Chris Lang's Blog
(stray comments on mathematical topics or other things that catch my attention; please email me if you have any comments or anything interesting to mention)
| 2009-11-12 1730: | An article on MSNBC.com reports that there is a shortage of teachers in only 1 of 61 subjects—mathematics. (In most subjects, there are a lot of applicants, but few jobs, due to the adverse economic situation.) |
| 2009-10-26 1630: |
Here's something a bit scary for Halloween: a plot of high
temperatures in Louisville for Halloween day, from the year 1873 to the
year 2008, showing (perhaps) the affect of global warming. I got the raw data from the local National Weather
Service web site, and spent a while with the statistical program R
to generate the plot. The plot shows a linear regression line,
showing the temperature trend over the years. The slope of the
line is 0.07765, which signifies that the high temperature on Halloween
has been rising at a rate of about 0.078 degrees Fahrenheit per year in
Louisville. The p-value for this slope is 0.0008, which is very
small—signifying that this rise in temperature is very unlikely to
be due to chance: the trend is real. (The standard error on the
slope is 0.022, which means the temperature has probably been rising by at least
0.055 degrees per year, and maybe by as much as 0.100 degrees per year.)
It turns out the average high temperature for the first 30 years of this
data is 60.5 while the average temperature for the last 30 years is
68.6. The p-value for these is 0.003, so again it is very
unlikely this is due to chance. |
| 2009-10-21 1515:: |
The following appeared in the Society for Mathematical Biology Digest (an
email newsletter I receive):
Call for submissions: Academics on Zombies The recent publicity over the academic work "When Zombies Attack!: Mathematical modelling of an outbreak of zombie infection": http://www.mathstat.uottawa.ca/~rsmith/Zombies.pdf illustrated the power that bridging popular culture and academia can have. As a result, the authors of that paper are putting together an edited collection, provisionally titled "Academics on Zombies". The aim is to do for your discipline what the Zombie-outbreak paper did for the field of mathematical modelling of infectious diseases: illustrate key concepts in a friendly and accessible way. Reports from readers of the modelling paper were that a) high school students were interested in mathematics for the first time ever, b) people who found the idea of equations horrendous nevertheless read the paper and c) people unaware that there even was such a field as mathematical modelling of infectious diseases were fascinated to learn of its existence and potential. The aim of the book is to treat zombies as real and apply techniques to understand them, or to intervene. Aside from that, the specifics are up to you. Possible topics might include:
Please submit a pitch to Robert Smith? <rsmith43@uottawa.ca> with the words "Zombie Pitch" in the title of the email. This pitch should describe, in some detail, your idea and your qualifications. Deadline: November 15. The aim is to have some fun with this, but also to showcase your academic field. Please pass this on to anyone who might be interested, especially anyone who's in a field different to yours. |
| 2009-10-13 1245: |
I happened across an interesting web site, www.wordle.net/,
which lets you create "word clouds" from text or from web site, where the size of the word
reflects how often it appears. I tried it with a portion of this blog, and it produced this
image.
|
| 2009-10-08 1045: | The New York Times has an interesting obituary about Israel Gelfand, a famous Russian mathematician who died this week at the age of 96. His work was important in the area of mathematics I wrote my doctoral dissertation in. |
| 2009-09-16 1250: | The MacArthur Foundation gives 24 "genius grants" each year, which are $500,000 awards to individuals who they believe merit recognition for their achievements in the arts, sciences or other domains; recipients of the awards are free to use them for any purpose, but the Foundation hopes the awards will enable them to accomplish new and unexpected things. Often, they recognize mathematicians. This year, they honor an applied mathematician, L. Mahadevan, a Harvard professor who "applies complex mathematical analyses to a variety of seemingly simple, but vexing, questions across the physical and biological sciences — how cloth folds when draped, how skin wrinkles, how flags flutter, how Venus flytraps snap closed." For more about about this MacArthur Fellow, see: L. Mahadevan. |
| 2009-09-16 1250: | In their newsletter for September, 2009, the Society for Mathematical Biology reports on the Annual Meeting of the Society, held in Vancouver, British Columbia in July of this year. This included a session on the mathematical modeling of an outbreak of zombie infection. |
| 2009-09-10 0930: | The American Mathematical Society has a web page for students, http://www.ams.org/news-for-students/. It seems to have a lot of interesting articles to browse that give a sense as to what is going on in the math world, and also information about career opportunities in mathematics. |
| 2009-08-06 0930: | The New York Times has an article this morning, For Today’s Graduate, Just One Word: Statistics. The article highlights the increased demand for statisticians in industry because of the enormous amounts of digital data that need to be analyzed. The reporter, Steve Lohr, says that new Ph.D. statisticians can earn $125,000 starting salary at top companies. He also says: "Though at the fore, statisticians are only a small part of an army of experts using modern statistical techniques for data analysis. Computing and numerical skills, experts say, matter far more than degrees. So the new data sleuths come from backgrounds like economics, computer science and mathematics." |
| 2009-08-01 1900: | I finally did something I've wanted to do for years: learn the proof of the famous continued fraction formula for e (the base of the natural logarithms). I've written a sketch of the proof, based on an outline I found in a book by a Reed College professor of mine, Joe Roberts. |
| 2009-07-20 1800: | On the 40th anniversary of the moon landing, I couldn't help mentioning to my students what my reactions were to that event, as a 9-year-old child. It might have been the space race that made me interested in science, and eventually lead me to my career in science. But the 1960s were a tremendously optimistic era in science and technology, and that affected me a lot. I told my class about waiting in a long line at the Smithsonian to see a moon rock. It was displayed in a cylindrical glass case, and looked like a piece of concrete held by three gold prongs. I also mentioned seeing an exhibit on lasers at the Smithsonian (I think in 1970), that had various colors of beams of laser light bouncing off various optics, and holograms—the latter was particularly amazing (long before every credit card had a hologram on it). (Lasers were invented in 1960, not so long before that exhibit.) There's been various articles in the media about how NASA's plans for building a manned outpost on the Moon, or manned missions to Mars, were frustrated. In that sense, it would appear that people were too optimistic in the 1960s about the future of science and technology. But this morning I read an article somewhere on Wikipedia about the first microprocessor—which made personal computers possible. This was the Intel 4004 microprocessor. I was impressed that it appeared in 1972, more than two years after the moon landing. No one needs to be reminded how tremendously important personal computer technology has been in transforming our economy and society. So while some of the things predicted in 1969 still have not come to pass, the optimism in the 1960s about science has certainly been vindicated. |
| 2009-07-14 1330: | The author of the calculus book we have been using at IU Southeast, James Stewart, has apparently made a good deal of money as a textbook author: He has built a $24 million dollar house, called the "Integral House," said to be one of the most important architectural projects of recent years. Stewart happens to be a violinist, and his house incorporates a performance hall. The Wall Street Journal has an interesting article about Stewart and his house, An Accordian of Wood and Glass. The MAA web site has an interview with Stewart (where I found the link to the article). |
| 2009-06-30 1430: | Here is a nice example of a "second-derivative" economics story, that appeared today: the new Case-Shiller real estate index numbers. (This index tracks how house prices are changing in 20 major cities, by tracking sales of existing homes.) It turns out that the 20-city composite index is still dropping but not as rapidly as several months ago. This was reported as a positive sign in the MSNBC story, Home prices fall, but trend is easing. (However, the article does warn: "But rising foreclosures fueled by layoffs could derail a meaningful turnaround. The number of homeowners at least two months behind or in foreclosure jumped in the first quarter from the previous quarter, a Treasury Department report said Tuesday.") |
| 2009-06-24 1345: | The New York Times has an article by Louis Uchitelle, Despite Recession, High Demand for Skilled Labor, that reports: "In only four of the categories [listed on Monster.com] — architecture and engineering, the physical sciences, computer and mathematical science, and health care — were the unemployed equal to or fewer than the listed job openings." |
| 2009-06-24 1330: | I
ran across an interesting little bit of calculus on a unusual blog this
morning. The blog,
News from 1930, tracks business news from 1930 so present-day
readers can compare the current recession with the Great Depression as
it began in 1930. In a page
explaining what the blog is about, the author offers a rather disturbing
observation:
In histories of the Depression the leaders of the time are commonly portrayed as oblivious to what was going on, do-nothing, and stupidly optimistic. For example, every schoolkid has seen the much ridiculed pronouncement by Herbert Hoover that "prosperity is just around the corner." Even from my limited reading so far it's clear this criticism is mostly unfair. It appears that the people in charge at the time were well aware of what was happening, and did most of the things that we're doing now to alleviate it (with a couple of notable exceptions). And as for unjustified optimism, we will see that at least in mid-1930 there was a fair amount of good news coming out about the economy. And I mean actual good news where things were improving month-to-month, not the asinine stories we see today where bad numbers are interpreted as good because they were "better than expected," and declining numbers are called good because the rate of decline is slowing down (AKA second derivative stories). But notice the last sentence, with its
mention of the second derivative. The author is saying that the news is
reporting that the second derivative is positive, which means that the
rate of decrease of certain economics numbers is not as large as before.
But the first derivative is still negative—economics numbers are still decreasing. E.g., last month, the economy lost
345,000 jobs instead of the 600,000+ jobs it was losing every month last
winter; but jobs are still being lost. The author's point is that
the economy is still in decline regardless as to the spin put on the
news. |
Blog archives: Spring 2009.
