" I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings .

Euclid's Elements of Geometry, with Greek and English texts in side-by-side columns.

This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.

Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics.

The significance of the spiral in nature, art, science, and the phenomena of life and growth is probed

Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study.

Sheaves also appear in logic as carriers for models of set theory. This text presents topos theory as it has developed from the study of sheaves.

This book is an introductory graduate-level textbook on the theory of smooth manifolds.

Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the ...

Written for the active reader with some background in the topic, this book presents problems in Hilbert space theory, with definitions, corollaries and historical remarks, hints, proofs, answers and constructions.