The Method of Coordinates

ISBN-13: 9780817635336 / Angielski / Miękka / 1990 / 74 str.

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Opis

-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 The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990's. As early as the 1960's, I.M. Gelfand and his colleagues in the USSR thought hard about this same question and developed a style for presenting basic mathematics in a clear and simple form that engaged the curiosity and intellectual interest of thousands of high school and college students. These same ideas, this development, are available in the following books to any student who is willing to read, to be stimulated, and to learn. 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.

Recenzje

"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 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

"This book is a concise and compact treatment of the essential ideas of coordinate geometry.  The authors demonstrate powerfully how geomtric ides may be communicated and studied effectively without the aid of pictures.  Graphics are of course of vital importance int he methods of Euclidean geometry. However, the methods of coordinate geometry are able to transform pure geometric ideas into algebraic manipulations where the meaning is very clear once the formalism is learnt. In particular the book demonstrates the value of conveying information in the form of images embedded in formulas.  This is very useful in the transmission of information by electronic means. . . This book is a valuable tool for teaching the redimentary concepts of analytical geometry.  It contains a number of excellent examples and exercises which go further than a mere introductory programme.  the exercises, while not numerous, are very thought-provoking and are bound to pose a serious challenge to the interested student."

---The Mathematical Gazette

Spis treści

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.