Numbers and Geometry

1. Front Matter

   Pages i-xiv

   PDF

2. Arithmetic

   • John Stillwell

   Pages 1-35

3. Geometry

   • John Stillwell

   Pages 37-67

4. Coordinates

   • John Stillwell

   Pages 69-109

5. Rational Points

   • John Stillwell

   Pages 111-142

6. Trigonometry

   • John Stillwell

   Pages 143-176

7. Finite Arithmetic

   • John Stillwell

   Pages 177-213

8. Complex Numbers

   • John Stillwell

   Pages 215-245

9. Conic Sections

   • John Stillwell

   Pages 247-279

10. Elementary Functions

    • John Stillwell

    Pages 281-309

11. Back Matter

    Pages 311-343

    PDF

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.

• Area
• Prime
• Volume
• calculus
• set

• Department of Mathematics, Monash University, Clayton, Australia

  John Stillwell

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