A Course of Pure Mathematics

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

The book was intended to help reform mathematics teaching in the UK, and more specifically in the University of Cambridge 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.[1]