This is a really great list. I'm currently about midway through a very similar list that I arrived at through trial and error. It would've saved me a lot of tim

This is a really great list. I'm currently about midway through a very similar list that I arrived at through trial and error. It would've saved me a lot of time to have seen this a couple of years ago :). I've got a couple additional suggestions/pieces of advice: First, if Calculus on Manifolds is too advanced Munkres's Analysis on Manifolds is very good and covers mostly the same material. Second if you are shaky on trigonometry it's worth taking a couple of days to relearn it since trig identities and manipulations are used all the time. It makes you feel a bit stupid to review stuff you probably learned in middle school but if you're like me and hadn't used this stuff in years the review will save you lots of time down the road. Third, get used to working problems. It's easy to fool yourself into thinking you understand something because you can follow the worked examples, but you can't actually apply it. I try to do at least a few exercises from each chapter. Shankar's QM book is awesome because the exercises are interspersed with the text, so doing them as you get to them really helps you understand the material. I wish more textbooks had this format.