Friday, January 6, 2012

An Example How to Learn Probability and Statistics Using World 1 and World 2 Approach

This is an example, actually guidelines, how to learn mathematics, specifically material in the book "Business Statistics" by D. Downing and J. Clark.

Please read my previous posts about separating mathematical world, World # 2 from non mathematical axioms and logic, called World #1. Here World # 1 is motivation to develop probability and statistics material. World # 2 is pure mathematics.

It is sufficient to recognize premises in World # 2 motivated by World # 1. Note that mathematics has well established set of axioms, and that these premises can be developed without any mentioning of real world examples related to the statistical analysis. Again, please read my previous post or my book.

Hence, it is sufficient, and necessary, to learn these premises. Note that they do not require proof, or more precisely, many of them follow direct from basic math axioms. Then, learn real world explanations that can motivate their selection and introduction. Clearly separating these two worlds you will be able to firmly understand mathematical treatment of business statistics. At any point you should be able to define the premises and show the separation boundary between pure mathematics and business field (hint: they even use different vocabulary). To help you further, no business term can ever be used to prove any mathematical theorem mentioned in this book no matter how business situation "motivates" mathematical concept introduction.

It is interesting that math students are taught how real examples motivate math new concepts and new directions of math development, but then it's not emphasized how no real world object or concept can be used in any mathematical proof.