" 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 .

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 bestselling book that has helped millions of readers solve any problem A must-have guide by eminent mathematician G. Polya, How to Solve It shows anyone in any field how to think straight.

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Mesopotamia, 1800 BCE --Sidebar 1: Did the Egyptians Know It? --2. Pythagoras --3. Euclid's Elements --Sidebar 2: The Pythagorean Theorem in Art, Poetry, and Prose --4. Archimedes --5. Translators and Commentators, 500-1500 CE --6.

Among these are “natural number,” “parallel lines” and “congruent triangles,” “trapezoid” and “isosceles trapezoid,” the formal definitions of the trigonometric functions and absolute value, and implicit definitions of ...

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.