I'm trying to close gaps in my education especially in Statistics and Optimization theory. I had an awful class on Statistics so I want to learn it by myself. As for Optimization we had a pretty good class on Calculus of variations but I never used it, time passed and I forgot a lot of stuff. Also there are few topics in Probability Theory that I still "can't feel" very well, they are: conditional expectation, multivariate distributions and sums/products of random variables.
What books or courses can you recommend for me? I'm interested from perspective of both rigorous pure math and applications.
To start with optimization you should first consider linear programming:
Linear Programming by Vasek Chvatal mostly an algebraical introduction to the topic
Linear Programming and Network Flows by Mokhtar S.Bazaraa and John
Jarvis which is a bit harder but introduce geometrical interpretation.