Saturday, October 1, 2011

Dancing with Functions

Check this out: dance lessons for mathematicians.
Now do the sin cos dance.  Hahaha.

Catching up fast: This is my AUGUST 2011 post

Friday, September 30, 2011

Should I say yes or should I say no?

Without mathematics, how would I know how to make good decisions?
Quick example: I like two jobs equally, one offers $1 a month and the other $1.20 per month. Which should I take (assuming they're the same in every other way?) Ok, that was too easy.

How about this, I could pay N100 to enter a lottery that pays out N1000 to one winner. Should I do it?
In maths actually, when things are uncertain, you think of "expected values." In this example, if you're spending N100, what do you EXPECT to receive? Mathematically, you multiply the amount by the PROBABILITY to get the EXPECTED AMOUNT.

Answers: If I have a 50-50 chance of winning (like if only two people entered the lottery) then yes, go for it!  On the other hand, if I have a 1 in 100 chance of winning, then I should just keep my money and wait for a better opportunity.

Why? In the first case, the expected payoff is big, you expect to get N1000 * 50% = N500 for spending only N100
in the second case, the payoff (expected) is negative since you expect to get N1000 * 1/100 = N10 only, which is less than the N100 you spent.

The gray area: sometimes a positive payoff may not be worth it (but that's a question of psychology or other factors, which you can learn to include in your calculations as well).  If you think about it, this DECISION THEORY stuff can help you make many different kinds of decisions in a way that is rational.

This is the JULY 2011 blog post - I'm still playing catch-up

Wednesday, September 7, 2011

Khan Academy makes math-lovers

When you visit, go straight to PRACTICE. Within one hour, math has become a fun, competitive sport. At least that's what my young cousin experienced; for days, he kept going back to do more math drills and score more points and badges.

So don't hate math, just play Khan.

For older folk, Khan trains in Contemporary Finance topics (example: Systemic Risk), Aptitude tests like SAT and GMAT, Entrance exams like IIT JEE (India), standard curricula like Singapore and some US states, a bit of the sciences - physics, chemistry...all for the price of your video-capable internet connection.

JUNE 2011 POST (to make up for being MIA ;)

Tuesday, May 31, 2011

Why half of Nigerians could not vote this year

Nigeria has a median age of 19 years. That means that half of the population is over nineteen years old and the other half is under nineteen.
The median age in the United Kingdom is about 40 years.

Median Age is closely related to fertility rate.

Maps from Wikipedia: Median Age , Fertility Rate
Learn the basics of measuring population.

If a country has a high fertility rate or birth rate, the median age will be low. At a fertility rate of around 2 per female, the population will be steady and have roughly the same number of people in all age brackets (except those that die.) However, at much higher fertility rates, the population multiplies in each generation.

The average Nigerian woman has 5 children, and this is why the population doubles every generation. In Niger, which has the highest fertility rate in the world at almost 8 children per woman, the population about triples every generation.

While some populations are ageing (see Canada, Japan, and most of Europe on the maps), some countries are getting younger (particularly in Africa).

With a VOTING AGE of 18 in Nigeria, half of the population is (by law) too young to vote. By comparison, only 20% of the UK population is too-young-to-vote.

I think the voting age in countries (like Nigeria) that have young populations should be lowered so that majority of citizens can vote.

Tuesday, April 12, 2011

Next topic

I will resume posting regularly soon. Not sure what to write about next. Some thoughts are:
solving Mahjonng solitaire (heuristics example)
solving Minesweeper (counting logic)

relationship between birth rate and the age distribution e.g. percentage of voter age
basic time-series analysis (web analytics and commodity price charts for example)

Saturday, March 12, 2011


Sorry I haven't blogged in a while.
Did you try the matrix questions?

I need to fix some typos but the answers are here now.

10 questions:
C A C A D || C C C D C

20 questions:
B C D C A || B C D B C || C C A D C || A C D B C

Tuesday, March 1, 2011

Matrices - Test yourself

This was one of the (easy) questions I gave in a first-year undergraduate matrix exam last year:

If you can answer that, try more test questions on matrices here.

In other news, Inception (a dream within a dream) won four at the Oscars and The Social Network (the technology startup film) won two.

Tuesday, January 25, 2011

Barrier Method to solve a maze

Can you help these butterflies reach the flower?

Try to solve the maze. You can print it first.

Check back to see how a barrier method helped me solve it.

By the way, I got the second picture by using the command Sharpen[ ] in Mathematica software.

One week later: This is my solution
Long time ago, when I first tried to solve this maze, I kept getting tangled up in loops and couldn't solve it. Then I remembered something from my friend's research on Barrier Certificates. It seems like common sense, actually - to prove that there is no possible path, you show that there is a wall/barrier.
I thought to myself, "what if this maze can't be solved?" So I tried to find a wall across the maze. (If I had found one, then that would have been proof of a bad "unsolvable" maze.) I couldn't find a complete wall, but I found a broken wall.

The broken wall is a great help in solving the maze. We know there is no path through the wall; if there's any path from butterfly to flower, then it passes through the crack in the wall. So search backwards from the crack to the flower and from the crack to the butterflies. Like this:

Here are some more mazes that you can solve more easily using barriers.

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