Synopses & Reviews
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.
Review
"Stillwell writes extremely well.In general, every topic is artistically developed, and its importance in the development of mathematics is made clear.Every section ends with an elegant set of exercises through which the reader is guided. Strongly recommended for all undergraduate and graduate students. CHOICE"
Synopsis
Numbers and Geometry is a beautiful and relatively an elementary account of the part of mathematics where algebra, analysis and geometry meet. Stillwell has chosen an array of exciting and worthwhile topics, and elegantly combines mathematics with mathematical history. This book covers the main ideas of Euclid, but with 2000 years of extra insights attached. It can be read by any well prepared student entering college.
Description
Includes bibliographical references (p. 311-315) and index.
Table of Contents
Arithmetic.- Geometry.- Coordinates.- Rational points.- Trigonometry.- Finite arithmetic.- Complex numbers.- Conic sections.- Elementary functions.