The Resource Real analysis through modern infinitesimals, Nader Vakil

Real analysis through modern infinitesimals, Nader Vakil

Label
Real analysis through modern infinitesimals
Title
Real analysis through modern infinitesimals
Statement of responsibility
Nader Vakil
Creator
Subject
Genre
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, self-study, 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"--
Member of
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
Instantiates
Publication
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 b-adic 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
Publication
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 b-adic 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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