## The Historical Context of Data, Using Data for Decision Making

This is still in draft mode The Historical Context of Data Collected Unless we look at the ‘context’ of the data that we collect, we may be missing the big picture. The Case of the top ranked Universities in the U.S. The Case...

## Statistical Fallacies

Selecting a truly RANDOM Sample If you choose every person who passes you on the sidewalk, that would not be a random sample, since you would miss out the people moving in vehicles. If you, likewise, stop every car on the...

## Some Cool Proofs (Books and Resources) in Math

Also see my – Problem Books for Pure Math, Physics and Mathematical Physics If you are looking for some of the most important, yet elegant math proofs, look no further than these two books. The first one – Proofs from the...

## Nash equilibrium, Prisoner dilemma

Under Construction Check out also Advanced Problem Books in Math and Physics and Rare Finds in Relativity Two prisoners have been accused of the same crime and are kept in separate rooms for questioning. If both confess to the...

## Continuous (Smooth) vs Differentiable versus Analytic

I had a lot of trouble distinguishing between continuous and differentiable and analytic functions… Analytic An analytic function is a function that is smooth (in the sense that it is continuous and infinitely times...

## The magic of Complex numbers

Check out also – Problems In Advanced Math and Physics and Rare Finds in Special and General Relativity Why are complex numbers so useful in the natural sciences? Analyticity (harder to do without complex numbers) Analytic...

## pigeonhole principle problem solving

Suppose 82 students are enrolled in a college – offering only 4 courses. Suppose that each course has 3 sections – and a student can choose any one of three sections. Show that at least TWO students have to share a...

## Remove a countable set of points from an open set

Let A be an open set. Show that if a finite number of points are removed from A, the remaining set is still open. Is the same true if a countable number of points are removed? Solution If we order the points removed from A, x1...