Acourse of pure mathematics - Hardy
A Course of Pure Mathematics (ISBN 0521720559) is a classic textbook in introductory mathematical analysis, written by G. H. Hardy. It is recommended for people studying calculus. First published in 1908, it went through ten editions (up to 1952) and several reprints. It is now out of copyright in UK and is downloadable from various internet web sites, free of charge including. It remains one of the most popular books on pure mathematics.
PREFACE TO THE THIRD EDITION
NO extensive changes have been made in this edition. The most
important are in 80-82, which I have rewritten in accord
ance with suggestions made by Mr S. Pollard.
The earlier editions contained no satisfactory account of the
genesis of the circular functions. I have made some attempt to
meet this objection in 158 and Appendix III. Appendix IV is also
an addition.
It is curious to note how the character of the criticisms I have
had to meet has changed. I was too meticulous and pedantic for
my pupils of fifteen years ago: I am altogether too popular for the
Trinity scholar of to-day. I need hardly say that I find such
criticisms very gratifying, as the best evidence that the book has
to some extent fulfilled the purpose with which it was written.
EXTRACT FROM THE PREFACE TO
THE SECOND EDITION
THE principal changes made in this edition are as follows.
I have inserted in Chapter I a sketch of Dedekind s theory
of real numbers, and a proof of Weierstrass s theorem concerning
points of condensation; in Chapter IV an account of limits of
indetermination and the general principle of convergence ; in
Chapter V a proof of the Heine-Borel Theorem , Heine s theorem
concerning uniform continuity, and the fundamental theorem
concerning implicit functions ; in Chapter VI some additional
matter concerning the integration of algebraical functions ; and
in Chapter VII a section on differentials. I have also rewritten
in a more general form the sections which deal with the defini
tion of the definite integral. In order to find space for these
insertions I have deleted a good deal of the analytical geometry
and formal trigonometry contained in Chapters II and III of
the first edition. These changes have naturally involved a
large number of minor alterations,
EXTRACT FROM THE PEEFACE TO THE
FIRST EDITION
THIS book has been designed primarily for the use of first
year students at the Universities whose abilities reach or
approach something like what is usually described as scholarship
standard . I hope that it may be useful to other classes of
readers, but it is this class whose wants I have considered first.
It is in any case a book for mathematicians: I have nowhere
made any attempt to meet the needs of students of engineering
or indeed any class of students whose interests are not primarily
mathematical.
I regard the book as being really elementary. There arc
plenty of hard examples (mainly at the ends of the chapters) : to
these I have added, wherever space permitted, an outline of the
solution. But I have done my best to avoid the inclusion of
anything that involves really difficult ideas. For instance, I make
no use of the principle of convergence : uniform convergence .
double series, infinite products, are never alluded to : and I prov<
no general theorems whatever concerning the inversion of limit-
C9 - Ci9 ./*
operations I never even define 5-^7 and . i . In the last tw
cxoy oyccc
chapters I have occasion once or twice to integrate a power-series,
but I have confined myself to the very simplest cases and give i
a special discussion in each instance. Anyone who has read this
book will be in a position to read with profit Dr Bromwich ?
Infinite Series, where a full and adequate discussion of all theso
points will be found.
PREFACE TO THE THIRD EDITION
NO extensive changes have been made in this edition. The most
important are in 80-82, which I have rewritten in accord
ance with suggestions made by Mr S. Pollard.
The earlier editions contained no satisfactory account of the
genesis of the circular functions. I have made some attempt to
meet this objection in 158 and Appendix III. Appendix IV is also
an addition.
It is curious to note how the character of the criticisms I have
had to meet has changed. I was too meticulous and pedantic for
my pupils of fifteen years ago: I am altogether too popular for the
Trinity scholar of to-day. I need hardly say that I find such
criticisms very gratifying, as the best evidence that the book has
to some extent fulfilled the purpose with which it was written.
EXTRACT FROM THE PREFACE TO
THE SECOND EDITION
THE principal changes made in this edition are as follows.
I have inserted in Chapter I a sketch of Dedekind s theory
of real numbers, and a proof of Weierstrass s theorem concerning
points of condensation; in Chapter IV an account of limits of
indetermination and the general principle of convergence ; in
Chapter V a proof of the Heine-Borel Theorem , Heine s theorem
concerning uniform continuity, and the fundamental theorem
concerning implicit functions ; in Chapter VI some additional
matter concerning the integration of algebraical functions ; and
in Chapter VII a section on differentials. I have also rewritten
in a more general form the sections which deal with the defini
tion of the definite integral. In order to find space for these
insertions I have deleted a good deal of the analytical geometry
and formal trigonometry contained in Chapters II and III of
the first edition. These changes have naturally involved a
large number of minor alterations,
EXTRACT FROM THE PEEFACE TO THE
FIRST EDITION
THIS book has been designed primarily for the use of first
year students at the Universities whose abilities reach or
approach something like what is usually described as scholarship
standard . I hope that it may be useful to other classes of
readers, but it is this class whose wants I have considered first.
It is in any case a book for mathematicians: I have nowhere
made any attempt to meet the needs of students of engineering
or indeed any class of students whose interests are not primarily
mathematical.
I regard the book as being really elementary. There arc
plenty of hard examples (mainly at the ends of the chapters) : to
these I have added, wherever space permitted, an outline of the
solution. But I have done my best to avoid the inclusion of
anything that involves really difficult ideas. For instance, I make
no use of the principle of convergence : uniform convergence .
double series, infinite products, are never alluded to : and I prov<
no general theorems whatever concerning the inversion of limit-
C9 - Ci9 ./*
operations I never even define 5-^7 and . i . In the last tw
cxoy oyccc
chapters I have occasion once or twice to integrate a power-series,
but I have confined myself to the very simplest cases and give i
a special discussion in each instance. Anyone who has read this
book will be in a position to read with profit Dr Bromwich ?
Infinite Series, where a full and adequate discussion of all theso
points will be found.
