Brie Finegold summarizes blogs on mathematical sculptures made from office supplies; bubbles; and election fraud.
"Mathematical Sculpture Made Out of Office Supplies," Huffington Post, 26 December 2011.
Paper clips have more in common with mathematics than their ability to hold together pages of homework. Zachary Abel, a second year mathematics graduate student at MIT, uses paper clips, hair bands, playing cards, and lollipop sticks to build geometric sculptures. His shapes have caught the attention of editors at Huffington Post, and while the article is short, the pictures are striking. Abel's research focuses on connections between geometry and theoretical computer science according to his web page.
"Measuring Churov’s Beard: The Mathematics Of Russian Election Fraud," by Anatoly Karlin. Sublime Oblivion, 26 December 2011 and "La loi normale de Gauss's invite dans les manifs," by Etienne Ghys. Images des Mathematiques, 12 December 2011.
While you may know that mathematical methods are used to detect election fraud, it is still surprising to see Russian protesters carrying signs bearing mathematical graphics accompanied by catchy phrases like "You can't fool Gauss" and "We believe Gauss, we don't believe Churov". In case you are not familiar, Vladimir Churov is a physicist and head of the Central Elections Commission of Russia. Churov's beard refers to the unusual tail on the distribution describing United Russia's election results during the most recent election held on December 4th. The unusual shape of the distribution points to election fraud. But it is unclear just how fraudulent the election was and whether the results were actually skewed. In his blog, Sublime Oblivion, Mr. Karlin gives a detailed analysis of the situation according to a variety of models which estimate the fraud at anywhere from 5-15%. Mr. Karlin, who has also written for Al Jazeera, also discusses other possible cases of fraud in Israel and the Ukraine. Dr. Ghys, a French mathematician, focuses more on the novelty of mathematical ideas opposing up on protest signs. In either case, this episode is one that might really catch the attention of your next set of statistics students.
"When Bubbles Get Comfortable," by Robert Krulwich. Krulwich Wonders Blog, National Public Radio, 19 December 2011.
A mesmerizing videos of dye being poured into a collection of bubbles made blogger Robert Krulwich wonder why bubbles lose their round nature when smashed together. An informal conversation between the author and Manu Prakash, an assistant professor at Stanford, brings to light soap bubbles' affinity for the number three and includes some very nice photos. While some commentators rank the information presented at a fifth grade level, it is still quite pleasing in its format.
--- Brie Finegold
"Ramanujan's birthday will be National Mathematics Day," by C. Jaishankar. The Hindu, 27 December 2011, and "Manmohan's concern over decline in quality of maths teachers," by K. Venkataramanan. The Hindu, 27 December 2011.
On the occasion of inaugurating the Ramanujan Centre for Higher Mathematics at the Alagappa University, Prime Minister Manmohan Singh "emphasised the need to carry forward the legacy of great mathematicians such as Srinivasa Ramanujan, Aryabhata and Brahmagupta so as to encourage and nurture the glorious tradition of the country in mathematics. [He] said mathematics had been widely used in the study of Science and other disciplines," writes Jaishankar in the Hindu. After recounting the many contributions of Ramanujan, the Prime Minister declared Ramanujan's birthday (December 22) as National Mathematics Day every year and declared 2012 as the National Mathematical Year. The article by Venkataramanan reports that "Human Resource Development Minister Kapil Sibal, who is also the chair of the national committee that is organising the celebrations, quoted from the correspondence between Ramanujan and Cambridge mathematician G.H. Hardy, in which Ramanujan admits to not having a conventional university education and describes himself as a "half-starving man." The correspondence demonstrated the fact that it was not necessary to follow a regular university course to realise one's genius and that there were discoveries to be made beyond formal education. It also showed that students should be encouraged to strike a new path for themselves and that [quoting Sibal] "the genius in many of our young minds may never be recognised because of extreme poverty."
--- Annette Emerson
"On the Six-Cornered Snowflake," by Philip Ball. Nature, 22/29 December 2011, page 455.
Four hundred years ago, Johannes Kepler gave his memorably-named friend Matthaus Wackher von Wackenfels an unusual New Year's Eve present. Instead of a hat, a noisemaker, or a drink, he gave him a 24-page meditation on the provenance of the hexagonal shapes of snowflakes. In his 400th-anniversary book review, Philip Ball traces the influences on and of Kepler's missive. Dating from a turning point in intellectual history, when the Neoplatonic conception of a world geometrically ordered according to God's design was giving way to a nascent mechanistic understanding of natural phenomena, Kepler's account wavers between the two viewpoints. First conjecturing that the hexagonal forms are the result of the way in which "the smallest natural unit of a liquid like water" must be packed together, and going on to ruminate on how similar structures might give crystals their facets, Kepler finally falls back on the conclusion that God must have imbued water vapor with a "formative reason" which causes it to seek the most aesthetic forms. As for those influences, the investigations of Kepler's contemporary, mathematician Thomas Harriot, into sphere packing inspired Kepler's famous conjecture that the hexagonal packing is the "tightest possible"--a conjecture finally proven (by mathematician Thomas C. Hales) only in 1998. Kepler's notion that packings of particles give rise to crystal structures can be traced to the seminal texts of crystallography, and Alan Mackay's seminal paper on quasicrystals is named for Kepler's treatise: "On the Five-Cornered Snowflake," a precipitate which, unlike Kepler's abundant snowflakes, remains theoretical. Oh, and the story of the snowflake's regularities was finally told in the 1980s: it turns out the "formative reason" governing them is the way branching instabilities are shaped by the crystal structure of ice.
(Image: "Snowflake Model 2," by David Griffeath, University of Wisconsin-Madison, and Janko Gravner, University of California, Davis. See more of their work on the Mathematical Imagery page.)
--- Ben Polletta
"Colleges Mine Data to Tailor Students' Experience," by Marc Parry. Chronicle of Higher Education, 16 December 2011, pages A1-A4.
In this article, Parry describes some examples of the ways that college teachers and administrators are mining student data to "forecast student success--in admissions, advising, teaching, and more." For example, last spring, Austin Peay State University, in Clarksville, TN, began using software "that recommends courses based on a student's major, academic record, and how similar students fared in that class." Next spring, they will be offering a tool that students can use to pick a major. Or consider the company ConnectEDU, which aspires to make the college application process obsolete by matching colleges and high-school students via their online platform. Parry reports that, "So far, 2.5 million high-school students have ConnectEDU profiles," enabling the software to suggest specific colleges or programs to each of these students and, conversely, providing colleges with prospective student data--minus their individual names and addresses.
A Harvard physics classroom is the location of a third example of the use of data mining by colleges. The software system, known as Learning Catalytics, automatically pairs students who have different answers to problems; the students then try to defend their answers to each other. Based upon the data so far, this technique appears to significantly improve students' learning.
--- Claudia Clark
Media coverage of study about the "gender gap" in mathematics:
"Anything Boys Can Do...," by Sharon Begley. Scientific American, January 2012, page 25
"Researchers Probe 'Myths' Around Mathematics Gap," by Sarah D. Sparks. Inside School Research, a blog on Education Week, 12 December 2011;
"'Gender Gap' is Cultural, Not Biological," by Jennifer Welsh. MSNBC, 12 December 2011;
"Girls are no worse than boys at maths," Daily Mail, 12 December 2011;
"Studie widerlegt Mythen über Mädchen und Mathematik" [Study refutes myths about girls and mathematics]," by Holger Dambeck. Der Spiegel, 13 December 2011;
"There really is no difference between men and women's math abilities," by Alasdair Wilkins. i09.com, 12 December 2011;
"Girls Are Good At Math, New Study Claims," by Ann Brenoff. Huffington Post, 13 December 2011;
"Study: Gender gap in math is a myth Cultural, social factors may predict whether someone good at math," by Stephanie Siek. CNN blog In America, 13 December 2011.
This is a sampling of the worldwide coverage of a new study about the "gender gap" in mathematics, which appeared in the January 2012 issue of the Notices of the AMS. The article, "Debunking Myths about Gender and Mathematics Performance," by Jonathan M. Kane and Janet E. Mertz, examines mathematical performance of boys and girls in 86 countries. One of the findings is that, in some countries, there is no gender gap in mathematics: Boys and girls perform equally well. In other countries, notably the United States, the gender gap has narrowed considerably in recent years, a finding that undermines arguments that the gender gap is biological. Kane and Mertz found that in countries with a high level of gender equity in terms of income, education, health, and political participation, the gender gap was smaller and both boys and girls tended to do well in mathematics. "We found that boys--as well as girls--tend to do better in math when raised in countries where females have better equality," Kane was quoted as saying. "It makes sense that when women are well-educated and earn a good income, the math scores of their children of both genders benefit."
--- Allyn Jackson
"Sir Isaac Newton's own annotated Principia Mathematica goes online," by Stephen Bates. The Guardian, 11 December 2011.
Cambridge University rarely displays Newton's annotated copy of the Principia Mathematica because the aged text is in a fragile state, which starkly limits public access to the important work containing Newton's initial undertakings on calculus. Not for long, however. The University is putting the book, which includes Newton's own marginal notes, onto the internet as part of a program to load original works by famous scientists onto the internet. The digitized text will also show the marginal notes of Thomas Pellet, a colleague Newton's family asked to review the material after his death. Interestingly, several of the pages Pellet marked "unfit to print" now receive significant attention, and may have been marked as such in an attempt to stifle Newton's religious views. Cambridge also plans to digitize Newton's work in devising a more accurate sea navigation system, as well as the notebook he carried while the University was closed during the Plague.
--- Lisa DeKeukelaere
"A food pyramid made of cookies," by Carolyn Y. Johnson. Boston Globe, 11 December 2011.
While you might think this article is about cooking-show contestants creating over-the-top desserts to be graded by nit-picking judges, in fact it is about how an interest in the science of cooking lead Harvard University applied mathematician Michael Brenner and computer science graduate student Elaine Angelino to apply materials science ideas to edible materials. Brenner and Angelino created a 3-dimensional map of thousands of recipes of 8 different types of baked goods, including chocolate cakes, brownies, and pancakes. As you can see, the map is in the shape of a tetrahedron, with each vertex representing one of four ingredients: flour, eggs, sugar, or liquid. The location of a recipe on any one face of the tetrahedron depends upon the ratio of the three ingredients represented by the vertices. For example, the most centrally-located recipes on the face with vertices representing flour, sugar, and eggs are of angel food cakes. On the other hand, recipes for loaves tend to cluster around the flour vertex on all 4 faces.
The project has received attention from a range of audiences, including culinary professionals and other scientists. Perhaps this map will inspire you to create an over-the-top dessert or two.
(Image: courtesy of Elaine Angelino and Michael Brenner .)
--- Claudia Clark
"Key mathematical tool sees first advance in 24 years," by Jacob Aron. New Scientist, 9 December 2001.
This article reports on an improvement in a standard algorithm used to multiply matrices. A matrix is simply an array of numbers. The numbers might, for example, be measurements of 5 parameters collected from a set of 5 sensors; the measurements could then be arranged into a 5 by 5 matrix. It is possible to perform arithmetic operations on matrices, and in particular one can multiply them. Because matrix multiplication is used in all kinds of calculations in science and engineering, finding efficient algorithms to perform it has been an important goal. The most obvious algorithm for multiplying matrices of size n by n requires n^{3} steps. An algorithm discovered in 1969 can do the job in n^{2.807} steps. This seemingly small reduction in the exponent meant a considerable savings. A 1987 algorithm reduced the exponent yet further, and there progress stalled for 24 years. This year Virginia Vassilevska-Williams tweaked the 1987 algorithm and knocked the exponent down to 2.373. "Although today's computers can't take advantage of this specific speed advance, Vassilevska-Williams has also created a mathematical framework that could allow for further theoretical improvements that might be practically useful for computing," the article says.
--- Allyn Jackson
"Mandelbrot Beats Economics in Fathoming Markets: Mark Buchanan," by Mark Buchanan. Bloomberg Business Week, 6 December 2011.
For decades, economists have believed that financial markets always tend toward an equilibrium, and therefore large market swings would be rare anomalies. In reality, however, physicists inspired by the work of mathematician Benoît Mandelbrot carefully plotted hundreds of millions of price data points from more than a decade to reveal that large movements occur much more frequently than the equilibrium theory would suggest, and with a specific probability relative to the size of the shift. This finding demonstrates an inherent pattern in "abnormal" events, and is a step toward developing a credible economic theory of markets. Pulling further on the mathematical thread, a new theory not based on equilibrium could also help explain why financial market movements appear to behave similarly to natural phenomena such as earthquakes, including the occurrence of "clusters" of events.
--- Lisa DeKeukelaere
"Good Morning. You’re Nobel Laureates," by Jeff Sommer. New York Times, 4 December 2011.
This in-depth profile of this year's Nobel laureates in economics highlights the mathematical nature of their work and their training. The prize is for the study of cause and effect in macroeconomics - how government policy and the economy influence each other - and the two laureates, Christopher Sims and Thomas Sargent, have worked independently on this question. Sims studied mathematics at Harvard, and wrote an undergraduate thesis on information theory before doing graduate work in economics. To study the relationship between monetary reserves and economic productivity, he developed a technique known as vector autoregression, which captures (linear) dependencies between multiple time series, and can be used to infer the direction of causality between them. Sargent was inspired by Sims' work to teach himself the mathematics required to understand it and take it further, and continued to sit in on higher-level math courses after becoming a tenured professor. Sargent's work has been in developing the theory of rational expectation, which introduced the idea that individuals' expectations about the future affect their economic decisions, and has been used to predict how government policies affect the economy, and vice versa. Both economists readily admit that their work - and macroeconomics as a discipline - has flaws, something many would readily agree with. And while their work, and especially the theory of rational expectation, is sometimes claimed to support conservative economic policies, both agree that government has a role to play in the economy, and stand behind many of the recent policies of both the Fed and the Obama administration. Neither man, however, is very political. As Sargent puts it, his most important work is "in the beautiful language of math ... I'm pointing out the constraints and the possibilities."
--- Ben Polletta
Math on New Scientist TV. Various dates.
New Scientist TV combines short articles with short videos to produce vivid illustrations of intriguing math and physics topics. Postings in December 2011 and January 2012 featured dramatic and instructive mathematical videos of Jos Leys, a Belgian video artist with a strong mathematical bent. (Aficionados of the AMS Feature Column will recall the November 2006 column by Leys and mathematician Étienne Ghys, "Lorenz and Modular Flows: A Visual Introduction", which uses Leys's sensational graphics to explain some quite deep mathematics.)
--- Allyn Jackson
"Fluid Dynamics in a Cup," by Charles Q. Choi. Scientific American, December 2011, page 22.
At a math conference, Rouslan Krechetnikov observed attendees carrying cups of coffee and wondered why the coffee spilled some times but not others. He and a graduate student analyzed video of people carrying coffee cups and found that once people got to their desired walking speed, cup motions consisted of "large, regular oscillations caused by walking, as well as smaller, irregular and more frequent motions caused by fluctuations from stride to stride." Outside factors, such as irregularities in the floor, can also play a role. Krechetnikov also found that the two types of oscillations can reinforce one another and increase the amplitude of sloshing. Read the abstract of his results, which were presented at the 64th Annual Meeting of the American Physical Society Division of Fluid Dynamics in late November.
--- Mike Breen
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