The Method of Coordinates - Gelfand, I. M.

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Résumé :
The Method of Coordinates is one volume in a series of books that present basic mathematics in a clear and simple form. The book describes a way of transferring images into formulas, describing pictures by numbers. The content is fundamental to the study of calculus and other mathematical topics. All through this volume, one finds a careful description of the step-by-step thinking process that leads up to the correct definition of a concept or to an argument that clinches in the proof of a theorem. High school students or teachers, reading this book will learn an enormous amount of good mathematics. More importantly, they would also get a glimpse of how mathematics is done....

Sommaire:

Preface.- Foreword.- Introduction.- PART I.- Chapter 1. The Coordinates of Points on a Line.- 1. The Number Axis.- 2. The Absolute Value of Number.- 3. The Distance Between Two Points.- Chapter 2. The Coordinates of Points in the Plane.- 4. The Coordinate Plane.- 5. Relations Connecting Coordinates.- 6. The Distance Between Two Points.- 7. Defining Figures.- 8. We Begin to Solve Problems.- 9. Other Systems of Coordinates.- Chapter 3. The Coordinates of a Point in Space.- 10. Coordinate Axes and Planes.- 11. Defining Figures in Space.- PART II.- Chapter 1. Introduction.- 1. Some General Considerations.- 2. Geometry as an Aid in Calculation.- 3. The Need for Introducing Four-Dimensional Space.- 4. The Peculiarities of Four-Dimensional Space.- 5. Some Physics.- Chapter 2. Four-Dimensional Space.- 6. Coordinate Axes and Planes.- 7. Some Problems.- Chapter 3. The Four-Dimensional Cube.- 8. The Definition of the Sphere and the Cube.- 9. The Structure of the Four-Dimensional Cube.- 10. Problems on the Cube.