Reddit reviews An Introduction to the Theory of Numbers

A good first course book is Niven and covers a lot of ground at a superficial level. You will probably have a feeling for what you like after that.

If you want to pursue algebraic number theory after, you will need to study Galois theory. If you want to pursue analytic number theory, you will need some complex analysis. You will basically need to know the major results and have an intuition for them before starting number theory proper.

A fantastic second book is "Ireland and Rosen". I highly recommend this and it covers both aspects of number theory and then some.

I have the Jones and Jones book. Since it wasn't my introduction to number theory, I can't say if it's a good introduction. Personally, I would go with another book, like the many already mentioned in other replies.


If you are looking for a nice cheap (free!) book, check out Stein's book Elementary Number Theory

I learned out of Niven et al, and thus it is my goto reference. But, it seems prohibitively expensive now: An Introduction to the Theory of Numbers

How much is it worth to you? The following book is expensive, but its a great, well-written, undergrad-level survey:

http://www.amazon.com/Introduction-Theory-Numbers-Ivan-Niven/dp/0471625469

You can look at your local book store for something cheaper, there's probably a Dover paperback on number theory for less than $20, but that's a crap-shoot. Good Luck!

There is Elementary number theory by William Stein, and A Computational Introduction to Number Theory and Algebra. The latter is better if you are also interested in some of the computation They are both available for free online (legally). I think you would prefer Stein's book but skim through both and see which one you like more.

For something more in depth, I looked at some of the books in this list at mathoverflow. Hardy & Wright , and Niven & Zuckerman's books seem best suited to you (from what I looked at, but go through that list yourself). Many of the other books require some background in abstract algebra.

I haven't read either but just looking through their table of contents I would go with Niven and Zuckerman's book. It seems to go into the more useful things more quickly, and it's not as densely packed with information you probably won't be interested in right now.

TLDR: Start here, or here.

For what it's worth, number theory is a fascinating field. I don't think you'll be disappointed going into it. Good luck!

I recommend http://www.amazon.com/Introduction-Theory-Numbers-Ivan-Niven/dp/0471625469. I'm currently reading through it

There are many books that I found helpful in high school for number theory, for example this classic by Niven et al.

http://www.amazon.com/Introduction-Theory-Numbers-Ivan-Niven/dp/0471625469