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1 of 1 people found the following review helpful
5.0 out of 5 stars A must have !
Don't expect a systematic treatise : Hardy guides you into the vast and intricate number theory via side tracks, leaving a few gaps to be filled in... Which allows him to cover an enormous range of topics, in his usual clear and concise style.

In my opinion, this book should be read after Gauss's masterpiece "Disquisitiones Arithmeticae" and before Apostol's...
Published 17 months ago by André Gargoura

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5 of 31 people found the following review helpful
2.0 out of 5 stars There is no such thing as 'number theory'!
I'm not as impressed as the other reviewers here with this book, despite it's being in some sense a 'classic'.

I take it some people - I have no idea what proportion of the population - now and then are struck by properties of numbers. For example, if a number AB is added to BA, the result always divides by 11. If the difference is work out, this is always a...
Published on 8 Aug 2010 by Rerevisionist


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1 of 1 people found the following review helpful
5.0 out of 5 stars A must have !, 20 Jan 2013
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André Gargoura "André Gargoura" (Paris, France) - See all my reviews
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This review is from: An Introduction to the Theory of Numbers (Paperback)
Don't expect a systematic treatise : Hardy guides you into the vast and intricate number theory via side tracks, leaving a few gaps to be filled in... Which allows him to cover an enormous range of topics, in his usual clear and concise style.

In my opinion, this book should be read after Gauss's masterpiece "Disquisitiones Arithmeticae" and before Apostol's "Introduction to Analytical Number Theory".
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4 of 5 people found the following review helpful
4.0 out of 5 stars An Introduction to the Theory of Numbers, 15 Nov 2010
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This review is from: An Introduction to the Theory of Numbers (Paperback)
I have owned a hard-back copy of this book (4th edition) since 1964, when I was still a student. At that time there were not many books on number theory available, and as far as I remember, Hardy-Wright used to be recommended as the best book in the field. I had always regretted the absence of an index, which made it very difficult to use the book.
I have been aware of more recent editions of the book, and finally decided to purchase the latest edition a few days ago. What an improvement! Even though the old style notation and terminology has been preserved, the notes have been updated to include more recent results, and a a new chapter on elliptic curves has been added. An index is now in place, but it could be more detailed.
One must not forget that the book is directed to students of mathematics and practising mathematicians. Comments made about the book by other people should be read with care.
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5.0 out of 5 stars A classic!, 13 July 2014
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Dr. Ron Knott - See all my reviews
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This review is from: An Introduction to the Theory of Numbers (Paperback)
Another great classic, at undergraduate level, but worth dipping into time and time again. It lacks an Index but you can download one free on the internet.
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1 of 10 people found the following review helpful
5.0 out of 5 stars Very good book., 21 Mar 2010
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T. Pagkniota "Humoryst" (Athens, Greece) - See all my reviews
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This review is from: An Introduction to the Theory of Numbers (Paperback)
My 17-year-old who likes Number Theory really likes this books. It's not his first Number Theory book but it doesn't matter. He's into it. So, he's happy, I"m happy.
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5 of 31 people found the following review helpful
2.0 out of 5 stars There is no such thing as 'number theory'!, 8 Aug 2010
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Rerevisionist (Manchester, England) - See all my reviews
This review is from: An Introduction to the Theory of Numbers (Paperback)
I'm not as impressed as the other reviewers here with this book, despite it's being in some sense a 'classic'.

I take it some people - I have no idea what proportion of the population - now and then are struck by properties of numbers. For example, if a number AB is added to BA, the result always divides by 11. If the difference is work out, this is always a multiple of 9. Or (e.g.) Any three consecutive numbers, say 6,7, and 8, if multiplied together, give a result which divide by 6. This sort of thing is the basis of 'number theory'.

There are at least two problems with this book. Firstly, there is in fact not yet such a thing as 'number theory'. This book is a ragbag of techniques and things which have been identified and passed down by lecturers. But it is NOT a coherent 'theory' in any sense. Perhaps I might compare it with a book on 'chess theory'. Chess books have accounts of such things as opening gambits, sacrifices, end games - including some with extremely precise techniques needed for victory. And there are things like 'zwischenzug' and assorted events which are rare, but have some interest. But does this make up a body of 'theory'? I'd say not. Anyone looking to this book for insight into the Pythagorean mystery of number will in my view be more or less disappointed.

Now, what follows from this is my second point, which perhaps is to do with human psychology, or the capacity of the human brain. What is it that makes some people fix on a certain type of problem? For example, this book, like most or maybe all on number theory, starts with prime numbers - probably discovered as a result of packaging and division of actual objects. This of course had practical applications, such as the Babylonian 360 degrees, and our 12 inches, 14 pounds, 1760 yards, and so on. A collection of techniques (e.g. Eratosthenes' sieve), formulas, limits and other results has accumulated. Looking at Euclid's proof of the infinity of primes, his method was to multiply all the primes, and add 1. This function in effect is designed to use the properties of primes to generate a new prime. However Hardy and Wright don't attempt to generalise this process. Maybe Fermat's Last Theorem could be proved elegantly by inventing some ingenious function which combines the properties of addition, multiplication, and powers - repeated multiplication by the same number? What is it that makes some problems (so far) insoluble - and many of them are very trivial to state?

So we have here a collection of results, embodied in symbolism which is far enough from the actualities to (perhaps) look more impressive than it really is. Integration, for example, is basically simple enough, but the long s and the notation removes the reader from the real world...

And there's a related problem, which is that the connective material, explaining why the next bit is there and what it is supposed to illustrate, is completely missing. The result is like a tour of museum exhibits, where the tourist is expected to infer the significance of all the specimens. Or like a concert, where one sample piece of music is played after another, from which the auditor is presumably left to infer a theory of music. In fact, I've just decided to demote the book to two stars!
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0 of 10 people found the following review helpful
4.0 out of 5 stars The joy of ignorance!, 29 Oct 2010
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This review is from: An Introduction to the Theory of Numbers (Paperback)
Need I say more! I think we are getting a little confused about the meaning of "theory" in this context. Whatever the "Pythagorean mysteries" are they have no place in a mathematics textbook! Best to stick to discussing topics we know something about I always say!
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An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers by E. M. Wright (Paperback - 31 July 2008)
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