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"Comment: Value judgements," by George Szpiro. Nature, 29 August 2013, pages 521-523.
It began 300 years ago with an intriguing problem sent by Swiss mathematician Nikolaus Bernoulli to French mathematician Pierre Rémond de Montmort. "If person A promises to give person B one coin if he throws six points on his first toss of a die, two coins if he gets six on the second throw, four coins if he gets six on the third, eight on the fourth, and so on, then what can B expect to get?" Over a period of 25 years, a simplified version of the problem--tossing a die became flipping a coin--drew the attention of a few other mathematicians, including Nicolaus' younger cousin, Daniel, who would eventually solve what is known as the "St Petersburg paradox." Daniel's solution would incorporate the idea that "the value of an item must not be based on its price, but rather on the utility it yields." Szipro continues: "Instead of multiplying the potential gains of a lottery with the probabilities of their occurrence, [Daniel] argued, it is the utility of each possible gain that must be multiplied by its probability. He suggested the logarithmic function as an indicator of the utility of wealth." The author goes on to describe the consequences of the resulting function--known as the "utility function"--on the field of economic theory.
--- Claudia Clark
"Davidson prof uses mime to explain complex math, science concepts to students – and adults," by Reid Creager. Charlotte Observer, 25 August 2013.
Mathematician Tim Chartier and his wife, Tanya, use mime "to help illustrate and simplify complex math concepts." The Chartiers have studied with renowned Marcel Marceau, and combine mime with mathematics in "Mime-matics" performances that entertain and inform both kids and adults who may not like--or do well in--math. They've performed at school assemblies, summer camps, colleges, and special meetings. Chartier tells the reporter, "It’s all about showing that math has real-world applications for all of us. It can be interesting and even fun." The couple can customize the performance depending on the audience--which has also included mathematicians at a national meeting. (Photo of Tim Chartier courtesy of Davidson College.)
--- Annette Emerson
"Edward Frenkel and a Love for Math," by Alexandra Wolfe. The Wall Street Journal, 24 August 2013.
What a world we live in! Danica McKellar, child actress turned textbook author, writes books about math for girls; and Edward Frenkel, math professor turned auteur, makes movies about girls for mathematicians. Frenkel, a self-described sentimental Russian, studies the geometric Langlands program from his position as professor at UC Berkeley. In this WSJ profile---accompanied by a dramatically lit photo of Frenkel that vaguely evokes Rod Stewart in the '80s---the professor shares some of his life story, his opinions on the perception of mathematics in American culture, and his efforts to bring math to the masses. These are many and various: in addition to his hot-off-the-presses memoir/introduction to the Langlands program "Love and Math," Frenkel has contributed articles and op-eds to Slate, The Wall Street Journal, and Scientific American; written, produced, co-directed, and starred in the film The Rites of Love and Math; and co-written a screenplay, "The Two-Body Problem," which is a kind of mathematical Sideways set in the south of France. Love and Math shares the story of how Frenkel's passion for mathematics triumphed over institutionalized anti-Semitism in the USSR, leading him to Harvard and eventually to Berkeley, while introducing the reader to the beauty of Kac-Moody algebras. Of the G.H. Hardy school of math appreciation, Frenkel believes that math is a "great connector," uniting cultures across time. Getting the American public talking about mathematics will be key to maintaining democracy in an increasingly technological world, he says: "where there is no mathematics, there is no freedom." To keep math from becoming the private plaything of the 1%, he believes in instituting universal standards like the Common Core, while piquing the public's interest in the subject by placing it alongside other adult subjects like art, music, sex, passion, romance, and love. After all, he notes sentimentally, "everyone loves love." [Note: Love and Math is reviewed by Marcus du Sautoy in Nature, 3 October 2013, page 36.]
--- Ben Polletta
"Should Math Really Be a Required Subject,” by Shaunacy Ferro. Popular Science, 19 August 2013.
In this article, Ferro discusses a recent several-page article in Harper's Magazine in which novelist and writer Nicholson Baker speaks out against today's high school math requirements, many of which he identifies as relics of the Cold War. He argues that since many educators have identified algebra as the major academic reason for students leaving school, eliminating this requirement would lower dropout rates. He points to some math teachers who agree that less math should be required for the average student. For example, Cornell University mathematician Steven Strogatz, with whom Baker spoke, expressed his concern for not just the lack of learning but the suffering he has seen some students experience in math classes. Strogatz stressed the need for more meaningful math: "We spend a lot of time avalanching students with answers to things that they wouldn’t think of asking." Baker suggests that “we should…create a new, one-year teaser course for ninth graders, which would briefly cover a few techniques of algebraic manipulation, some mind stretching geometric proofs, some nifty things about parabolas and conic sections, and even perhaps a soft-core hint of the infinitesimal, change-explaining powers of calculus."
--- Claudia Clark
"Danica McKellar poses $1 million math challenge," segment with Danica McKellar and Jordan Ellensburg. Today Show, 15 August 2013.
In this frenetic and amusing clip from (the) Today (show), Danica McKellar and Jordan Ellenberg do their best to announce Andrew Beal's million-dollar conjecture, plug McKellar's newest book ("Girls Get Curves: Geometry Takes Shape"), and put hosts Kathie Lee Gifford and Hoda Kotb through their mathematical paces, all in three minutes. Hoda introduces McKellar and Ellenberg as "math geniuses"--the seemingly obligatory term for anyone with post-secondary mathematics education--and makes a noise of disgust on pronouncing that Ellenberg is a professor of mathematics at UW Madison, while Kathie Lee, confused by the idea of a math genius teaching anywhere else, insists that Ellenberg is really at Harvard. McKellar, a frequent Today guest, then takes a moment to spread her message that, as Hoda puts it, "girls need to know math." Her four books on math for girls--which cover pre-algebra through high school geometry, and hopefully will continue on to calculus for girls, group theory for girls, and analytic number theory with inter-universal Teichmuller theory for girls--are intended, McKellar says, "to make math fun and take the scary out of math." But hold on just a minute, KLG and Hoda wonder, isn't the pair of geniuses in fact "naturally good at it"? No, the geniuses protest, "every girl" and "every person" can learn the subject well, and, in fact, "we're all doing math all the time." McKellar next does her best to state Beal's conjecture, with appropriate references to her books, but there's no need to get into the details-- "it'll be on our website, so you can try to solve it," says Hoda. The assembled then rush onward into a brief tournament of math problems, for which Ellenberg is "the math coach on site." Kathie Lee correctly answers the first problem ("If you're driving 80 miles an hour, how many minutes will it take you to drive 80 miles?"), and then triumphantly exclaims "I hate this!" But it's Hoda who eventually takes home the gold by finding a pattern in the answers--all of which are 60 (which happens to be Kathie Lee's age this year). "I love this game," she summarizes. It's an eye-rolling good time for all.
--- Ben Polletta
"Mathematical Impressions: Making Music with a Möbius Strip," by George Hart and Quanta. Scientific American, 14 August 2013.
Using paper and a bagel, George Hart demonstrates in a simple, amusing video how to construct the geometric spaces corresponding to musical chords. Starting with the basics of pitch as frequency and musical notes as discretization of pitches, similar to the number line of integers, Hart advances to a two-dimensional graph with musical notes on the x and y axes to demonstrate the concept and various types of two-note chords. Hart first explains how to visualize the chords as both a flat plane and a torus (enter the bagel), and then shows that aligning the notes within each pitch class (e.g. all A's, all B’s, etc.) requires folding, which results in a Möbius strip in which each point represents a possible chord and the edges are the unison chords (e.g. two C's). Hart’s visual demonstrations with simple pen and paper, in addition to three-dimensional computer modeling graphics and an appropriate soundtrack of musical chords, make the concept of musical chords as geometric spaces quick and easy to understand.
--- Lisa DeKeukelaere
"Cowboys are Hoping Practice + math = Playoffs," by Kevin Clark. The Wall Street Journal, 12 August 2013.
To improve their offense, Dallas Cowboy wide receivers and quarterbacks are being quizzed on basic geometry concepts—such as the Pythagorean Theorem and colinearity—by their head coach, Jason Garrett. "Once they grasp the concept, [wide receiver Anthony] Armstrong said, receivers can better understand how they're attacking different spots on the field and adjust their stride accordingly. Quarterbacks, of course, need to better understand how wide-receiver routes work together in concert on a given play. Giving them teaching points about angles will help simplify the quest to find holes in defense, said veteran backup quarterback Kyle Orton." Garrett is not the first coach to apply mathematics to designing offensive strategies, but he may be requiring players to understand more of the mathematics behind the concepts than other coaches. Clark notes that wideout Cole Beasly finds Garrett's lessons "a gift compared with the monotony of most football meetings, which typically offer the same tired teaching points over and over again." However, Beasly admits that "he and his teammates aren't math geniuses and haven't yet grasped all the concepts." File this under "When am I ever going to use this [math concept]?"
--- Claudia Clark
"The birthday problem: what are the odds of sharing b-days?," by Adrian Dudek. The Conversation, 12 August 2013.
Adrian Dudek, a mathematics Ph.D. candidate at Australian National University, explores the odds of sharing a birthday. Dudek first illustrates step-by-step how to answer the question "How many people do you have to put into a room before you are guaranteed that at least two of them share a birthday?" using what mathematicians call the 'pigeon hole principle'. Adrian writes in a very academic yet easy-to-follow style, making the answer a fun read. He next tackles the question "How many people do you have to put into a room before you have a more than 50% chance that at least two of them share a birthday?" The correct answer is surprisingly small--just 23 people--and Dudek explains in a manner that everyone can understand just how the probabilities are calculated.
--- Baldur Hedinsson
"Central Texas professor brings expertise to Shark Week," by Katherine Stolp. KEYE-TV, 7 August 2013.
The CBS affiliated news station KEYE-TV aired a 'cover story' about how a complex mathematical algorithm originally developed catch serial criminals, is now being used to predict the hunting habits of great white sharks. The method, developed by Texas State Professor Kim Rossmo, is known as geographic profiling. It was originally used as a tool to catch serial criminals by narrowing the search of a suspect's home to a small range of possible locations and is currently used by the FBI, Scotland Yard and even the U.S. Military to find terrorist headquarters. Professor Kim Rossmo appeared on Shark Week on the Discovery Channel, describing how his algorithm is leading to a greater understanding of how and where these large predators hunt. "It's all about understanding their hunting behavior, the predator/prey relationship and their eco-systems," Rossmo said. "There's a specific site they kept returning to, sort of an optimal site in which they started their hunt for seals." Rossmo determined that the return of sharks to this specific site is not based on the greatest likelihood of capturing seals, but on a balance among prey detection, capture rates and competition.
--- Baldur Hedinsson
"One shape to rule them all!," by Burkard Polster and Marty Ross. The Age, 5 August 2013.
Columnists Burkard Polster and Marty Ross explore the mighty geometric form of the cube and how it relates to the other four shapes that comprise the "regular solids" – tetrahedrons, octahedrons, icosahedrons, and dodecahedrons. Starting with a standard soccer ball as an example, the columnists explain, with helpful pictures, how shapes that initially appear to be non-cube-like actually contain at least one, if not several, cubic forms. More generally, the columnists also use pictures to illustrate how a tetrahedron (a four-sided figure composed of equilateral triangles) or an octahedron (an eight-sided figure composed of equilateral triangles) can be viewed as contained within a cube, and, similarly, how an icosahedron (a 20-sided figure composed of equilateral triangles) or a dodecahedron (a 12-sided figure composed of pentagons) can be formed using a cube as a building block.
--- Lisa DeKeukelaere
"What Would You Ask? A Dozen Fantasy Questions for the New SAT." The New York Times, 2 August 2013, Education Life page 25.
In this supplement, various educators each write a question that they'd like to see on the SAT or ACT. David Bressoud of Macalester College (and former MAA president) leads off (at least in the hard-copy version) with a question on conditional probability, specifically about false positives connected with a blood test. Bressoud also gives an explanation of the answer and notes that although students entering college should understand conditional probability, they usually don't. So even though Bressoud gives five choices for the answer to his question, it's likely to stump most entering freshmen.
--- Mike Breen
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