Undergraduate math major here. Currently a noob in the Calculus sequence. I felt like there were some difference between different topics covered in stat class (regression vs bayesian, etc.). I took an intro to stat class (for non-math majors) before I decided to become a math major which spoon-fed an abridged version of regression and basic probability. I did get more curious about Math and Stats though!
I am interested in taking a class in a few semesters that will go more in detail about this, because the philosophy behind randomness is one of the things I find to be really cool.
What are your opinions of Stat and Probability? How do they complement each other? How do they Differ? Is stat a science that uses theory of probability and analysis?