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...

# Category - Math

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

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...

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...

Integers from 1 to N are randomly generated . Each integer has an equal probability of being selected and unlimited repetition is permitted. A running sum is maintained. Given any integer k, such that 1 <= k <= n , what is...

Whenever I read a physics article, I try to visualize the quantities that the author is talking about. I do this by ASSOCIATING the quantity with some REAL thing. Example – if the article talks about FREQUENCY, I think of...

A small bag is lying on the floor. The room is big – with high ceilings. Yet, no one can jump over the bag. Why? I posed this to several grown-ups. No one got it. Next, I posed it to my 5th grade class. They spent exactly...