I realize now that my undergraduate program is not nearly as rigorous as it should be - it required almost no math to complete. This is concerning because I've been accepted into a decent (top 30) PhD program. However, I (luckily) am also completing a degree in mathematics.
Can anyone recommend a good textbook(s) to help me bridge the gap between my non-rigorous program and a PhD program (level of rigor is whatever might be typical of a top 30 school??). I would also love any online resources such as video lectures, problem sets with solutions etc.
I looked at MIT's OCW but most of the courses beyond the principles do not include lectures, which was really disappointing.