Handbook of Analysis and Its Foundations

Rating:
Summary: From an amateur's point of view.
Review: I've always wanted to know more math. Finally, I've discovered a big book that makes the tough stuff accessible without sacrificing detail or over-simplifying the hard concepts. For someone with a little bit of college math - calculus and maybe a few more courses - this is it. Analysis, abstract algebra, set theory, topology .... It's all here despite the focus on foundations. And it's organized in a way that makes it possible to follow the thread of a topic throughout the book without reading everything from the beginning. A CDROM version (the one I'm using) not only allows the sort of random access that makes surfing the book convenient but also presents the text in either HTML or PDF format. Open it up in a Java-enabled browser and you can play with the fonts until it suits your reading style. Ideally, for the reader, the CDROM might have been bundled with the book.

Books geared to self instruction need to enlist the readers' aid in educating themselves. Good teachers have that knack. It is a gift to be able to make complicated ideas understandable by building up gradually from simple and familiar concepts to ones that are unusual, obscure, or even initially incomprehensible. Eric Schecter must be a good teacher because in reading his book I am learning more math than I ever thought I would or could. I need to leave questions about the quality of the math itself in depth or scope to the judgment of the professionals but the text appears to make few concessions of substance to us amateurs. Armchair or would-be mathematicians as well as teachers and researchers might find this book a place in their personal libraries.