Since its first printing in 1964, Abramowitz and Stegun's Handbook of Mathematical Functions has been a standard (and public domain) reference manual for special functions and applied mathematics. This week, NIST released its successor, the Digital Library of Mathematical Functions, online to the public.
If politicians were mathematicians. "I would like to suggest two systems for parliamentary votes, one that would weaken the party system but without killing it off entirely, and one that would protect large minorities. Neither has the slightest chance of being adopted, because they are both too complicated to be taken seriously. But mathematicians wouldn’t find them complicated at all — hence the title of this post." Fields medalist Tim Gowers messes around with political axioms.
A generating function is a way to keep track of a lot of related numbers all at once... The study of generating functions is an art and a science known as 'generatingfunctionology,' and its bible is free for all to download. [more inside]
Every number from 1 to 9,999 has a special meaning. (much mathematical terminology, scrolling)
Robert Hodgin's Magnetic sculptures: "These forms are created with cylinder magnets, spherical magnets, and ball bearings. Magnetism is the only thing holding the forms together. They are fairly fragile and picking them up will likely crush them. All of the forms I created were variations of the 12 sided dodecahedron. This particular platonic solid seems to be the form the magnets are happiest with." [via]
Mathematics Illuminated is a set of thirteen surveys in varied topics in mathematics, nicely produced with video, text, and interactive Flash gadgets for each of the topics.
"Crazy as it sounds, over the next several weeks I’m going to try to do something close to that. I’ll be writing about the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it." Mathematics in the pages of the New York Times! [more inside]
"Take a little bad psychology, add a dash of bad philosophy and ethics, and liberal quantities of bad logic, and any economist can prove that the demand curve for a commodity is negatively inclined." MIT economist Andrew Lo and string theorist turned asset manager Mark Mueller on the "physics envy" that plagues economics, and how to stop worrying and love uncertainty.
Trigonometric Delights. This book is neither a textbook of trigonometry—of which there are many—nor a comprehensive history of the subject, of which there is almost none. It is an attempt to present selected topics in trigonometry from a historic point of view and to show their relevance to other sciences. It grew out of my love affair with the subject, but also out of my frustration at the way it is being taught in our colleges.
Sure, big numbers are fine. But infinity (in the set theoretic sense) is where the fun really starts. Developed almost entirely by one man in the late 19th century, set theory now forms the foundation of modern mathematics. Cantor showed that not all infinite sets are the same size. Notably, while there are just as many integers as rational numbers, there are more real numbers than integers. These results, along with others that soon followed like the axiom of choice, led to several fascinating consequences: [more inside]
Everyone knows about the Six Degrees of Kevin Bacon, right? Pursuant to this authoritative source I learned of Erdos numbers, which are fascinating in their own right, but not nearly as much as Erdos-Bacon numbers. Sir Alec Guiness does surprisingly well with a 3. Bacon does not. [more inside]
There's always been hyperbole in fashion; but fashion became truly hyperbolic this week when mathematican William Thurston, winner of a 1982 Fields Medal for his revolutionary re-envisioning of low-dimensional topology and geometry, teamed up with designer Dai Fujiwara (of the house of Issey Miyake) to produce a Paris runway show based on the fundamental geometries of 3-dimensional spaces. Thurston and Fujiwara briefly interviewed. Thurston's famous essay "Proof and Progress in Mathematics" concerns, among other things, Thurston's belief that the production of mathematical understanding can be carried out by means other than the writing down of formal proofs (though fashion shows are not specifically mentioned.) Previously in wearable non-Euclidean geometry: Daina Taimina's hyperbolic skirt.
Uncoiling the spiral: Maths and hallucinations So common are these geometric hallucinations, that in the last century scientists began asking themselves if they couldn't tell us something fundamental about how our brains are wired up. And it seems that they can. (via MAPS)
Early elementary school teachers in the United States are almost exclusively female (>90%), and we provide evidence that these female teachers’ anxieties relate to girls’ math achievement via girls’ beliefs about who is good at math. A study (abstract and full-text [pdf]) by the University of Chicago Department of Psychology and Committee on Education found a link between math anxiety in elementary school teachers and their female students' math abilities. [more inside]
From 1980 - 1988, a science education series called 3-2-1 Contact ran on PBS. Produced by Children's Television Workshop, the series was geared toward an older audience than other popular CTW offerings Sesame Street and The Electric Company, and focused on teaching kids about science, math and the world around them. [more inside]
Nontransitive dice are sets of dice (A, B, C, etc.) with counterintuitive properties: die A beats die B and die B beats die C, but die C beats die A. [more inside]
The Sexaholics of Truthteller Planet - yes, it's one of those rotten logic problems, one of many that can be found at Tanya Khovanova’s Math Guide to the MIT Mystery Hunt.
Calculus of Averages - Newton and Archimedes did not possess this knowledge. No mathematics professor today can provide this knowledge and depth of understanding. Author John Gabriel maintains a blog, Friend of Wisdom, and contributes articles such as Are real numbers uncountable? to Google's Knol project.
The beauty of roots. From Dan Christensen and Sam Derbyshire via John Baez. If you like algebra: these are plots of the density in the complex plane of roots of polynomials with small integral coefficients. If you don't: these are extravagantly beautiful images produced from the simplest of mathematical procedures. Explore the image interactively here.
Chisenbop - a tool for doing simple math on your fingers, invented by Sung Jin Pai in the '40s, it uses the same principles as the abacus. Tutorial 1 and 2, and a cute kid.
A gathering of puzzles including many old chestnuts but also perhaps one or two you haven't met before.
"Center the bagel at the origin, circling the Z axis. A is the highest point above the +X axis. B is where the +Y axis enters the bagel. C is the lowest point below the -X axis. D is where the -Y axis exits the bagel."
Eminem's "Lose Yourself" re-envisioned as a high school math course. The math and film departments of Madison East High School collaborate on a video, starring math teacher Philip Galarowicz. Not to be confused with The Rappin' Mathematician (hear "The Number Line Dance" here), or these high school math rappers, or the rap battle of TI-83 and Fitty Slope. The quadratic formula, rapped. The quadratic formula, rapped again. The quadratic formula, rapped, strangely compellingly, by a teacher in a tie.
How should math be taught? The Kumon Math curriculum provides a simple and clear description of one possible sequence of skills. Hung-Hsi Wu decries the bogus dichotomy of basic skills versus conceptual understanding (PDF, Google Docs). David Klein provides a detailed history of US K-12 math education in the 20th century. The NYT describes the 2008 report of the National Mathematics Advisory Panel (full text as PDF). [more inside]
The strength of post-Soviet math stems from decades of lonely productivity. Russian math.
"Pynchon, postmodern author, is commonly said to have a non-linear narrative style. No one seems to have taken seriously the possibility, to be explored in this essay, that his narrative style might in fact be quadratic." Number theorist Michael Harris on Pynchon and conic sections.
Math Overflow is the first attempt to use the Stack Exchange platform, already popular with programmers, as a scientific research tool. Founded this month by a group of young mathematicians, including Scott Morrison and Ben Webster of the Secret Blogging Seminar, the site is already wrestling with hundreds of questions, ranging from the technical ("When is a map given by a word surjective?") to the historical ("Most interesting mathematics mistake?")
The eyeballing game: compare your best attempts at several instinctive everyday tasks - determining a point of convergence, bisecting an angle, finding the midpoint of a line - against mathematical certainty. In a more financial mood? Play Chartgame: given a random historical stock chart of an unnamed S&P 500 company, choose to buy and sell as time advances to see if you can beat the market.
42.7 percent of all statistics are made up: After Strategic Visions refused to share the methodology behind some of their polling, Nate Silver of fivethirtyeight analyzed the firm's poling results and found evidence of fraud. Strategic Visions responds to The Hill. More amusingly, Nate went on a look at an even more questionable study by the same company claiming that only 23 percent of Oklahoma students know that George Washington is the first president. [more inside]
For math geeks. How to Draw the Voronoi Diagram. Voronoi diagrams, as a geometric model are fascinating because they can be used to describe almost literally everything: from cell phone networks to radiolaria, at every scale: from quantum foam to cosmic foam. See also the Wallpaper Group: there are only 17 ways to fill a plane with a regular 2 dimensional pattern. Fred Scharmen [weblog home] is known as 765 and also produces a number of shapes, textures and patterns.
Photographer Mariana Cook has a new book of portraits of well-known mathematicians. Here's a slideshow with some interesting audio, and more of the photographs.
The Status of the P Versus NP Problem It's one of the fundamental mathematical problems of our time, and its importance grows with the rise of powerful computers. (via mr)
Figure 3. Basic model outbreak scenario. Susceptibles are quickly eradicated and zombies take over, infecting everyone.
Why bureaucracy, like gas, fills up all available space. From the archive of The Economist, 1955 [via ArchiveDigger.]
"This day may be celebrated in a variety of ways. Pause and give thought to the role that the number pi has played in your life. Imagine a world without pi. Attempt to memorise pi to as many decimal places as you can. If you're feeling creative, devise alternative values for pi. Go to a party (I will). Or just celebrate in the time-honoured fashion of ignoring Pi Approximation Day altogether."
Happy Pi Approximation Day. [more inside]
Happy Pi Approximation Day. [more inside]
The Free Will Theorem - "If there exist experimenters with (some) free will, then elementary particles also have (some) free will." (previously)
The Cornell Historical Math Monographs archive has a great many famous papers, including works by De Morgan, Hamilton, Descartes (warning: French) and of course Lewis Carroll. [more inside]
Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid has been recorded as a series of video lectures for MIT's Open Courseware project.
Theory versus Statistics, Financial Economics Edition. "You can almost here the lament of this quant that the real math theory has been dead since 1980, and that it has all been applied and statistics ever since. It’s like Fischer Black was Kool Herc and Myron Scholes was Afrika Bambaataa, and they’d all go plug in their computers into lamp posts and do martingale representations in the streets and at house parties. And, of course, it was all ruined in 1979 when it went commercial." A response to The Last Temptation of Risk by Barry Eichengreen.
Stephen Wolfram discusses Wolfram|Alpha: Computational Knowledge Engine - at the same time Google Adds Search to Public Data, viz: "Nobody really paid attention to the two hour snorecast" -- like a cross between designing for big data and a glossary of game theory terms -- on Wolfram|Alpha (previously), yet the veil is being lifted nonetheless: "[on] a platonic search engine, unearthing eternal truths that may never have been written down before," cf. hunch & cyc (and in other startup news...) [via] [more inside]
Following the recent uproar over Texas and the possibility of its secession (previously), Fivethirtyeight.com puts forward a theoretical division of Texas into five states: Plainland, Trinity, Gulfland, New Texas, and El Norte.