I'd like to acquire more than a casual understanding of LQG, and to do that I need the math first. My math background has been acquired ad-hoc while pursuing a degree in Astronomy. A smattering of group theory here, enough differential geometry and tensor gymnastics to read Gravitation (Thorne & Wheeler), your standard linear algebra for QM (Cohen & Tanoudji), and all the prereqs. If possible, I'd like to know what books a math major would use because the pick-it-up-as-you-go method of learning math has left me with a very unreliable foundation. I'm actually serious about this as I'm trying to decide what I'd like to do for grad school (I have a preference for GR and Astrophysics). So what math topics would I need to study and what books/resources are recommended in order to understand LQG at the graduate level?