I am a graduate student in mathematics studying algebraic logic. For quite some time now, I have been meaning to study physics -- it turns out that some ideas in foundations of mathematics have found promising applications in theoretical physics (topos quantum theory and quantum logic come to mind). I want to get a somewhat rigorous picture of classical and quantum mechanics, so that I can contextualize some of the things I will be reading later on. Is there a good resource that I can use for this? I would prefer to read something that has a careful development of ideas starting with classical mechanics, eventually culminating in a broad formulation of quantum mechanics. All suggestions are welcome!