Zakon E. Mathematical Analysis. Volume I

The Saylor Foundation, 2004. — 365 pages.Set Theory.
Real Numbers. Fields.
Vector Spaces. Metric Spaces.
Function Limits and Continuity.
Differentiation and Antidifferentiation.
This text is an outgrowth of lectures given at the University of Windsor, Canada. One of our main objectives is updating the undergraduate analysis as a rigorous postcalculus course. While such excellent books as Dieudonn´e’s Foundations of Modern Analysis are addressed mainly to graduate students, we try to simplify the modern Bourbaki approach to make it accessible to sufficiently advanced undergraduates.