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Posted by tpc at April 30th, 2007

Here’s my solution to a nice little trigonometric problem posted by miss loi.
Show that

(QED)

Posted by tpc at April 30th, 2007

This article in BBC news about a competition from the Royal Society of Chemistry, made its rounds last week. I had wanted to submit my solution for the 500 pound prize, but decided not to when I realized how quickly the news was spreading. A related article has a Professor Shaw claiming that the article was not fair because of curriculum differences.

Of course, everyone is entitled to his or her own opinion. If you want mine, I’m of the view that mathematics training in the UK has been watered down over the past years. Singaporeans usually take the Cambridge GCE O and A levels, and have easy access (thanks to overzealous parents, teachers and publishers) to all the past year exam papers dating all the way back to the 70s. A cursory inspection would reveal that the questions are getting easier. So, the difference in difficulty between the two questions reflect not so much China vs UK standards, but perhaps UK standards of the 70s vs now. It seems that the general curricula is regressing everywhere. Will the same thing happen in China? It is already happening in Singapore. The ministry has just announced the Primary school examinations will incorporate the use of calculators - the nation is well on its way to innumeracy soon.

On a lighter note, some enterprising local produced a tongue in cheek variant of the entrance exam

Now, part (ii) was pretty obvious to me. Since nothing is faster that the speed of light, we can expand the denominator as a series. I cheated for part (i) because I forgot what was the formula for momentum. I gave up on parts (iii) to (v), but I hope everybody knows the answer to part (vi) is 42.

Posted by tpc at April 15th, 2007

By Keith Ball. Yet another popular maths book, with the usual suspects of Fibonacci numbers and fractal curves. But this book is different in the topics chosen. Influenced by his own tastes, he discusses Stirling’s formula and Pade approximation among other things. The last three chapters are especially interesting for me. I love the way continued fractions keep popping up here, there and everywhere. His discussion on the Fibonacci also carries some depth and goes beyond what is normally done. A section is devoted to showing the for primes p,
, for Lucas numbers.

Posted by tpc at April 15th, 2007

My favourite sum:

To Euler,
The master of infinity, who summed with impunity!

PS: A nice article on infinity, explaining concepts up to Cantor’s work.
via http://www.mathed.org via amazon.

Posted by tpc at April 14th, 2007

I was randomly surfing when the title Weapons of Math Destruction caught my eye. This is a site/blog about “new” math taught to American school children. There are some comics and also this interesting link to a video. In the video, a supposedly well known personality illustrates how two textbooks used in schools are no longer teaching traditional multiplication and long division, but substituting it with a more heuristic approach. It’s pretty interesting if you have 15 mins to spare. At about the 10th minute, the video quotes the following passage:

The authors of Everyday Mathematics do not believe it is worth student’s time and effort to fully develop highly efficient paper-and-pencil algorithms for all possible whole number, fraction, and decimal division problems. Mastery of the intricacies of such algorithms is a huge endeavor, one that experience tells us is doomed to failure for many students. It is simply counter-productive to invest many hours of precious class time on such algorithms. The mathematical payoff is not worth the cost, particularly because quotients can be found quickly and accurately with a calculator.

At the end, there is a plug for Singaporean mathematics textbooks. The irony is that at the pre university level, the Ministry of Education in Singapore is doing exactly the same thing. Pushing for expensive graphing calculators as a substitute for mathematical ability.

Posted by tpc at April 7th, 2007

How many times have you tried to search for a particular item and find that the only thing missing is the one that you want?

Two years back, I was searching for a 1995 article in the Rocky Mountain Journal of Mathematics, Volume 25 no. 4. I couldn’t believe my bad luck when I discovered the library had every volume, every issue for the past 35 years, since volume 1 in 1971, except the very issue that I was looking for! I was so amazed that I even went to ask the librarian about it.

A similar thing happened again today. The local newspaper had a 100 word column with the headlines Untrained S’porean’s maths Ideas on print. It’s about a Mr Bertrand Wong who claims to have proven the Twin Prime conjecture. His work was published in a peer reviewed journal known as the International Mathematical Journal. Some googling revealed that this is a relatively new journal started in 2002 and since 2006 has changed its name to International Mathematical Forum. Some 2006 articles are available online.

Wong’s article appeared in vol 3 no 8 pg 873-886. It got me piqued because just last week I was looking for some material on the twin prime problem to share with some students. Unfortunately, our very well stocked library does not carry this journal, so I tried to go into Math Reviews to find out more about the article. But no matter how I search, I could not find a review. When I pulled out all the reviews for Int. Math. J vol 3 no 8, I discovered that out of 12 articles in that issue, all 11 have review entries except the very last article. Another coincidence?

On a related note, I found this page on exceptional Math Reviews.