I would like to learn basic statistical methods for quantitative data analysis in the social sciences. I volunteer for a nonprofit, and I want to take on a quantitative research project analyzing things like demographic and law-enforcement data. The (admittedly rather vague) goal is to learn things from existing raw data that would be useful in informing policy decisions.
I have a Master's in pure math, focus on algebra. I know how to learn independently out of dense textbooks, but I'm quite weak on applied math and statistics.
I think what I want is to give myself the crash course version of an "Intro to Quantitative Research Methods" class taken by sociology PhD students, but leaning more on mathematical sophistication. (I'm not claiming to be any more "sophisticated" than sociology students. I'm guessing that embracing the math side of things helps you learn enough to do basic research, and I want to take advantage of my background.) So I want a book that does not presuppose any knowledge of statistics but also does not shy away from expounding on the theoretical framework when it's helpful.
If it matters, I'll be using R. Yes, I am prepared to invest plenty of time in the learning curve.
Does anyone have suggestions as to resources? Thanks for the help!
P.S. I thought this question might have been asked before, but I couldn't find it. If I've started a duplicate thread then my apologies and I'd be grateful to be directed to the existing question.