I study physics and i find math very interesting. I'm using Michael Spivak's "Calculus" and i think it's really good book. Spivak's book is great sample of book that i desire - it's for mathematicians, not for physicist, but you can understand it even if your not a mathematician. And it have problems that demand more than just using some kind of pattern (atleast it seems so, i solved just few). I'm looking for linear algebra book, abstract algebra and number theory book (for freshman). If this is book without problems, then i need one with problems too - but problems that require more than just using a pattern. And any other book that is as good as Spivak's Calculus.