Archives for Math - Page 2
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…
Single Event Probabilities
Binomial Random Variable - and Probability of SINGLE event happening more than once (multiple heads in a coin-toss etc.) Whenever you have a variable that can take on two possible…
Joint Event Probabilities
See also ‘Single Event Probabilities’ The probability of a 'joint' event - drawing a white ball followed by two black balls (from a jar containing 7 white and 5 black…
Open sets and limit points
A set $A$ is open iff for every point $a\in A$, there exists a $\delta$ such that the neighborhood $\left(a-\delta,a+\delta\right)$ surrounding $a$ is completely contained within (is a subset of)…
The Monty hall problem, Quantum Games
The original problem Three doors, a prize behind only one door (say, a new car). Other two doors are each hiding a goat. Contestant has to pick a door –…
Prove that there are a countable number of intervals (in R) with rational endpoints
Counting Elements versus Counting Intervals The interval is one interval, is another and so on. Start with one end-point Just count the left end points of . Now for a…
Math Problem Books
Math Problem Books (Also read - Physics Books for self learning) How often have you stared at a math (or physics) problem, unsure of where to begin? Most math books…
Some Math Paradoxes
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…
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…
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…