Handbook of Analysis and Its Foundations

by Eric Schechter

Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook.

Genres: Mathematics

883 pages, Hardcover

First published January 1, 1996

Reviews

[Michael]

The preface to this book says, "I believe that the reading of part or all of this book would be a good project for the summer vacation before one begins graduate school in mathematics."

Well, I tried to do this. Unfortunately, for someone with my mindset about mathematics, this is essentially impossible. It's just so much boring stuff to wade through.

However... this book is still really good. An example of what's so good about it: the discussion on nets and filters. This book gives the "right" definition of subnet, compares it to the other possible definitions, explicitly gives the connection between nets and filters... For some reason this information isn't really available in other books. But I have no desire to just sit down and read this book (or a significant portion of it) straight through.