## The Monty hall problem

The original problem Treating non-random information as if it were random (Phillip Martin’s Probability Trap) Host knowingly opens a door – is different from a host RANDOMLY opening a door. It is based on the deeply...

## Prove that there are a countable number of intervals (in R) with rational endpoints

Counting Elements versus Counting Intervals  The interval [0,1) for example is uncountable, but we are not counting ELEMENTS of an interval, we are counting INTERVALS. [0,1] is one interval, [0,1/3] is another and so...

## Problem books for advanced math ( and physics ) students

How often have you stared at a math problem, unsure of where to begin? The thing is, most math books cover the basic lemmas and theorems – but provide little instruction on the TYPES of problems those lemmas can help with. So...

A Logical Paradox – The British Air Force Bombing Paradox The British Airforce announces that it will bomb the city sometime during this week; but at an unpredictable date. Why is this paradoxical. Suppose, they announce this...

## Income Inequality–GINI index

A number that ranges from 0 to 1 – to capture the Income inequality for a COUNTRY. By itself, the number means little, but in comparison with other countries, can convey much. A GINI index of 1 – would be if ONE family had...

## Write computer programs to learn physics and math

Where I grew up, we were taught math the hard way. We HAD to struggle through problems. No matter how complex or convoluted the problem was, it was almost a given that students would stay up – until they had solved it...

## Shortest ever Intro to Lie Algebras and Lie Groups

A Lie algebra is simply a) a vector space b) with an “operation” such that the operation [x,y] of any two vectors x and y is again a vector, and such that the following hold: skew-symmetry: [x,y] =...

## Lie Groups–Notes

Algebraic equations vs. Differential equations Galois Theory – dealt with symmetries in algebraic equations Lie – Tried to do the same (look for underlying symmetries). Lie Groups Are a Group Are a Manifold Groups vs. Rings...