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"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. Functions and Graphs provides instruction
in transferring formulas and data into geometrical form. Thus,
drawing graphs is shown to be one way to "see" formulas and
functions and to observe the ways in which they change. This skill
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.Contents Preface
Foreword Introduction Chapter 1 Examples Chapter 2 The Linear
Function Chapter 3 The Function y =] x ] Chapter 4 The Quadratic
Equation Chapter 5 The Linear Fractional Function Chapter 6 Power
Functions Chapter 7 Rational Functions Problems for Independent
Solution Answers and Hints to Problems Marked with the Sign
"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. Contents Preface
Foreword Introduction PART I Chapter 1 TheCoordinates 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
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