# Numbers and Geometry

• John Stillwell
Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xiv
2. John Stillwell
Pages 1-35
3. John Stillwell
Pages 37-67
4. John Stillwell
Pages 69-109
5. John Stillwell
Pages 111-142
6. John Stillwell
Pages 143-176
7. John Stillwell
Pages 177-213
8. John Stillwell
Pages 215-245
9. John Stillwell
Pages 247-279
10. John Stillwell
Pages 281-309
11. Back Matter
Pages 311-343

### Introduction

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.

### Keywords

Area Prime Volume calculus set

#### Authors and affiliations

• John Stillwell
• 1
1. 1.Department of MathematicsMonash UniversityClaytonAustralia

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-0687-3
• Copyright Information Springer-Verlag New York, Inc. 1998
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-6867-3
• Online ISBN 978-1-4612-0687-3
• Series Print ISSN 0172-6056
• Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking
Electronics
Aerospace