A Course of Pure Mathematics (Cambridge Mathematical Library)

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Summary: 1900 yrs from now....
Review: ...people will look at this like we look at Euclid's Elements today, it's just one of those immortal books. Hardy starts by constructing the real numbers & then doing all the calculus you'd ever want to know, and with a bunch of math 'trivia' that can't be found anywhere. I can't add much to what the other reviewers have said, except this book has some evil integrals from old Cambridge Tripos exams that would make some Putnam problems look easy. lol At least, if you're only allowed to use real variables (& not complex variables & residues). Get this book for an excellent reference no matter what level you're at.

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Summary: What style! This book will live forever.
Review: 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!

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Summary: My God? What a book!
Review: Godfred Harold Hardy is one of the greatest mathematicians of the 20th century. A Course of Pure Mathematics is an introduction to Analysis, but he only starts Limits on page 110. Until there he talks about real numbers, Dedekind cuts and complex numbers as vectors. I have no words to describe his style: it seems that he is talking with you. If you are looking about a book of Calculus, stop here in buy it.

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Summary: Indispensable reference on pure math
Review: This book is a classic for differential and integral calculus. As welll an excellent book for historical reasons as for the excellent exposition of math.

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Summary: A truly elegant work
Review: This book is a classic, and deservedly so. It is comprehensive but not overloaded (like so many modern textbooks), crystal clear, well organized, rigorous. A wonderful text for teaching yourself higher math, which is how I am using it. But there is something beyond its didactic effectiveness that makes Hardy's work a must-have for anyone interested in math: This is a truly beautiful book, and working through it, while by no means easy, is an intellectual and aesthetic delight of the first order. Hardy is a genuinely elegant, subtle, incisive thinker, and his unbounded enthusiasm for his subject, duly controlled by British understatement, shines through every page. He conveys the irresistible, almost addictive quality of math.

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Summary: [e-mail]
Review: This book is a gem of the introductory calculus classics. However, in recent years, there exist a lot of other excellent calculus texts. I would recommend you to use this classic as a reference rather than a formal text.

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Summary: Best introduction to mathematical analysis
Review: This book is simply beyond any rating whatsoever. Giving 5 stars is to undermine the value of this classic.
The first time I got this book, I was neither aware of it not of its author. I just picked it up randomly from school library. From the contents I figured it was a book on calculus. I immediately searched for the proof that "every continuous function is integrable." This was the first book I encountered which had a rigorous proof of this.
Then I began reading the chapters sequentially thinking that this seems to be a good book on calculus. The book went much beyond my expectation and it satisfied all my mathematical curiousities. All the mysteries of calculus were revelaed. Hardy demystified calculus in the first chapter itself by creating reals out ot rationals.
The Dedekind's construction of reals as presented in this book is the best I have seen. The properties of reals were not stated as axioms (common approach in books on analysis) but rather deduced from those of rationals.
The concepts of functions, limits, continuity, derivative etc. were explained in a prosaic style which has no parallel. This was also my first book on maths which had far more english words than mathematical symbols.
After finishing the entire book I was wondering who was this guy G. H. Hardy who has written such a masterpiece.
Only a few months later I came to know that he was one of the greatest British mathematicians of the century and was responsible for making our Indian Ramanujan famous. After that I read most of his books including "A Mathematician's Apology" and "An Introduction to Theory of Numbers"
Any persons who thinks maths is dull should just read few pages from this book and I bet his old beliefs would be shattered.

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Summary: A classic work by a modern legend
Review: This book is to pure maths what Knuth's Art of Computer Programming is to computer science or Feynman's lectures are to physics. If I was to be a castaway on a desert island, and was permitted to take only one book on mathematics, this is the one I would choose. I cannot recomend it too highly.

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Summary: A Classic for Decades and For Decades to Come
Review: This book may be a little quaint. The terminology is a little out of date, e.g. "sequences" are "functions of a positive integral variable." It is marked by great organization and copious examples. What I appreciate most is the clarity and simplicity of the proofs. This is a great book for any serious student of real analysis prior to the Lebesque integral.

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Summary: Much better than any textbook I've ever seen...
Review: This is simply one of the best math books I've ever read. I've never seen any better definitions of limits, derivatives, and integrals. Although the notation is a wee bit outdated and confusing at times (full of phis, psis, deltas et cetera), this book was very easy to understand, which is weird considering I'm only 15, a junior and in Pre-Calculus. But this book means AP Calculus should be very easy for me next year...