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The Resource Real analysis through modern infinitesimals, Nader Vakil
Real analysis through modern infinitesimals, Nader Vakil
Resource Information
The item Real analysis through modern infinitesimals, Nader Vakil represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Real analysis through modern infinitesimals, Nader Vakil represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary

 "Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Internal Set Theory (IST) introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the book provides a careful development of this theory representing each external class as a proper class. This foundational discussion, which is presented in the first two chapters, includes an account of the basic internal and external properties of the real number system as an entity within IST. In its remaining fourteen chapters, the book explores the consequences of the perspective offered by IST as a wide range of real analysis topics are surveyed. The topics thus developed begin with those usually discussed in an advanced undergraduate analysis course and gradually move to topics that are suitable for more advanced readers. This book may be used for reference, selfstudy, and as a source for advanced undergraduate or graduate courses"
 "This book provides a course in mathematical analysis using the methods of modern infinitesimals, which are developed within the framework of internal set theory (IST), introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the author provides a careful development of the theory in which each external class is represented as a proper class. The basic standard and nonstandard properties of the real numbers follow, together with a thorough discussion of the central topics of analysis that begins with those usually discussed in an advanced undergraduate course and gradually moves to topics suitable for more advanced readers"
 Language
 eng
 Extent
 xix, 565 pages
 Contents

 Machine generated contents note: Preface; Introduction; Part I. Elements of Real Analysis: 1. Internal set theory; 2. The real number system; 3. Sequences and series; 4. The topology of R; 5. Limits and continuity; 6. Differentiation; 7. Integration; 8. Sequences and series of functions; 9. Infinite series; Part II. Elements of Abstract Analysis: 10. Point set topology; 11. Metric spaces; 12. Complete metric spaces; 13. Some applications of completeness; 14. Linear operators; 15. Differential calculus on Rn; 16. Function space topologies; A. Vector spaces; B. The badic representation of numbers; C. Finite, denumerable, and uncountable sets; D. The syntax of mathematical languages; References; Index
 Isbn
 9781107002029
 Label
 Real analysis through modern infinitesimals
 Title
 Real analysis through modern infinitesimals
 Statement of responsibility
 Nader Vakil
 Language
 eng
 Summary

 "Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Internal Set Theory (IST) introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the book provides a careful development of this theory representing each external class as a proper class. This foundational discussion, which is presented in the first two chapters, includes an account of the basic internal and external properties of the real number system as an entity within IST. In its remaining fourteen chapters, the book explores the consequences of the perspective offered by IST as a wide range of real analysis topics are surveyed. The topics thus developed begin with those usually discussed in an advanced undergraduate analysis course and gradually move to topics that are suitable for more advanced readers. This book may be used for reference, selfstudy, and as a source for advanced undergraduate or graduate courses"
 "This book provides a course in mathematical analysis using the methods of modern infinitesimals, which are developed within the framework of internal set theory (IST), introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the author provides a careful development of the theory in which each external class is represented as a proper class. The basic standard and nonstandard properties of the real numbers follow, together with a thorough discussion of the central topics of analysis that begins with those usually discussed in an advanced undergraduate course and gradually moves to topics suitable for more advanced readers"
 Assigning source

 Provided by publisher
 Provided by publisher
 Cataloging source
 DLC
 http://library.link/vocab/creatorName
 Vakil, Nader
 Index
 index present
 LC call number
 QA300
 LC item number
 .V28 2011
 Literary form
 non fiction
 Nature of contents
 bibliography
 Series statement
 Encyclopedia of mathematics and its applications
 Series volume
 140
 http://library.link/vocab/subjectName

 Mathematical analysis
 Set theory
 MATHEMATICS
 Mathematical analysis
 Set theory
 Analysis
 Differentialrechnung
 Reelle Analysis
 Label
 Real analysis through modern infinitesimals, Nader Vakil
 Bibliography note
 Includes bibliographical references (p. [554]556) and index
 Carrier category
 volume
 Carrier category code
 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Machine generated contents note: Preface; Introduction; Part I. Elements of Real Analysis: 1. Internal set theory; 2. The real number system; 3. Sequences and series; 4. The topology of R; 5. Limits and continuity; 6. Differentiation; 7. Integration; 8. Sequences and series of functions; 9. Infinite series; Part II. Elements of Abstract Analysis: 10. Point set topology; 11. Metric spaces; 12. Complete metric spaces; 13. Some applications of completeness; 14. Linear operators; 15. Differential calculus on Rn; 16. Function space topologies; A. Vector spaces; B. The badic representation of numbers; C. Finite, denumerable, and uncountable sets; D. The syntax of mathematical languages; References; Index
 Dimensions
 24 cm.
 Extent
 xix, 565 pages
 Isbn
 9781107002029
 Isbn Type
 (hardback)
 Lccn
 2010050333
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code
 n
 System control number

 (OCoLC)694616467
 (OCoLC)ocn694616467
 Label
 Real analysis through modern infinitesimals, Nader Vakil
 Bibliography note
 Includes bibliographical references (p. [554]556) and index
 Carrier category
 volume
 Carrier category code
 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Machine generated contents note: Preface; Introduction; Part I. Elements of Real Analysis: 1. Internal set theory; 2. The real number system; 3. Sequences and series; 4. The topology of R; 5. Limits and continuity; 6. Differentiation; 7. Integration; 8. Sequences and series of functions; 9. Infinite series; Part II. Elements of Abstract Analysis: 10. Point set topology; 11. Metric spaces; 12. Complete metric spaces; 13. Some applications of completeness; 14. Linear operators; 15. Differential calculus on Rn; 16. Function space topologies; A. Vector spaces; B. The badic representation of numbers; C. Finite, denumerable, and uncountable sets; D. The syntax of mathematical languages; References; Index
 Dimensions
 24 cm.
 Extent
 xix, 565 pages
 Isbn
 9781107002029
 Isbn Type
 (hardback)
 Lccn
 2010050333
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code
 n
 System control number

 (OCoLC)694616467
 (OCoLC)ocn694616467
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