The Method of Coordinates

Av Gelfand-Glagoleva

88 sidor, 210 kr (exkl. moms och frakt)

The Method of Coordinates is a way of transferring geometric images into formulas, a method for describing pictures by numbers and letters denoting constants and variables. It is fundamental to the study of calculus and other mathematical topics. Teachers of mathematics will find here a fresh understanding of the subject and a valuable path to the training of students in mathematical concepts and skills.

"All through both volumes [Functions & Graphs and The Methods of Coordinates] , 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. We are ... very fortunate that an account of this caliber has finally made it to printed pages... Anyone who has taken this guided tour will never be intimidated by n ever again... High school students (or teachers) reading through these two books would learn an enormous amount of good mathematics. More importantly, they would also get a glimpse of how mathematics is done."
(H. Wu, The Mathematical Intelligencer)

Table of Contents
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