I took classical (engineering) thermodynamics a few years ago, and this semester I am taking a statistical thermodynamics class from the physics department. We are using the book "Fundamentals of statistical and thermal physics" by Reif, which seems to be a pretty good book. Unfortunately I get the feeling that I am playing around with a lot of poorly defined mathematics. The main problem is that differentials are constantly interchanged without any real discussion or justification of how you can break up the derivatives. Partial derivatives and full derivatives are often intermixed, and so on. It might just be my fault for not reading very carefully, but I feel like the author (and the subject) relies very heavily on "hand-wavy" type of differential manipulation. I was wondering if people could recommend me some other books or resources that do a better treatment of making things more rigorous. Have other people noticed this kind of phenomenon with stat. mech.?