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The Philosophy of Mathematics
About Author:
What is the Philosophy of Mathematics?
PREFACE.
INTRODUCTION.
GENERAL CONSIDERATIONS.
THE OBJECT OF MATHEMATICS.
TRUE DEFINITION OF MATHEMATICS.
ITS TWO FUNDAMENTAL DIVISIONS.
CONCRETE MATHEMATICS.
ABSTRACT MATHEMATICS.
THE EXTENT OF ITS FIELD.
BOOK I.
ANALYSIS.
CHAPTER I. GENERAL VIEW OF MATHEMATICAL ANALYSIS.
THE TRUE IDEA OF AN EQUATION.
THE TWO PRINCIPAL DIVISIONS OF THE CALCULUS.
THE CALCULUS OF VALUES, OR ARITHMETIC.
THE CALCULUS OF FUNCTIONS, OR ALGEBRA.
CHAPTER II.
ORDINARY ANALYSIS, OR ALGEBRA.
ALGEBRAIC EQUATIONS.
ALGEBRAIC RESOLUTION OF EQUATIONS.
NUMERICAL RESOLUTION OF EQUATIONS.
THE THEORY OF EQUATIONS.
THE METHOD OF INDETERMINATE COEFFICIENTS.
IMAGINARY QUANTITIES.
NEGATIVE QUANTITIES.
PRINCIPLE OF HOMOGENEITY.
CHAPTER III.
DIFFERENT MODES OF VIEWING IT.
ITS EARLY HISTORY.
METHOD OF LEIBNITZ.
METHOD OF NEWTON.
METHOD OF LAGRANGE.
FUNDAMENTAL IDENTITY OF THE THREE METHODS.
COMPARATIVE VALUE OF THE THREE METHODS.
CHAPTER IV.
ITS TWO FUNDAMENTAL DIVISIONS.
THEIR RELATIONS TO EACH OTHER.
THE DIFFERENTIAL CALCULUS.
THE INTEGRAL CALCULUS.
CHAPTER V.
THE CALCULUS OF VARIATIONS.
PROBLEMS GIVING RISE TO IT.
METHOD OF LAGRANGE.
ITS RELATIONS TO THE ORDINARY CALCULUS.
CHAPTER VI.
THE CALCULUS OF FINITE DIFFERENCES.
GENERAL THEORY OF SERIES.
PERIODIC OR DISCONTINUOUS FUNCTIONS.
APPLICATIONS OF THIS CALCULUS.
BOOK II.
CHAPTER I.
GENERAL VIEW OF GEOMETRY.
THE FINAL OBJECT OF GEOMETRY.
INFINITE EXTENT OF ITS FIELD.
EXPANSION OF ORIGINAL DEFINITION.
PROPERTIES OF LINES AND SURFACES.
THE TWO GENERAL METHODS OF GEOMETRY.
CHAPTER II.
ANCIENT OR SYNTHETIC GEOMETRY.
ITS PROPER EXTENT.
GEOMETRY OF THE RIGHT LINE.
GRAPHICAL SOLUTIONS.
DESCRIPTIVE GEOMETRY.
ALGEBRAIC SOLUTIONS.
TRIGONOMETRY.
CHAPTER III.
MODERN OR ANALYTICAL GEOMETRY.
ANALYTICAL REPRESENTATION OF FIGURES.
PLANE CURVES.
CHOICE OF CO-ORDINATES.
SURFACES.
CURVES OF DOUBLE CURVATURE.
IMPERFECTIONS OF ANALYTICAL GEOMETRY.
FOOTNOTES:
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