Posted by tpc at July 13th, 2010
There are lots of nice videos out there which would be ideal to show to students before lectures or during breaks just to break the monotony. Here’s one about Fibonacci numbers and nature that’s pretty impressive, although I don’t think one will learn much maths from it.
Posted by tpc at June 6th, 2010
Yesterday (5th June) was World Environment Day. I wouldn’t say I’m a green fanatic but I do try my best to recycle, use the air conditioner only when it is unbearable and bring my own non-plastic shopping bags whenever I know I was going shopping. According to this webpage, a total 17,291 species are known to be facing extinction.
I wonder what is the source of the number. If you google World Environment Day 17291, 17 of the first 20 webpages has a variation of that same sentence. Out of these 17 only this one suggests that the number is not exact. I quote (emphasis mine)
“In totality, there are roughly 17,291 species that are on the threatened list”
The number 17291 stood out for me. It turns out to be prime! In fact wolfram alpha tells me it is a twin prime. No prizes for working out which is its twin. Of course, 1729 is the famous Ramanujan Taxicab number. Perhaps that’s why it looked familiar.
Update 1: Google’s spider is amazing. I just googled 17291 and this post has been indexed within 13 minutes.
Update 2: The source seems to come from The IUCN Red List of Threatened Species and this blog post has a breakdown. So the number does appear to be exact at least at a certain point in time.
Posted by tpc at April 1st, 2010
The national paper - the Australian - publishes a puzzle called number crunch. You have to insert the numbers 1 to 9 into a grid to make the arithmetic work. For example, it could look like
The first row would need to be filled with 8 - 2 - 5 = 1 and the first column 
Note that unfortunately, the answer required the sum in the middle column to give
2 + 1 x 7 = 21
which is wrong in an arithmetic sense.
A staff of UQ maths dept noticed this and wrote several email and made several phone calls to the papers. The newspaper guys, it seems, needed some firm encouragement before being willing to get their computer programmer to change the code. I’m glad to report that perseverance paid off and now the instruction includes this line - “Multiplication and division are performed before addition and subtraction.”
Posted by tpc at February 28th, 2010
while a rose by any other name may smell as sweet, a mathematician might just be discriminated by his/her name. The perceived ability of a mathematician (as well as most academics) is by publications. There are two norms in listing authorship of joint work. One adopted by mathematics and economics is to list the authors alphabetically, regardless of amount of contribution. On the other hand, for disciplines like psychology and biology, the norm is to list the author in terms of contributions. It’s an interesting phenomenon, because I’ve seen biology papers with many authors. It seems that if you are in a lab which publishes 10 papers, chances are high that you get your name in every one of them, maybe as the 7th author. Perhaps, I can get my name as the 8th author by just walking past the lab! In a sense, as long as the main author’s name is first, he probably wouldn’t mind sharing credit with people, maybe in the hope that the favour is reciprocated.
I must say both practices have their pros and cons. Suppose you are a young person writing with an established guy, people would tend to think the established person did the work, unless you put your name first. On the other hand, a co-authorship might result in A providing an idea and B doing all the work. Now, who should deserve more credit? The one who did the work? Not really. A good idea is usually hard to come by. Plus it can be touchy to always have to establish who should get main credit. I suspect the relationship wouldn’t last or at least be as cordial. Compare that to the Hardy-Littlewood rules for collaboration.
I’m not one to want to upset the established order, so I stick to the alphabetical routine. As my surname is in the last quartile of the alphabet, I’m always the second or third author. I do have this nagging suspicion that this might have impact on how people perceive your contribution. This was confirmed when I read superfreakonomics. That book mentioned the following paper in Economics that concluded that there is some bias towards academics with names arriving later in the alphabet. Here’s the reference if you are interested.
What’s in a Surname? The Effects of Surname Initials on Academic Success, Liran Einav and Leeat Yariv, Journal of Economic Perspectives - Volume 20, Number 1—Winter 2006—Pages 175–188.
One main point is that tenured faculty in the top 5 economics departments in the US have surnames arriving earlier in the alphabet than junior faculty. But the bias disappear as the data is expanded to the top 20 or 35 departments. So perhaps the impact of that bias is not as great as things like race, gender and other forms of discrimination.
Posted by tpc at September 3rd, 2009
A nice poem I saw in the newsletter of the LMS.
http://www.lms.ac.uk/newsletter/384/384_10.html
A WEEK IN THE LIFE OF A MATHEMATICIAN
(with apologies to Michael Flanders and Donald Swann)
’Twas on a Monday morning I had a bright idea,
I was lying in the bath tub and the strategy seemed clear,
For a problem posed by Erdös back in nineteen forty nine,
On sequences dilated into subsets of the line.’Twas on a Tuesday morning I jotted down my thoughts,
I covered backs of envelopes with surds and aleph noughts.
After several cups of coffee I began to feel inspired,
And a lengthy calculation gave the answer I desired.’Twas on a Wednesday morning I wrote the details out.
My lemmas and corollaries left little room for doubt.
I filled up many pages just to get the logic right,
And with epsilons and deltas I made it watertight.’Twas on a Thursday morning I typed the paper up,
With ’slash subset’ and ’slash mapsto’ to say nothing of ’slash cup’.
My LaTeXing was perfect, printed out it looked so good,
Should I send it to the Annals? I rather thought I would!’Twas on a Friday morning I read the paper through,
I checked out every detail as good authors ought to do.
At the bottom of page twenty in an integral I found,
I’d divided through by zero and the proof crashed to the ground.On Saturday and Sunday I was too depressed to care,
So ’twas on a Monday morning that I had my next idea.Kenneth Falconer
This brings to mind the secret diary of a mathematician, found at this link
http://iims.massey.ac.nz/iimsnews/2006/IIMSNwsltrMay2006.pdf
Posted by tpc at May 11th, 2009
The International Congress in 2010 will be held in Asia again, in Hyderabad, India. I love the conference logo.
To the uninitiated, the picture is about hyperbolic geometry and is related to the equivalent fundamental regions for a modular form and the inequality is the Ramanujan’s Conjecture for the Fourier coefficients of the delta function - the cusp form of weight 12 for the modular group.
Posted by tpc at March 4th, 2009
The newspaper (26 Feb) reported an economist made this prediction. That’s an alarming figure, but not because the economy is so bad, rather the mathematics is so bad. Can anyone without divine powers get that kind of accuracy? So this Mr Irvin Seah’s job loss model probably takes into account whether the cleaning lady at the coffeeshop downstairs can keep her job, since he is able to predict job losses to the exact number. With such clever economists, no one wonder everyone is bashing the number crunchers. Including, Warren Buffet’s famous or infamous:
Beware of geeks bearing formulas.
This blog is turning out to be something like a mini version of John Allen Paulos’ “A Mathematician reads the newspapers.” By the way, Paulos is apparently in Singapore this week and giving a talk at NTU.
The said article is available here if you care to read it.
Posted by tpc at January 13th, 2009
Apparently my job has been rated as the best in the world by careercast. See also the WSJ report. In fact, the top 3 are all math related and physicists got number 13!
Posted by tpc at January 7th, 2009
Pronouncing names has always been a problem and I think it is embarrassing and just not right to mispronounce names, if one can help it. I always cringe when I hear Euler pronounced as “U-ler” instead of “Oil-ler”. Thankfully we now have a guide, via the Notices of AMS.
Posted by tpc at November 8th, 2007
Really cool video on mobius transformation.
http://www.ima.umn.edu/~arnold/moebius/
Posted by tpc at May 4th, 2007
Craig Laughton’s blog and Jorge Cham’s comic sums up the ups and (mostly) downs of the life of a grad student. Here’s a wonderful sequence from the phd comics.
“Rediscovery 1″
“Rediscovery 2″
“Rediscovery 3″
“Rediscovery 4″
“Rediscovery 5″
“Rediscovery 6″
Posted by tpc at March 3rd, 2007
according to J-P Serre. I spent an hour watching this video of his talk. Considering I may never have the chance to meet him in person, this was not a bad way to spend Saturday morning. It is accessible to a general audience although you probably need to know some homological algebra, analytic number theory and other stuff to appreciate the points he was trying to convey.
I first saw the link via Steve’s weblog although many sites are also carrying the link. Not surprising since there are so many mathematicians blogging now, including Terry Tao and Alain Connes. Read this nice post by Steve.
No time to spare? This article by David Goss, which incorporates hints from Serre, contain a few of the points highlighted in the talk. In trying to link it, I discovered this version was updated Feb 2007.
Posted by tpc at September 9th, 2006
That’s what I occasionally do when I pick out books in the library. I look at those with nice covers, or those with familiar covers (for example the Contemporary Maths series from AMS), then I look at the title and its contents.
Now that there are a huge number of blogs and mathblogs in cyberspace, sometimes the only thing one can do is to click the link with the most attractive title.
Today I chose Good Math, Bad Math, and found the following post/article which explains neatly why the Romans use their strange number system.
http://scienceblogs.com/goodmath/2006/08/roman_numerals_and_arithmetic.php
Posted by tpc at August 26th, 2006
In theory, you could just become an expert, but in any sufficiently technical field there will be results that “everyone knows†but won’t be published anywhere, so unless you are part of “everyoneâ€, it will be difficult for you to fill in the gaps without a great deal of rediscovery.
Quoting Walt from Ars Mathematica.
How true.
Interestingly, the post is about an article in the New Yorker about the controversy surrounding the Poincare conjecture and Perelman’s rejection of the Field’s Medal. Well worth a read.
Posted by tpc at June 6th, 2006
I was browsing through an American study guide and it recommended remembering the order of arithmetic operations through this mnemonic:
PEMDAS (Please Excuse My Dear Aunt Sally) -
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Locally, I learnt and teach kids this:
BODMAS -
Brackets, Order, Division, Multiplication, Addition, Subtraction.
According to this wiki page, this is the UK way.
Another interesting one is
SOHCAHTOA - for the three trigonometric functions.
Locally, we teach students to remember “Toa Cah Soh” which in a local dialect actually means Big Feet Aunty.
Posted by tpc at June 1st, 2006
When you are based in a small Asian country, you get precious little opportunities to hear good lectures from distinguished lecturers. Luckily, there is an increasing trend of video-casts available on certain websites. The silly thing is that even when the video is available, I cannot find time to sit down and watch it.
One of the few I’ve watched:
Ben Green’s talk on Arithmetic Progressions of Primes.
A series I intend to watch someday:
Alf van der Poorten - Topics in Number Theory
Conway, Silverman and Weeks - Young Mathematician Conference
Posted by tpc at April 20th, 2006
I’m a fan of google. I mean who would not like a story of how math geeks triumph over the world. (Although now that they are in the big leagues, it remains to be seen if they can stay rooted to their original mindsets and not end up being big bullies.)
If you are a user of gmail, you know that they are constinously increasing your storage quota. Today’s snapshot shows 2716….
I have been waiting for it to show 2718.2818 for quite sometime. Would they stop at exactly e or would they go to 
?
Update: They went past e (or more precisely 1000 e ) without stopping. The best screen cap I got was at 2718.000001 megabytes.
Posted by tpc at April 8th, 2006
We are all familiar with the process of tallying, putting down a vertical stroke for each count and for every fifth count, crossing out the four vertical stokes with a horizontal one.
An interesting quote from The Lady Tasting Tea by David Salsburg
It is a foolish way to tally, said John Tukey. Consider how easy it is to make a mistake. You might put the cross over three instead of four lines, or you might put down five lines and then a cross. The incorrect tally is hard to spot.
Quite true. Interestingly, the old folks here use the following Chinese character: æ£ , as a tally. Every five strokes give you a complete character, which addresses what Tukey was unhappy about. Moreover, this character “zheng” actually means upright or correct.
Somewhat related to this, for certain chinese dialect, there is actually no words for right and left. Right is also denoted by the same character æ£, while left is denoted by a character signifying opposite. In case you are wondering, in official Chinese “Han” the character for right is å³, while left is å·¦.
Posted by tpc at December 8th, 2005
I remembered the first time I was aware that there were people who thought mathematics was an art, I was quite offended. This has probably something to do with being Singaporean. Our country is tiny and we are where we are due to a conscious effort of the government to promote science and technology in the 70s. (Some think that it was such a rousing success that we are now a cultural desert and hence the current emphasis on the arts.) Back in school, if your result was good you go to the science stream as opposed to the arts or commerce streams. That was then, things are quite different now, although there is an unhealthy (at least to me) push towards life sciences.
Yet, as my interest in mathematics grew, I began to see and feel otherwise. Pure mathematics is no different from arts. I study numbers because they are interesting and beautiful to me, without any recourse as to what uses they would have. Much like someone who studies Tolkien’s work and researches middleearth.
An interesting blog whose title evoked the question Ars Mathematica.
Anyway the answer is right there.
Mathematics = Arts V Science. (Not XOR)
