A Course

of Pure

Mathematics

of Pure

Mathematics

I have endeavoured to make Chapter IV one of the principal features of the book. The notion of a limit is one that has always presented grave difficulties to mathematical students even of great ability. It has been my good fortune during the last eight or nine years to have a share in the teaching of a good many of the ablest candidates for the Mathematical Tripos; and it is very rarely indeed that I have encountered a pupil who could face the simplest problem involving the ideas of infinity, limit, or continuity, with a vestige of the confidence with which he would deal with questions of a different character and of far greater intrinsic difficulty. I have indeed in an examination asked a dozen candidates, including several future Senior Wranglers, to sum the series 1 +m+m2+ and not received a single answer that was not practically worthless — and this from men quite capable of solving difficult problems connected with the curvature and torsion of twisted curves.

I cannot believe that this is due solely to the nature of the subject. There are difficulties in these ideas, no doubt: but they are not so great as many other difficulties inherent in mathematics that every young mathematician completely overcomes. The fault is not that of the subject or of the student, but of the text-book and the teacher. It is not enough for the latter, if he wishes to drive sound ideas on these points well into the mind of his pupils.

PIBN | 10020144 |

ISBN | 978-1-4400-7907-8 |

ISBN (Hardcover) | 978-1-5281-4892-4 |

Language | English |

Category | Calculus |

Pages | 439 |

Words | 126493 |

Vocabulary | 1907 |

A Treatise on

the Calculus

of Finite

Differences

the Calculus

of Finite

Differences

Elements of

Quaternions

Vol. 1

Quaternions

Vol. 1

The

Foundations

of Geometry

Foundations

of Geometry

AlgebraAn Elementary Text-Book for the Higher

Classes of Secondary Schools and for Colleges

Vol. 2

Classes of Secondary Schools and for Colleges

Vol. 2

Hyperbolic

Functions

Functions

The Philosophy

of MathematicsTranslated From the Cours De

Philosophie Positive of Auguste Comte

of MathematicsTranslated From the Cours De

Philosophie Positive of Auguste Comte

A Treatise

on Plane

Trigonometry

on Plane

Trigonometry

Vector

AnalysisAn Introduction to Vector-Methods and Their

Various Applications to Physics and Mathematics

AnalysisAn Introduction to Vector-Methods and Their

Various Applications to Physics and Mathematics

Pure Mathematics,

Including

Arithmetic, Algebra,

Geometry, and

Plane Trigonometry

Including

Arithmetic, Algebra,

Geometry, and

Plane Trigonometry

The

Calculus for

Engineers

Calculus for

Engineers

Introduction

to Theory

of Analytic

Function

to Theory

of Analytic

Function

Advanced

Course in

Algebra

Course in

Algebra

The Theory of

Functions of a

Real Variable and the

Theory of Fourier's

Series, by E. W Hobson

Functions of a

Real Variable and the

Theory of Fourier's

Series, by E. W Hobson

Functions

of a Complex

Variable

of a Complex

Variable

The Integration

of Functions of

a Single Variable

of Functions of

a Single Variable

AlgebraAn Elementary Text-Book for the Higher

Classes of Secondary Schools and for Colleges

Vol. 2

Classes of Secondary Schools and for Colleges

Vol. 2

Theory of

Functions of a

Complex Variable

Functions of a

Complex Variable

Differential

and Integral

Calculus

and Integral

Calculus

Complex Roots

of Polynomial

Equations

of Polynomial

Equations

A Course

of Pure

Mathematics

of Pure

Mathematics

An

Introduction

to Mathematics

Introduction

to Mathematics

Functions

of a Complex

Variable

of a Complex

Variable

Elements of

Quaternions

Vol. 2

Quaternions

Vol. 2

Graphical

Calculus

Calculus

An Elementary

Course in

Differential

Equations

Course in

Differential

Equations

A History of

Mathematics

Mathematics

Lectures on

the Theory

of Elliptic

Functions

Vol. 1

the Theory

of Elliptic

Functions

Vol. 1

College

Algebra

Algebra

A Treatise on the

Integral CalculusWith Applications,

Examples, and Problems

Vol. 2

Integral CalculusWith Applications,

Examples, and Problems

Vol. 2

Calculus

Harmonic

Functions

Functions

Lectures on

Elementary

Mathematics

Elementary

Mathematics

Studies on

Divergent Series

and Summability

Vol. 2

Divergent Series

and Summability

Vol. 2

An Elementary

Treatise on Laplace's

Functions, Lamé's

Functions, and

Bessel's Functions

Treatise on Laplace's

Functions, Lamé's

Functions, and

Bessel's Functions

A Treatise on

the Circle and

the Sphere

the Circle and

the Sphere

College

Algebra

Algebra

Smithsonian

Mathematical

Formulae and

Tables of Elliptic

Functions

Mathematical

Formulae and

Tables of Elliptic

Functions

The Philosophy

of MathematicsWith Special Reference to the Elements of

Geometry and the Infinitesimal Method

of MathematicsWith Special Reference to the Elements of

Geometry and the Infinitesimal Method

Higher

Algebra

Algebra

On the Study

and Difficulties

of Mathematics

and Difficulties

of Mathematics

The Method of

Fluxions and

Infinite SeriesWith Its Application to the

Geometry of Curve-Lines

Fluxions and

Infinite SeriesWith Its Application to the

Geometry of Curve-Lines

Lectures on

MathematicsDelivered From Aug. 28 to Sept. 9, 1893 Before Members of the

Congress of Mathematics Held in Connection With the World's

Fair in Chicago at Northwestern University, Evanston, Ill

MathematicsDelivered From Aug. 28 to Sept. 9, 1893 Before Members of the

Congress of Mathematics Held in Connection With the World's

Fair in Chicago at Northwestern University, Evanston, Ill

Archimedes

The

Nature of

Mathematics

Nature of

Mathematics

Algebra for

Beginners

Beginners

A Brief History

of MathematicsAn Authorized Translation of Dr. Karl Fink's

Geschichte Der Elementar-Mathematik

of MathematicsAn Authorized Translation of Dr. Karl Fink's

Geschichte Der Elementar-Mathematik

General Investigations

of Curved Surfaces

of 1827 and 1825Translated With Notes

and a Bibliography

of Curved Surfaces

of 1827 and 1825Translated With Notes

and a Bibliography

An Elementary

Treatise on

the CalculusWith Illustrations From

Geometry, Mechanics and Physics

Treatise on

the CalculusWith Illustrations From

Geometry, Mechanics and Physics

A History

of Greek

MathematicsFrom Thales to Euclid

Vol. 1

of Greek

MathematicsFrom Thales to Euclid

Vol. 1

Correlated

Mathematics for

Junior Colleges

Mathematics for

Junior Colleges

History of

Modern

Mathematics

Modern

Mathematics

Vector

Analysis and

Quaternions

Analysis and

Quaternions

Differential

and Integral

Calculus

and Integral

Calculus

The Axioms of

Descriptive

Geometry

Descriptive

Geometry