presented and pedagogical considerations are given priority to help cement the reader's knowledge.
Preliminary discussion of each major topic is supplemented with examples and diagrams, and historical asides. Examples follow most major results to improve comprehension, and exercises at the end of each chapter help with the refinement of proof and calculation skills.
Reviews / Votes
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. * Miklos Bona, 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 * This attractively produced book covers all of the topics one would expect to find in an introductory text on real analysis. Thus a short scene-setting chapter is followed by a background chapter on sets, functions, logic and countability and then six long chapters on sequences and limits, the real numbers (constructed in detail using Q-Cauchy sequences), infinite series, differentiation and continuity (in that order), Riemann integration (using the Darboux formulation) and infinite series of functions. * Nick Lord, Mathematical Gazette *More details
Language
English
Place of publication
Oxford
United Kingdom
Target group
College/higher education
Product notice
sewn/stitched
Cloth over boards
Illustrations
109 black and white illustrations
Dimensions
Height: 235 mm
Width: 161 mm
Thickness: 34 mm
Weight
1111 gr
ISBN-13
978-0-19-289562-2 (9780192895622)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Hassan Sedaghat
Real Analysis and Infinity
E-Book
03/2022
1st Edition
OUP eBook
€69.99
Available for download
Person
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.
Content
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
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