The method of Lagrange Multiplier ! Optimize multivariate functions.

Yesterday I learned the beautiful method of Lagrange Multiplier, to find the minima or maxima of multivariate functions. eg

If I ask you what’s the minimum value of a function, f(x,y) = xy, subject to the constraint 5x-y = 4, the answer would be -4/5. The method is this. Ensure that first-partials of function f(x,y) exist. That is fx = (∂f)/(∂x) is not zero, and fy = (∂f)/(∂y) is not zero. Else method won’t work.

For the given example the f(x,y) = xy, because fx = y and fy = x, our method will work.

According to the method, we have 3 equations:

(1) fx + λgx = 0

(2) fy + λgy = 0

(3) 5x − y = 4

read more The method of Lagrange Multiplier ! Optimize multivariate functions.

The Singapore maths puzzle.

Now that I could lean back I guessed the answer for this puzzle after reading it a couple times mindfully. I think the answer is August 17. WHY? I will explain in detail. But first of all the answer I came across here (in NY Times) is obviously misleading and incorrect. They give July 16 as the answer, but their method is wrong because they eliminated both May and June and there isn’t enough information for such a step. What they should do is eliminate May 19 and June 18. Because these two dates (18, 19) are not duplicated in the list of dates.

Once they did so it would be clear from the conversation between Albert and Bernard that June 17 could also be eliminated. Because since Albert knows that June 18 and May 19 are not good candidates for DOB, neither can June 17 be. If June 17 was the date he would not claim “I don’t know the date of birth” because he already knows the month and there is only one date in this month that is June 17.

read more The Singapore maths puzzle.

Something interesting here?

Quora has this; \sqrt 2 + \sqrt 3 ~= \pi. I see some good use. \sqrt D + \sqrt D+r ~= A [D; diameter, r; radius, A; area] Is this a new relation? and this another; 2\sqrt (D.r) + D \sqrt 3 = C OR even; D (\sqrt 2 + \sqrt 3) = C. well thats trivial. where C is circumference. What If D, D+r are simultaneously perfect-square or Dr is perfect-square. But this trivial statement (D (\sqrt 2 + \sqrt 3) = C. well thats trivial) can be re-written into some sort of theorem. The circle can always be divided into two parts where one part is 41% more stretched than the diameter and the remaining arc is 73% more stretched than the diameter. and the semicircle is always 11/7 times bigger than the diameter. [so its each part is 57% more stretched than the diameter]

A new optimization parameter in a statistical sample !

It reflects the quality scope of the citations. Its the total percentage of a citation that goes into defining a particular citation index. Let me call it q-index therefore (q for quality)

See this example.

My h-ind is 60. So total (minimum) citation it accounts for is 60*60 = 3600. My total citation is 12215. So my q-ind is 3600/12215 = 29.47% Or 29.47% of my total citation were important for this parameter. Hence my q-index is 29.47. In this way if someone has 500 total citation with h-index 60, he has a much better q-index than mine, because more of his paper are highly cited

read more A new optimization parameter in a statistical sample !

Whats the population; if male and female literacy is given as percentage.

May I add one more small note, see how easy it becomes to understand an “order of estimate”; A good student, that is one with a good maths background, should immediately pick up, population ~ 1.19 million. 61.26 % male. 58.04 % female. (Not only literate but total male and female). Then even, one question can be asked, what is male-female disparity, in terms of their population. (That is, without regard, to any further attributes, such as literacy numbers, or purchasing power distributions etc, which are btw non-existent variables in India, because research in India means Governmental Apathy.)

Its a slightly tricky question, if you already note, there is a mistake in the above, The % is not scaled to 100. Its an over-estimation by a factor of 1.193, and the really smart student recognizes this, (s)he doesn’t go and change all calculations. See how all numbers came just from the first few digits of the given numbers; 11,92,948 >> 1.19 million, vs over estimation factor; 1.193 (or less precise 1.19). Male: 6,12,597 >> overestimated percentage: 61.26. Female; 5,80,351 >> overestimated percentage: 58.04.

You would know they are over-estimated, because these two numbers, male and female population, while exclusive parameters, hence must add up to normal: 100 or 1.00, added up to 61.26+58.04 = 119.30, or (61.26+58.04)/100 = 119.30/100 = 1.193, do you see how easily, without doing any further adding etc, I caught the actual overestimation factor, above, to be 1.193? Cool Huh? Just from the first few numbers. If maths runs in your mind, you can do all these, if it doesn’t, but you have the right numbers, you will be led to believe nobody would catch your mistakes, and lie about the numbers. Possible. Just from the numbers as are stated, we can, catch the inconsistency, thats why maths education is important. In-fact, I committed the mistakes and wanted to catch the inconsistency, and from the calculations gradually caught it, so a more consistent picture was envisaged.

read more Whats the population; if male and female literacy is given as percentage.