Numbers and Geometry

by John Stillwell, John Stiilwell

A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of calculus, without being a calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He covers the main ideas of Euclid, but with 2000 years of extra insights attached. Presupposing only high school algebra, it can be read by any well prepared student entering university. Moreover, this book will be popular with graduate students and researchers in mathematics due to its attractive and unusual treatment of fundamental topics. A set of well-written exercises at the end of each section allows new ideas to be instantly tested and reinforced.

Genres: Mathematics, Geometry

357 pages, Hardcover

First published October 30, 1997

About the author

John Colin Stillwell (born 1942) is an Australian mathematician on the faculties of the University of San Francisco and Monash University

Reviews

[Yofish · Rating 4 out of 5]

Really a textbook for, maybe an advanced non-math major. Lots of interesting stuff. (Interesting bit on solving Hilbert's third problem---whether a tetrahedron an be cut up and repasted into a cube. Awesome use of tensor products!) It would have been a lot better if I had had more time (or patience) to go carefully through the exercises. And reading in dribs and drabs before work probably broke it up in the wrong places.