Real Analysis Through Modern Infinitesimals

כריכה קדמית
Cambridge University Press, 17 בפבר׳ 2011 - 565 עמודים
0 ביקורות
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.
  

מה אומרים אנשים - כתוב ביקורת

לא מצאנו ביקורות במקומות הרגילים

תוכן

Part I Elements of real analysis
15
Part II Elements of abstract analysis
331
Vector spaces
521
The badic representationof numbers
523
Finite denumerableand uncountable sets
536
The syntax ofmathematical languages
544
References
554
Index
557
זכויות יוצרים

מונחים וביטויים נפוצים

מידע על המחבר (2011)

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.

מידע ביבליוגרפי