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The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990s. As early as the 1960s, I. M. Gel'fand and his... Read more
The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990s. As early as the 1960s, I. M. Gel'fand 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 same content, unchanged by over thirty years of experience and mathematical development, are available in the present 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.
The Method of Coordinates Paperback edition by Isarel M. Gelfand
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.
The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases.
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of...
Two-part treatment discusses coordinates of points on a line, coordinates of points in a plane, coordinates of points in space, and peculiarities of four-dimensional space. Abundance of ingenious problems.
Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, introduction to tensors, and more. 1961 edition.
Irene Dorfman died in Moscow on April 6, 1994, shortly after seeing her beautiful book on Dirac structures [I]. The present volume contains a collection of papers aiming at celebrating her outstanding contributions to mathematics. Her most important discoveries are associated with the algebraic structures arising in the study of integrable equations. Most of the articles contained in this volume...
It is very tempting but a little bit dangerous to compare the style of two great mathematicians or of their schools. I think that it would be better to compare papers from both schools dedicated to one area, geometry and to leave conclusions to a reader of this volume. The collaboration of these two schools is not new. One of the best mathematics journals Functional Analysis and its Applications...
The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990s. 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.
The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990's. 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.
I.M. Gelfand (1913 - 2009), one of the world's leading contemporary mathematicians, largely determined the modern view of functional analysis with its numerous relations to other branches of mathematics, including mathematical physics, algebra, topology, differential geometry and analysis. In this three-volume Collected Papers Gelfand presents a representative sample of his work. Gelfand's...
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