Introductory number theory textbook

[battousai]

What is a good introductory textbook for beginners?

 

[hitmeoff]

If you want a real basic, survey type of book (say for non-math majors) then Id recommend Friedbergs "An Adventurers Guide to Number Theory." Its light reading but its not fluff and it'll give you a bit of a taste of what number theory is about.

If you want a beginner's book that's more rigorous (say for sophomore/junior level math major) Underwood Dudley's Elementary Number Theory is a great place to START.

 

[battousai]

I'm looking for the 2nd type of book (for math majors).

 

[xristy]

Three to consider are:

Apostol - Introduction to Analytic Number Theory -- the analytic side of numbers
Rosen - Elementary Number Theory and Its Applications -- basic ideas and relations
Stillwell - Number Theory -- some feel for the algebraic aspects

There's also the classic:

Hardy and Wright - Introduction to the Theory of Numbers 4th ed -- older more toward analytic aspects

 

[hitmeoff]

I'm looking for the 2nd type of book (for math majors).

I would say then the Dudley book is most approachable, especially for self study. Its a Dover book, so it can be had for cheap.

I took number theory as an undergrad over the summer and we used an absolutely horrendous book (but at least is was free: http://www.shoup.net/ntb/ ) and I had the Dudley book the whole time, but never bothered to read it for the better part of the session until the last couple of weeks when, I then realized that I would have gotten much much more out of my course had I used that book for the bulk of my studying. Everything that I was left in a fog with was immediately cleared up by the Dudley book. Plenty of exercises, answers to exercises, etc.

I think its worth picking up, even if after reading some of it, you feel its not rigorous enough (I don't feel that way, I think its perfect for a first intro to the subject) and you need a more challenging book, at least you'll get your feet wet and won't spend much cash to do it.

Personally, I would love to learn more and might move on to some of the books suggested by xristy. I am personally looking at picking up Apostol's book.

 

[mathwonk]

the number theorists in my department often recommended van den eynden as a beginning book. as a more advanced book i always liked that by trygve nagell.