Winding Around

John Roe, Pennsylvania State University, State College, PA, USA.

• Prelude: Love, hate, and exponentialsPaths and homotopiesThe winding numberTopology of the planeIntegrals and the winding numberVector fields and the rotation numberThe winding number in functional analysisCoverings and the fundamental groupCoda: The Bott periodicity theoremLinear algebraMetric spacesExtension and approximation theoremsMeasure zeroCalculus on normed spacesHilbert spaceGroups and graphsBibliographyIndex

This book covers a lot of ground. But it does so in a clear and careful manner that would make a terrific read for the prepared undergraduate. It is a study in how an intuitive idea can transport one into some deep waters of mathematics, and that is an important story to tell." - John McCleary, Mathematical Reviews"People who teach university-level mathematics for a living often find themselves reading lots of books on the subject. But even for the book-lovers among us, after you've just read about ten linear algebra texts, all of which look like they were stamped from the same cookie cutter, the process can occasionally wear thin. It's very pleasant, then, to stumble across a book that is genuinely unique, that addresses a topic in a way not found elsewhere, and that teaches you something that you didn't know before. It's even nicer when the book in question does a really good job of it, as is the case with the book under review. ...Roe's writing style is succinct, but clear and quite elegant; I could practically hear a British accent as I read the book. This clarity of writing and the numerous appendices help make the book accessible." - MAA Online