3 of 3 people found the following review helpful
on 21 July 2011
G H Hardy's book is the pioneer in the field of introducing the formal and rigorous principles of Mathematical Analysis. By Hardy's own admission, the book sprang from the void that existed prior to its publication in 1907.
In a word, the hallmark of this book is "style", and Hardy must be the original style guru as far as Pure Mathematics goes.
The book covers all the essential elements one would expect to see in an introductory course in the subject, namely the notion of a limit and its application to sequences, series, a comprehensive yet elementary exposition of convergence and its use in the definition of functions, differentiation and integration. All of the main theorems of the calculus of the real variable are covered. The latter chapters address the general theory of logarithmic, exponential and circular functions.
Despite the glut of books on the subject of Real Analysis that are on the market, and there are some VERY GOOD ones, this is the classic text that every serious student of Pure Mathematics should begin with. Texts with more general coverage of real analysis such as Tom Apostol's Mathematical Analysis can follow thereafter.
This book is nearly 100 years old. You can bet that it will still be around 100 years from now!
on 9 February 2015
Although the sequence of the presentation of the fundamentals of mathematics has changed over the last century, the substance has not. There is no greater evidence of this fact than this classic work by Hardy, which could be used without alteration or additional explanation as a text in modern college mathematics courses. Hardy was rightfully known as a bit of an eccentric, yet he was a brilliant pure mathematician and he will always be held in the highest regard for his actions in aiding the Indian prodigy Ramanujan. Less well known but still extremely significant is his expository writing; there are few who wrote as clearly as he did.
This book was extremely influential in the teaching of mathematics over the last century. The primary subject matter is:
*) Real variables
*) Functions of real variables
*) Complex numbers
*) Limits of functions of a positive integral variable
*) Limits of functions of a continuous variable
*) Derivatives and integrals
*) Theorems on the differential and integral calculus
*) Convergence of infinite series and infinite integrals
*) Logarithmic, exponential and circular functions of a real variable
*) General theory of the logarithmic, exponential and circular functions
There are few proofs, but an enormous number of examples. The mathematical influence of G. H. Hardy over mathematical education was and remains strong, as can be seen by reading this masterpiece.
Published in Journal of Recreational Mathematics, reprinted with permission
2 of 2 people found the following review helpful
on 16 July 2010
This is an excellent work which I have used for over half a century, but I'm glad that as a student I bought the hardback for 30 shillings - a paperback would have fallen to loose pages years ago.
on 20 January 2013
The book that anyone interested in maths must have on his bookshelf : the prelude to any other book on analysis !
Hardy's crystal-clear, no fuss, precise and concise style at its best.
My preferred chapter to be found nowhere else : chapter X, on the general theory of the logarithmic, exponential and circular functions
When in doubt, I always go back to Hardy.