I'm currently taking this Coursera course on financial engineering, which is fine but it's very focused on applications instead of proofs. They recommend Investment Science as a companion text, but some of the comments on Amazon seemed to indicate that this book also isn't very proof oriented. I've also heard of Options, Futures and Other Derivatives as a recommended text, but again the Amazon comments indicate that this might not be very rigorous.
Are there any texts which require a similar amount of knowledge about finance but are more math focused? If it's relevant, my background is in pure math so I'm decently skilled mathematically but I may have forgotten some particulars about calculus and probability.