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Title: A Course of Pure Mathematics (Cambridge Mathematical Library) by G.H. Hardy ISBN: 0-521-09227-2 Publisher: Cambridge University Press Pub. Date: 01 June, 1993 Format: Paperback Volumes: 1 List Price(USD): $35.00 |
Average Customer Rating: 4.9 (10 reviews)
Rating: 5
Summary: Best introduction to mathematical analysis
Comment: 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.
Rating: 5
Summary: What style! This book will live forever.
Comment: 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!
Rating: 5
Summary: 1900 yrs from now....
Comment: ...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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Title: A Mathematician's Apology (Canto Book) by G.H. Hardy ISBN: 0521427061 Publisher: Cambridge University Press Pub. Date: 01 April, 1992 List Price(USD): $17.00 |
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Title: Fourier Series by G. H. Hardy, Werner Rogosinski ISBN: 0486406814 Publisher: Dover Publications Pub. Date: 01 February, 1999 List Price(USD): $7.95 |
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Title: Riemann's Zeta Function by Harold M. Edwards ISBN: 0486417409 Publisher: Dover Publications Pub. Date: 01 June, 2001 List Price(USD): $14.95 |
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Title: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire ISBN: 0309085497 Publisher: Joseph Henry Press Pub. Date: 23 April, 2003 List Price(USD): $27.95 |
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Title: Inequalities (Cambridge Mathematical Library) by G.H. Hardy, J.E. Littlewood, G. Polya ISBN: 0521358809 Publisher: Cambridge University Press Pub. Date: 01 February, 1988 List Price(USD): $40.00 |
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