Rigorous Introductory physics textbook

[Riemannliness]

I'm wondering if anybody knows about or has used a good introductory physics textbook that is mathematically rigorous. I'm really interested in physics, but I'm a mathematics student and I CAN'T STAND any of the books I've tried to use so far (eg. Knight's Physics). I've really grown to dislike texts that continually do things that are mathematically sketchy (or outright incorrect) but are "good enough for the purposes/scope/level of this textbook".

 

[Fredrik]

I don't know any book that fits that description, but there are a few about specific areas of physics that you might like, for example "Mathematical methods of classical mechanics", by V.I. Arnold. For quantum mechanics, you might like "Lectures on quantum theory: Mathematical and structural foundations", by Chris Isham. It's supposed to be a fairly easy read, so it's not exactly filled with rigorous proofs, but it's at least not giving you the wrong ideas about anything. For special relativity, consider "The geometry of Minkowski spacetime", by Gregory Naber.