Enhanced descriptions from Syndetics:

NUMBERS AND GEOMETRY is a beautiful and relatively elementary account of a part of mathematics where three main fields--algebra, analysis and geometry--meet. The aim of this book is to give a broad view of these subjects at the level of calculus, without being a calculus (or a pre-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. The key is algebra, which brings arithmetic and geometry together, and allows them to flourish and branch out in new directions. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He believes that most of mathematics is about numbers, curves and functions, and the links between these concepts can be suggested by a thorough study of simple examples, such as the circle and the square. This book covers the main ideas of Euclid--geometry, arithmetic and the theory of real numbers, but with 2000 years of extra insights attached. NUMBERS AND GEOMETRY presupposes only high school algebra and therefore can be read by any well prepared student entering university. Moreover, this book will be popular with graduate students and researchers in mathematics because it is such an attractive and unusual treatment of fundamental topics. Also, it will serve admirably in courses aimed at giving students from other areas a view of some of the basic ideas in mathematics. There is a set of well-written exercises at the end of each section, so new ideas can be instantly tested and reinforced.

Table of contents provided by Syndetics

• Arithmetic
• Geometry
• Coordinates
• Rational points
• Trigonometry
• Finite arithmetic
• Complex numbers
• Conic sections
• Elementary functions

Reviews provided by Syndetics

CHOICE Review

This lovely book contains a selection of topics from elementary number theory (unique factorization, primes, finite arithmetic, rational points on quadratic curves), foundations of geometry (constructions, length, area and volume, conic sections) and foundations of the theory of elementary functions (trigonometry, exponentials, and logarithms). Stillwell's ambitious goal, at which he largely succeeds, is to present, at the level of calculus, topics from arithmetic, algebra, and geometry that "every aspiring mathematician should know." The result is a book that can be usefully read by college or university mathematics students at just about any stage of their education. Stillwell writes extremely well. In particular, the historical discussions at the end of each chapter are terrific. In general, every topic is artistically developed, and its importance in the development of mathematics is made clear. In addition, most chapters include some more advanced topics; examples include Kleins's view of geometry, rational points on spheres, and Dehn's solution of Hilbert's third problem. Every section ends with an elegant set of exercises through which the reader is guided. Strongly recommended for all undergraduate and graduate students. M. Henle Oberlin College