Real Analysis through Modern Infinitesimals (Encyclopedia of Mathematics and its Applications Book 140) 1st Edition by Nader Vakil (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excerpt from the AMS Mathematical Reviews (MR2752815):”The book intends to be a reference in real analysis for undergraduate and more advanced students in mathematics … contains a quick introduction to the axiomatic approach of mathematics … provides the reader with an elementary introduction to nonstandard analysis, mainly Internal Set Theory (IST) … is written in a very clear style, with many examples and exercises … on the whole, this book is commendable and will provide the reader with a clear introduction to analysis, and to the use of nonstandard analysis for learning analysis.”

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