I'm coming to the end of my masters degree in Mathematics and will be starting a PhD in Logic in August. The more logic I study, the more theoretical computer science I am exposed to, e.g. recursion theory, lambda calculus, but the underlying CS is brushed under the rug. My main areas of interest - set theory and category theory - also have applications in computer science, but so far I've only studied them from the point of view of pure mathematics.
My lack of any computer science background sometimes makes it difficult to see the motivation or intuition behind what is going on, or how it could be applied. I get by, but I feel like it would be healthier to branch out a little bit... it occurs to me that, for the benefit of my future research, I should learn some computer science.
Most CS books I've looked at haven't been very suitable for my purposes, either being too basic and untechnical, or presupposing the kind of CS background that I don't have. They seem to be aimed at people who are quite computer-savvy but who have little in the way in mathematical background - my situation is the opposite.
What books or other resources are there which could help a mathematician-turned-logician in their goal of gaining a working knowledge of (theoretical) computer science?
I'm looking for something more wholesome than a few seminar talks and more in-depth than The New Turing Omnibus, but I don't have the time or resources to do another undergraduate degree. (It may be that I'm asking for something that doesn't exist.)
Sorry if the question is too vague or ill-posed. I felt it was more suitable here than on MSE but I'll be happy to migrate it if needs be.