Abstract

This self-contained handbook providing broad coverage on the foundations of mathematical analysis, is intended as a study guide for advanced undergraduates and beginning graduate students in mathematics and is a reference for more advanced mathematicians. It provides an introduction to a wide range of topics including set theory and mathematical logic; algebra; toplogy; normed spaces; integration theory; toplogical vector spaces; and differential equations. The author demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples in the presentation of classical pathological objects through nonconstructive proofs.