A set is open iff for every point , there exists a such that the neighborhood surrounding is completely contained within (is a subset of) . A point is a limit point of a set iff given any , all neighborhoods intersect the...

# Category - Math

Number theory, complex variables (applications), fourier analysis and applications.

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 – and hope that she wins the car. At just this stage, the chance of...

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...

How often have you stared at a math (or physics) problem, unsure of where to begin? Most math books are unusually pedantic and dull – all in an attempt to be more ‘rigorous’. Screw rigor, I say. Students are...

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...

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...

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...

Under construction Stock Trading – Incorrect Probability Conclusion Stock can either go up , down or stay still. Hence, probability of any one stock going down is 1/3 rd. Soldiers and Shell Bunkers – Incorrect...

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] =...

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...