Real Analysis through Modern Infinitesimals

Nader Vakil

ଫେବୃଆରୀ 2011 · Encyclopedia of Mathematics and its Applications 140 ବହି · Cambridge University Press

ଇବୁକ୍

587

ପୃଷ୍ଠାଗୁଡ଼ିକ

ରେଟିଂ ଓ ସମୀକ୍ଷାଗୁଡ଼ିକୁ ଯାଞ୍ଚ କରାଯାଇନାହିଁ ଅଧିକ ଜାଣନ୍ତୁ

ଏହି ଇବୁକ୍ ବିଷୟରେ

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.

ଲେଖକଙ୍କ ବିଷୟରେ

Nader Vakil is a Professor of Mathematics at Western Illinois University. He received his PhD from the University of Washington, Seattle, where he worked with Edwin Hewitt. His research interests centre on the foundation of mathematical analysis and applications of the theory of modern infinitesimals to topology and functional analysis.

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