Originally Posted by

**chiro** If you want to analyze something you need to be able to chop things up and know the information in each thing you chop up.

Statistics looks at understanding information since you have a sample and want to extract something common to that sample.

Information also comes in chunks which means that discrete mathematics and some computing is useful for knowing how and why to chop things up in a specific way.

If you want to be an analyst then you need to chop things up in a way relevant to the thing you are analyzing. This means you take additional courses in the area of interest [finance, economics, physics, whatever] and think about what the information is and how to chop up and bring together things to get it.

As for solving problems, every area of mathematics and statistics gets you to do that. The difference is what you chop up and why and what you are looking for.

As for teaching, high school means you need to take things and make them simple to follow [far simpler than you would think]. University is obviously different.

In terms of logical reasoning, you will need to be able to take lots of non-mathematical information and make sense of how to combine them in a way where you can do so for a matrix [linear system] or set of relations. That intuition is gained by working in a particular field and thinking about it mathematically.