classique parmi les classiques: an enthralling book
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it is surprising to find that so few people have anything to say about this book; Hardy was a giant among mathematicians and at last this book is translated in french...but only two reviews...I must add that although it is an old book, the younger author saw that it was updated through 5 editions in the 20th century; this book cannot truly become obsolete because it is about number theory from an elementary viewpoint; so no complex analysis, no modular forms and no proof of Fermat's last theorem but a wealth of results that could keep you busy quite for a while. De plus certaines preuves n'ont vraiment pas vieilli et restent valables au niveau de l'enseignement secondaire; ainsi la plupart des démonstrations concernant les fonctions arithmétiques peuvent se retrouver dans des ouvrages plus récents comme le livre de Natanson: Elementary methods in number theory qui tout de même prouve le theorème tauberien de Littlewood via la méthode de Karamata. Let say it again: a wonderful book.
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Essential Classic
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For the amateur (or student) enthusiast of Number Theory, this is clearly (and resoundingly) the essential reference book. It is dated (very dated), but still contains a good and thorough grounding in the subject with unmatched prose from the masters. That said, this book doesn't treat the theory in the way that a modern student or professional needs to treat it, and of course, it is very old now. So, if you want up-to-date coverage you have to have other books, too. For personal use, I tend to look in here for (traditional) definitions and some approaches to older theorems, but never to explore the proofs in detail. For those, I use more modern texts.
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If you want to learn mathematics, study the masters, not ...
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the pupils - N.H. Abel If you want to follow the advice of N.H. Abel, then you should definitely read this book, written by two of the greatest number theorists of their generation. Even though this book was first published in 1938, it has still retained
its charm and importance. Witness the innumerable citations for this book. The reason for that is the selection of topics and their masterly presentation. But coming from such luminaries, what else could you expect. And yes, this is the book, your professors turn to.
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