Any Good Literature or Books on Number Theory

[bomba923]

I'm not saying PF is a bad forum...but

*What are some good books on number theory?

--I'm a HS senior, currently taking CalcIII.
--I don't care about the difficulty or how the book is written-->only that it is comprehensive.
(does not leave out details, whether they be significant or insignificant).

Any good book recommendations?

 

[shmoe]

--I don't care about the difficulty or how the book is written-->only that it is comprehensive.
(does not leave out details, whether they be significant or insignificant).

Do you mean you want a book that shows every gory detail of proofs? Or that it somehow covers *all* topics? The later requires a full library while the former is not something you'll find. Once you hit more and more advanced topics authors will skimp on the details of what you're already expected to know, for their sanity and yours.

You might have a look at this thread, many introductory books are suggested:

https://www.physicsforums.com/showthread.php?t=85248

 

[bomba923]

Do you mean you want a book that shows every gory detail of proofs? Or that it somehow covers *all* topics? The later requires a full library while the former is not something you'll find. Once you hit more and more advanced topics authors will skimp on the details of what you're already expected to know, for their sanity and yours.

Actually I'm referring to the latter-->"that somehow covers *all* topics"

I know that no book can possibly cover ALL topics , but I'm looking for one without a particular slant or total focus on just a few topics...unless those happen to be very important topics indeed. But I think you see what I mean, just a book to introduce myself to number theory-->but a book that's not too watered-down, moving beyond just vague statements (e.g., not like an "Aristotle for Everybody/kids" books, if you see what I mean) and actually introduces some rigor.

 

[shmoe]

Hardy and Wright covers a wide range of topics, as does Niven, Zuckerman, and Montgomery. Both are great books and would be good introductions to number theory (though I prefer Hardy and Wright).

I also mentioned Silvermans intro book in that thread. It also covers a wide range of topics but is more basic.

 

[mathwonk]

now you should go to the library and look at the books on the number theory shelf.
but your question is the wrong one. you are a cook if you can make a good cup of coffee, and a mathematician if you can prove one theorem, and you know some number theory if you understand one topic deeply.
the 'covers all topics approach" is a bit naive and even impossible.
there is no encyclopedia of number theory, and even the best professors at my university specializing in the field, do not come close to knowing something about "all" of number theory.
try something feasible.

the book of hardya nd wright is almost 70 years old and hence obviously does not cover all topics in number theory.

to a bright young person, I would recommend a book on a single deep topic, rathewr than an elementary introduction to everything, like edwards' book on the riemann hypothesis, or fermat's last theorem, (proved over 50 years after hardy and wrights book.)