Real Analysis Through Modern Infinitesimals Nader Vakil

ISBN: 9781139633017

Published: June 6th 2013

ebook

586 pages


Description

Real Analysis Through Modern Infinitesimals  by  Nader Vakil

Real Analysis Through Modern Infinitesimals by Nader Vakil
June 6th 2013 | ebook | PDF, EPUB, FB2, DjVu, AUDIO, mp3, RTF | 586 pages | ISBN: 9781139633017 | 9.67 Mb

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 carefulMoreReal 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.



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