# Difficulty (mathematical rigor, usage of calculi) of undergraduate math. statistics

## Main Question or Discussion Point

I was wondering what a introductory (1 year sequence) mathematical statistics would be like in terms of mathematical rigor and usages of calculus 1 - 3. The course I'm thinking about taking requires calc 3. I've heard that graduate level mathematical stats courses can be just as rigerous as a graduate level analysis or algebra course. So would an undergraduate stats course give light on whats to come in graduate school?

chiro

Hey selig5560.

The stuff in undergraduate is meant to be a basis for giving intuition before you move to a completely symbolic representation where the rigor is introduced.

It's the same for non-statistical math with calculus: you get some intuition first before you go to real and complex analysis.

A probability course with measure theory and analysis will have a good chance of being just as rigorous as a normal real analysis course if the course is using analysis and measure theory as the starting point for analyzing things.

Statistics though (and probability), is best understood in the context of the real world.

Statistics is an applied discipline, and this means looking at things that are real-world and have some basis in reality. Because of this, anything that has more rigor that it needs to have is often ignored due to the focus being an applied pursuit as opposed to a theoretical one.

There is a place for this analysis and I would compare it to the case of the engineer where they use the calculus results to do their job without having to worry about why it works.

The important thing though, is for the statistician (and the engineer in the above example) to understand the limitations of the result. If you are going to use it you need to understand how it holds and when it doesn't and the context in this regard.