eon

Posted by tpc at June 20th, 2009

Erdös apparently liked to have children sit on his lap. See this 1969 conference photo
http://staff.spd.dcu.ie/johnbcos/oxford.htm
(There is also a young dashing George Andrews on the left.)
So it was funny to see this page on the lap number.

Unfortunately, my Erdös number is still 4. I probably could decrease it to 3 by randomly putting my thesis advisor’s thesis advisor’s name into some future paper. It is either that or wait till the apocalyse.
http://xkcd.com/599/

Posted by tpc at June 18th, 2009

I got myself a hp tx2 tablet running on amd Turion with 4GB ram. A dear friend helped me upgraded to vista 64 bit in order to fully utilize the ram. I tested it against the desktop running xp 32 bit on pentium core 2 duo. I was told that this desktop actually has 8GB ram but xp 32 bit only recognise 3 GB.

It was not a rigourous test by any means but I got both systems to try and factor

(3)(5)(17)(257)(641)
(93461639715357977769163558199606896584051237541638188580280321)
(5704689200685129054721)(59649589127497217)(1238926361552897)
(67280421310721)(6700417)(65537)(274177)

Anyone want to verify the computation?

It took 2141 seconds on the notebook which, according to the software, utilized 2.3 GB but 2300 seconds on the desktop which utilized 2GB. So it’s probably the memory that made all the 10% difference.

Posted by tpc at June 6th, 2009

I’ve never met him, but he did research in the area of partitions and was a friend of several people I know. One of them - Shaun Cooper - by pure chance found a reference to Richard in the 1996 autobiography of Howard Marks named “Mr Nice”. On the cover it said of Marks “He was Britain’s most wanted man. He has just spent seven years in America’s toughest penitentiary. You’ll like him.”

On page 73, here’s a paragraph of what he had to say.

There were one or two ex-Oxford students attached to the University of Sussex. One was a brilliant mathematics lecturer, Richard Lewis, who would often visit Ilze and me along with Johnny and Gina Martin. Richard came from a relatively wealthy family, owned property in Brighton and London, drank like a fish, smoked everything at hand, thought mathematical profundities, and was a keen and talented chess player. He had heard of Go, was interested in the game, but had never played. I taught him. After a dozen games, he beat me. He still beats me.

There are a few more references to Richard and his wife in the following pages, get the book and read it!

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 April 17th, 2009

A classical and computational introduction is a new book by L.J.P. Kilford. New enough that it even has reference to the resolution of Serre’s conjecture. But this book is really an introduction to the classical aspects of the theory of modular forms and it does a great job. I took a few days to read through the book (of course, ignoring the details and proofs) and I would say it is very enjoyable. Kilford adds in lots of funny and quirky anecdotes, most of which I’ve read from different places but it’s nice to have everything collected in one book. For example, he mentioned Lang’s famous foreword:

“It is possible to write endlessly on elliptic curves. (This is not a threat.)”

I remembered being so tickled when I first saw this in Lang’s book.

Back to this book. Even with the subject of modular forms it is the same. He knows he can’t possibly explain everything and so is not afraid to be a little vague at times and cite the various references to where more in depth discussions can be found. Thus, he is able to accomplish much in this modest sized (200+ pages) book. My one small complaint is the title should not include “and computational”. I found the last chapter on computational aspects too brief. He highlighted some history, discussed MAGMA and SAGE, giving some examples of the codes used, but I believe that this is not enough for someone interested in computing modular forms to get started on. And the appendixes on MAGMA and SAGE codes are each one page long with two longish lines of commands.

Posted by tpc at April 11th, 2009

by Yoko Ogawa. I remember watching half a movie on a plane which was called “The Gift of Numbers” (Hakase No Aishita Sushiki) and was based on the 2004 Japanese novel by Ogawa. Since then, I place the book in my to read list and it so happened that two weeks ago, I read a review of the book on the Sunday times. Apparently, the english translation just appeared under this new title and it turned out fortuitously that the library carried this book.

The story of the book is about how the housekeeper was assigned to this number theory professor who had an accident, lost his short term memory and only retained 80 mins of memory. To remind himself, he pinned a note on his clothes that says “I have only 80 minutes of memory.” It’s an interesting proposition to say the least, but what is engaging is the relationship developed between the professor, the housekeeper and her son called Root because he has a flat head. There was only a very brief and subtle exploration into the anguish of the professor at his state.

There are quite some mathematics mentioned by the professor, for example, on amicable numbers, Ruth-Aaron numbers 714 and 715, as well as the perfect number 28 which happened to be the shirt number of the professor’s favourite baseball player Yutaka Enatsu.

For another review see Math fiction.

Posted by tpc at April 8th, 2009

I chanced upon this neat number puzzle devised by William Wallace, via wild about maths. It’s form is certainly recognizable, but still the effort deserves praise.

I remember a similar puzzle played with a deck of cards. You lay out the cards in rows and ask the participant to tell who which row his card is in. The trick is to collect the cards back horizontally, but deal out the next four rows vertically, this way after a few deals, you can tell which card is it.

This happen to tie in with a class I’m teaching tomorrow, maybe I’ll print out the cards and try it in class.

Posted by tpc at March 23rd, 2009

I came across the following identity today.

It is not exactly difficult to establish if one uses the Pascal relation repeatedly.

An alternative proof is to extract the coefficient of from the generating function identity:

I’m thinking that this must have a nice combinatorial proof, but all my references are in my office.

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 February 11th, 2009

The government announced today that Deepavali, a public holiday will have its date changed from 15th November to 17th October, a difference of one whole month. This Indian holiday is based on the lunar calendar and sightings of the moon. Apparently a local mathematician who is into calendars, did the computations and showed the original computation is wrong. Well, at least this time, they listened to the one who knows maths.

Posted by tpc at January 24th, 2009

I was reading this light-hearted article by jeremy au yong in the local papers. It’s mainly about how the economy is bad and he was retrenching his girlfriend. As compensation he offered a gift.

The value of this gift will be determined by using the formula $15 x years of service + cube root of pi, differentiated over the limit of zero to infinity.

Something is wrong right? Does he mean integrated rather than differentiated, since nobody differentiates over a range. As the only variable is y for years of service, does he mean

Well, how does one pay off this infinite debt? Once again, mathematics to the rescue. He can pay his girlfriend 1 cent today, 1/2 cent tomorrow and 1/3 cent the day after …

Posted by tpc at January 24th, 2009

I’ve recently came across several good books that are recently published by PUP and I’m further impressed by that fact that their books are usually cheaper than Springer and significantly cheaper than Oxford. I really liked the Fourier Analysis and the Complex Analysis titles in the four part series by Stein and Shakarchi. Another book that I really liked was Google’s PageRank and Beyond by Langville and Meyer.

They also published quite a number of general maths book. One of which I’ve wrote about. It’s not always hits. One that I didn’t like was A Certain Ambiguity by Suri and Bal which is a fiction. It started out promising, a young Indian studying in stanford saw a reprint of a paper by his grandfather (who was based in India) with the footnote that ideas came to him during his term in prison in the US. So he set out to discover how his grandfather was incarcerated. Then the story unravels in two lines, a transcript of conversations between his grandfather and a judge, plus a parallel line where the protagonist learns mathematics in a class. There is also a third fictional line in the form of journals of famous mathematicians. Much of the action is actually discussion on mathematics focusing on geometry and the 5th postulate, and also ideas on logic, truth, Cantor’s theory of infinity. Somehow, I just don’t find the book engaging at all and I particularly dislike it when authors take liberties in fictionalizing real mathematicians.

Isn’t it funny how I have so much to say about books I don’t like and not much to say about those I recommend.

Posted by tpc at January 17th, 2009

The tour de force by E.T. Whittaker and G.N. Watson. The Math Reviews says that the 1996 reprint of the 1927 fourth edition has 608 citations! It’s certainly a magnificent book and worthwhile to have on your shelf.

The 1996 cambridge version on amazon is listed at USD$94. But I just found a new version from merchant books also listed at amazon for USD$25! The details state that the new version has 568 pages vs the 616 pages of the original. So are these two the same? Obviously if I refer to page 408, it would be a different page altogether and it would be in my mind insane to re-typeset the whole book. Unfortunately, Amazon links the reviews for the 1996 versions to the new version, including the previews. So there’s no way of confirming my suspicions that there are differences.

Posted by tpc at January 13th, 2009

We should all be familiar with the method of separation of variables for first order ordinary differential equations. Here’s a neat example from John Starrett’s article in Amer. Math. Monthly.

(more…)

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 December 15th, 2008

to the bomb scenario in the Dark Knight. I’m not a game theorist, so I shan’t comment but read this post to form your own opinion.

Posted by tpc at December 13th, 2008

I don’t believe I have seen the following identity before, although it is pretty easy to prove it by induction.

I should mention I saw it in Edward Barbeau’s book Power Play.

Posted by tpc at November 7th, 2008

Read something quite cool. Professor Brown from Dalhousie, used fourier transforms to reconstruct a mysterious chord from the Beatles `A Hard Day’s Night’

Posted by tpc at October 12th, 2008

In the midst of recession and oil prices falling from $145 to below $80, the ridiculous power company announced that electricity prices are going up by 21%, based forward oil pricing. The best thing is that our electricity are generated through natural gas, not crude oil!

Even more ridiculous is the following quote taken by the report written by one Liaw Wy-Cin.

The scope for savings is high considering that power consumption patterns show that 40 per cent of households, from one-room flats to landed properties, use more than the monthly average, said Mr Khoo (Chin Hean, EMA chief executive.) EMA is the electricity and gas industry regulator.

Well, if the report was accurate, the statement defies common sense! By the very definition of average, 50% of every household would use more! I’m guessing the 40% comes because they banded the average consumption into ranges. (I made a terrific blunder here, see the comments.)

Another report from Reuters said

People who take long spells of sick leave at least once in three years face a higher risk of early death,…

What a magnificent revelation, almost as strange as rooster crows leading to a higher chance of the sun coming out. Come on, which part of ’sick’ in sick leave do you not understand? People suffering from serious ailment take sick leave and have a high chance of premature death. Common sense tells you that. Again, either it was a worthless paper in the British Medical Journal or it’s the reporters missing the point.