Archive for the 'Mathematics' Category

02
Mar
12

We’ve Got Great Alumni

Here is the latest example of our great alumni in the Department of Information and Mathematical Sciences here at Messiah College. In the controversial rankings of 4th through 8th grade teachers in New York City, class of 2005 alumna Kelly (Toolan) Hudson is listed as the 10th best mathematics teacher in the city. She’s also the second 8th grade teacher listed. Like all rankings, the methodology is fair to discuss. The methods seemed to be an attempt to model the benefit a teacher gave their students on standardized testing. Other variables were controlled for. While I’m not a fan of basing everything on standardized tests, I do think that this methodology does not take away from the honor that this ranking bestows. Congratulations, Kelly!

29
Feb
12

Math Humor from Frazz

If you don’t read Frazz daily, I really think that you are missing out. Here is a particularly good one from a few days ago:

25
Jan
12

The Mathematics of the Game SET

The Cover Image for the Game SET

SET is an extremely addictive, fast-paced card game found in toy stores nationwide. Although children often beat adults, the game has a rich mathematical structure linking it to the combinatorics of fi nite affine and projective spaces and the theory of error-correcting codes. Last year an unexpected connection to Fourier analysis was used to settle a basic question directly related to the game of SET, and many related questions remain open.

So begins a recent paper on the elegant mathematics of the card game SET. For those of us who enjoy card games that require logic and quick thinking, rather than simply luch, and the mathematical beauty and surprising interconnectedness of different mathematical fields, this paper is interesting. Warning: you need a certain level of algebraic understanding to follow the paper (having had an algebraic structures course beyond “linear algebra” in college will help). The paper starts out by giving the background of the development of the game, and how it is played. Then the authors turn to problems of algebraic interest regarding the game and show how to answer some of these questions.

Personally, I love the game. I was introduced while visiting my graduate alma mater (Virginia Tech) by a former student here at Messiah College who was in graduate school at Tech. She introduced my wife and I to the game, and I fell in love. For those familiar with the game SET, or would like to try it out, it is available online here.

23
Jan
12

It Is Exam Day Again …

In honor of the Intro Stat exam I gave from 1:00-2:00 or so today:

20
Jan
12

Beautiful Mathematics Behind Ugly Music

For those of us with an interest in the correspondence between mathematics and music, this TEDx talk is a fascinating look at the deceptively difficult job of writing music with no patterns.

 

28
Oct
11

Stat/Probability Quiz of the Day

Good luck with this one!

28
Oct
11

Demography: Predicting the Downfall of China?

A very interesting look at where all of the earth’s billions of people are now, and where the population is heading. Projections place the occurrence of the world population of humans passing 7 billion at some point between 31 Oct 2011 (UN estimate) and March 2012 (US Census Bureau estimate). The most interesting piece of this article is the pointing out that the rate of increase is now slowing. (The second derivative is now negative, for my math inclined readers.) Where the fertility rate is high, and where it is low, helps to predict the economic future of countries around the world. The pertinent section follows this graph of fertility rates (live births per woman).

The low-fertility countries face the biggest demographic problems. The elderly share of Japan’s population is already the highest in the world. By 2050 the country will have almost as many dependents as working-age adults, and half the population will be over 52. This will make Japan the oldest society the world has ever known. Europe faces similar trends, less acutely. It has roughly half as many dependent children and retired people as working-age adults now. By 2050 it will have three dependents for every four adults, so will shoulder a large burden of ageing, which even sustained increases in fertility would fail to reverse for decades. This will cause disturbing policy implications in the provision of pensions and health care, which rely on continuing healthy tax revenues from the working population.

At least these countries are rich enough to make such provision. Not so China. With its fertility artificially suppressed by the one-child policy, it is ageing at an unprecedented rate. In 1980 China’s median age (the point where half the population is older and half younger) was 22 years, a developing-country figure. China will be older than America as early as 2020 and older than Europe by 2030. This will bring an abrupt end to its cheap-labour manufacturing. Its dependency ratio will rise from 38 to 64 by 2050, the sharpest rise in the world. Add in the country’s sexual imbalances—after a decade of sex-selective abortions, China will have 96.5m men in their 20s in 2025 but only 80.3m young women—and demography may become the gravest problem the Communist Party has to face.

Many countries with intermediate fertility—South-East Asia, Latin America, the United States—are better off. Their dependency ratios are not deteriorating so fast and their societies are ageing more slowly. America’s demographic profile is slowly tugging it away from Europe. Though its fertility rate may have fallen recently, it is still slightly higher than Europe’s. In 2010 the two sides of the Atlantic had similar dependency rates. By 2050 America’s could be nearly ten points lower.

But the biggest potential beneficiaries are the two other areas with intermediate fertility—India and the Middle East—and the high-fertility continent of Africa. These places have long been regarded as demographic time-bombs, with youth bulges, poverty and low levels of education and health. But that is because they are moving only slowly out of the early stage of high fertility into the one in which lower fertility begins to make an impact.

At the moment, Africa has larger families and more dependent children than India or Arab countries and is a few years younger (its median age is 20 compared with their 25). But all three areas will see their dependency ratios fall in the next 40 years, the only parts of the world to do so. And they will keep their median ages low—below 38 in 2050. If they can make their public institutions less corrupt, keep their economic policies outward-looking and invest more in education, as East Asia did, then Africa, the Middle East and India could become the fastest-growing parts of the world economy within a decade or so.

Demography, though, is not only about economics. Most emerging countries have benefited from the sort of dividend that changed Europe and America in the 1960s. They are catching up with the West in terms of income, family size and middle-class formation. Most say they want to keep their cultures unsullied by the social trends—divorce, illegitimacy and so on—that also affected the West. But the growing number of never-married women in urban Asia suggests that this will be hard.If you look at the overall size of the world’s population, then, the picture is one of falling fertility, decelerating growth and a gradual return to the flat population level of the 18th century. But below the surface societies are being churned up in ways not seen in the much more static pre-industrial world. The earth’s population may never need a larger island than Maui to stand on. But the way it arranges itself will go on shifting for centuries to come.

Here are a couple more helpful graphs of the world population and world fertility rate.

World Population Graph: Note the change in concavity in the last few years.

The Declining World Fertility Rate

You can read the rest here.

27
Oct
11

Imaginary Friends

It isn’t only kids that can have imaginary friends, numbers can have them too.

10
Oct
11

Math Humor for the Day

Well, since I’m again caught up on my piles of grading, I’m back in the swing of blogging again. Since my grading is all mathematics and statistics (entirely statistics last week) I thought a math funny a former student shared via Facebook would be appropriate! Enjoy.

28
Sep
11

Trig Humor

I can understand if some of my readers find that the title is an oxymoron, but I enjoyed this little image shared by several AP Stat friends via facebook:




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