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Old 2005-09-20, 11:57   #19
R.D. Silverman
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Nov 2003

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Originally Posted by Numbers
Some time ago I started a thread in the lounge for this very purpose. I posted a recommendation of my own but no one seems to have followed it up. One thing you can do is search the forum for threads that mention books; there is one thread where many members list their favourite maths books here:

And two books in particular are mentioned quite often. One is the Crandall and Pomerance book called Prime Numbers, A Computational Perspective, which can be found here:

The other is Art of Computer Programming, 3-vols, by Donald E Knuth.
At the end of 1999 American Scientist named this among the best twelve scientific monographs of the century and it is frequently referred to in this forum simply as “Knuth”. It used to be titled The Art… and so is often known by the acronym TAOCP.

Other books that come well recommended (not by me, by experts who know what they are talking about) include:
Richard Guy - "Unsolved Problems in Number Theory".
H. Cohen - "A Course in Computational Algebraic Number Theory",
And either Reisel's or Bressoud's books on Factoring .

But obviously much will depend on what kind of book you are looking for, what you want to study, what level you are currently at and where you want to go. Just asking people to recommend books doesn’t give them much to go on. Another thing to be wary of is that I have in my house a book that came highly recommended by a number of people. I use it as a doorstop because it is completely impenetrable to me as a book.
I would add:

Hardy & Wright Introduction to the Theory of Numbers
D. Shanks Solved & Unsolved Problems in Number Theory

If more advanced books are desired, I can recommend them.

Stay away from Serre's "A Course in Arithmetic" or any of Serge Lang's
books [RIP]
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