Real analysis through modern infinitesimals
Material type: TextSeries: Encyclopedia of mathematics and its applicationsPublication details: Cambridge ; New York : Cambridge University Press, 2011, ©2011Description: xix, 565 pagesISBN: 9781107002029 (hardback)Subject(s): Mathematical analysis | Set theory | MATHEMATICS / Mathematical AnalysisDDC classification: 515 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"--Summary: "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"--Item type | Current library | Collection | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|---|
BK | Kannur University Central Library Stack | Stack | 515 VAK/R (Browse shelf (Opens below)) | Available | 33054 |
Browsing Kannur University Central Library shelves, Shelving location: Stack, Collection: Stack Close shelf browser (Hides shelf browser)
515 SOM/F First course in mathematical analysis | 515 STE/E Essential calculus with applications | 515 THO/C Calculus | 515 VAK/R Real analysis through modern infinitesimals | 515 ZOR/U Understanding real analysis | 515 ZWO/S Semiclassical analysis | 515.028553 CRI/E Exploring calculus : labs and projects with Mathematica |
"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"--
There are no comments on this title.