''A Course of Pure Mathematics'' is a classic textbook in introductory
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...
, written by
G. H. Hardy
Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...
. 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. It remains one of the most popular books on pure mathematics.
Contents
The book contains a large number of descriptive and study materials together with a number of difficult problems with regards to number theory analysis. The book is organized into the following chapters, with each chapter further divided.
I. REAL VARIABLES
II. FUNCTIONS OF REAL VARIABLES
III COMPLEX NUMBERS
IV LIMITS OF FUNCTIONS OF A POSITIVE INTEGRAL VARIABLE
V LIMITS OF FUNCTIONS OF A CONTINUOUS VARIABLE. CONTINUOUS AND DISCONTINUOUS FUNCTIONS
VI DERIVATIVES AND INTEGRALS
VII ADDITIONAL THEOREMS IN THE DIFFERENTIAL AND INTEGRAL CALCULUS
VIII THE CONVERGENCE OF INFINITE SERIES AND INFINITE INTEGRALS
IX THE LOGARITHMIC, EXPONENTIAL AND CIRCULAR FUNCTIONS OF A REAL VARIABLE
X THE GENERAL THEORY OF THE LOGARITHMIC, EXPONENTIAL AND CIRCULAR FUNCTIONS
Appendices
INDEX
Review
The book was intended to help reform mathematics teaching in the UK, and more specifically in the
University of Cambridge
, mottoeng = Literal: From here, light and sacred draughts.
Non literal: From this place, we gain enlightenment and precious knowledge.
, established =
, other_name = The Chancellor, Masters and Schola ...
and in schools preparing to study higher mathematics. It was aimed directly at "scholarship level" students – the top 10% to 20% by ability. Hardy himself did not originally find a passion for mathematics, only seeing it as a way to beat other students, which he did decisively, and gain scholarships.
However, his book excels in effectively explaining analytical number theory and calculus following the rigor of mathematics. Its publication came a year after that of Theory of Functions of a Real Variable by
E.W. Hobson, which may partly have been its inspiration.
Whilst his book changed the way the subject was taught at university, the content reflects the era in which the book was written. The whole book explores number theory and the author constructs real numbers theoretically. It deals with single-variable calculus, sequences, number series, properties of cos, sin, log, etc. but does not refer to mathematical groups, multi-variable functions or vector calculus.
References
External links
Online copies
Third edition (1921) at Internet ArchiveThird edition (1921) at Project GutenbergFirst edition (1908) at University of Michigan Historical Math Collection
Other
''A Course of Pure Mathematics'' at Cambridge University Press(10 e. 1952, reissued 2008)
{{DEFAULTSORT:Course of Pure Mathematics
1908 non-fiction books
Mathematics textbooks
Mathematical analysis