Wednesday, October 22, 2008

WSO2 Book Authors

Wow, we now have two new books from employees at WSO2 where I used to work before getting into grad school. A few months ago, Deepal published his book, Quick Start Apache Axis2. Now, Samisa has published his book, RESTful PHP Web Services. Given the publishing friendly environment at WSO2 I sense there will be many more books in the pipeline to be published.

Tuesday, October 21, 2008

Time to cut back by half

During last summer (from May to July), I helped a friend of mine with his summer undergrad
math course (MA 153), a first course on Algebra and Trigonometry. (Side Note: I've got to say
that even though he is a Management major, he went to top the class in this course - such was
his dedication to the course!)

Having done all my studies up to bachelor's through the education system in Sri Lanka, I
realize that this freshmen undergrad course here is very much similar to the preliminary material covered in Pure Mathematics (now Combined Mathematics) in Physical Science stream. We spent 3 years for Advanced Level (A/L) examination and then got selected to follow an engineering degree which usually takes another 4 years to complete. In between the two courses (A/L and Bachelor's) , we at least have to idle around for about 1 year. So, if you do the simple
math, it is going to be around 8 years; In USA what they achieve in 4 years, we take 8 years.

It is unfortunate to see that the transition from A/L to bachelor's not a well-planned smooth
one - some materials are repeated and some not used at all; there's little coordination
between two major courses. I think it is high time we combine these two courses together and
graduate young people when they approach 20's or early 20's so that they have ample opportunities both in academia and industry. (We first need to iron out practical issues in making such a fundamental change. Any change is quite difficult to initiate - it's the true nature of human kinds to resist changes, but the choice is ours - do we want to stagnate or progress?)

Thursday, October 9, 2008

CAPTCHA solving/breaking economy

Every week, when I post a blog or other comments, create a new online account, etc. I have to solve a few CAPTCHA's which are mainly used to make sure real people, but not bots, fill in HTML forms to prevent spams. It works on the assumption that it is hard to solve CAPTCHA's in difficult-to-read images by computers. What if you get a pool of people to solve them for you? I came across this interesting post where there's actually a market for solving CAPTCHA's manually. This could be used for both good and bad purposes. I didn't know people solve them for money!

Customer: I want to get xxx number of CAPTCHA's solved. Not a problem. We charge $2 for 1000 CAPTCHA's and minimum deposit is $8.
Customer: Wow, it's only $0.002 for a CAPTCHA!

Wednesday, October 8, 2008

Can you count the number of soldiers..

You are given that there are less than 1000 soldiers assembled in a battle field. They have done three 'count off's. (Each one remembers the number the last soldier shouted out and shouts out the next number if it is less than the 'count off' number or starts with number one). They have carried out 'count off by sevens', then 'count off by tens' and finally 'count off by thirteen'. The numbers the last soldier in the assembly shouted out were one, three and eight respectively. The commander wants to know the exact soldier count.

The answer is 463!

Notice 7, 10 and 13 are relatively prime in pairs. You can apply the Chinese Remainder Theorem! The three congruences x ~ 1 (mod 7), x ~ 3 (mod 10) and x ~8 (mod 13) have common solutions, where x is the exact soldier count. Any two common solutions are congruent modulo 910 (that is 7 * 10 * 13).

Using number theory, we can show that x ~ 463 (mod 910). The solutions are 463, 1373 (463 + 910), 2283 and so on. Since there are less than 1000, the answer is 463.

(Note: I have used '~' as the congurence symbol, but we usually use 'equivalent' notation for that)

(Courtesy: The Art of War by Sun Tsu in the 17th century; adapted from the Wagstaff's Number Theory book)

Isn't it cool..

Here are some more similar challenges:
Eggs in the basket
Five pirates and a monkey