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my close friend intend to study number theory and he asked me if i know a good text on it , so i thought that you guys can help me to help him !

he look for a text for the beginners and for a first course he will study it as a self study ..

so what texts do you recommend ?

are there any lectures or videos online on internet can help them ??

also , what do you advice him ?

amWhy
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FNH
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  • You might want to look into opencourseware (like MIT). Also, review these three posting on books: http://math.stackexchange.com/questions/329/best-book-ever-on-number-theory, http://math.stackexchange.com/questions/1774/undergraduate-high-school-olympiad-level-introductory-number-theory-books-for-se , http://math.stackexchange.com/questions/350833/what-is-a-good-book-to-learn-number-theory?rq=1 – Amzoti Apr 27 '13 at 21:55
  • I think it depends largely on what your friend already knows, and how he studies, but if your just looking for a list of books, there are many similar questions out there with responses in this form. – Ethan Splaver Apr 27 '13 at 21:58

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I'm assuming your friend is quite young, pre-college?

The Art of Problem Solving website has some great articles and resources with respect to number theory, e.g., the nuts and bolts aimed to very bright young folks. That would be a terrific start. (Author: Naoki Sato).

See also this post for some great references, all varying with respect to complexity. One recommendation on that post that seems particularly relevant is the book by Rosen: Elementary Number Theory.

Also, this post offers recommendations for the self study of elementary number theory geared to high-achieving high-school students, and undergraduates.

Community
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amWhy
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There are plenty of answers on past SE threads, but I'll recommend my favourite anyways:

The Higher Arithmetic by H. Davenport is a quite difficult and very rigorous introduction, but is a wonderful text that can also serve as a reference. It assumes no prior knowledge at all and has exercises ranging from introductory to very difficult.

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My two pennyworth: for introductory books try ...

  1. John Stillwell, Elements of Number Theory (Springer 2002). This is by a masterly expositor, and is particularly approachable.
  2. G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers (OUP 1938, and still going strong with a 6th edition in 2008). Also aimed at beginning undergraduate mathematicians and pleasingly accessible.
  3. Alan Baker, A Comprehensive Course in Number Theory (CUP 2012) is a nice recent textbook (shorter than its title would suggest, too).
Peter Smith
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    An Introduction to the Theory of Numbers is a wonderful, fascinating text, but I wouldn't say it's a good introduction, though it can be interesting to read even when it becomes hard to follow. Unfortunately it has no exercises and moves very very quickly at some stages, requiring some alternative reference for all but the most Ramanujanish beginners, in my opinion. –  Apr 27 '13 at 22:07
  • @LevLivnev You could be right! The students round my ivory tower are an unrepresentative lot – Peter Smith Apr 27 '13 at 22:30