Happy Tau Day! τ (2 × π, that is, 6.28...) is the number of radians in a turn. Translating the digits to notes even makes beautiful music. (By comparison, what pi sounds like). Previously.
92 years young, the delightful Raymond Smullyan is a mathematician, logician, magician, concert pianist, and Taoist philosopher - who also pioneered retrograde chess problems.
Microsoft Mathematics is a free Computer Algebra System (CAS) available from Microsoft. A CAS is a program that can solve purely symbolic mathematical equations. For example, the program can tell you that the derivative of 6x^2 + 12x is 12x + 12. The program has functions for calculus, statistics, linear algebra, and graphing. One interesting feature of the program is that in some cases it can show and describe the intermediate steps involved in solving an equation. Here’s a 16 page tutorial (in MS Word docx format) showing how to use the program. The program can be downloaded from the Microsoft download page. Thirty-two and sixty-four bit versions are available. The program only works on XP/Vista/Windows 7.
"Value-added modeling is promoted because it has the right pedigree -- because it is based on "sophisticated mathematics." As a consequence, mathematics that ought to be used to illuminate ends up being used to intimidate." John Ewing, president of Math for America and former executive director of the American Mathematical Society, criticizes the "value-added modeling" approach used as a proxy for teacher quality, most famously in a Los Angeles Times story that called out low-scoring teachers by name. A Brookings Institution paper says value-added modeling is flawed but the best measure we have of teacher value, arguing that the metric's wide fluctuations from year to year are no worse than those of batting averages in baseball. (Though the weakness of that correlation is mostly a BABIP issue.) Can we assign a numerical value to teacher quality? If so, how?
Vortex-based mathematics is the most advanced ever known to mankind. Don't have time for a time cube? Time need no longer limit us. Here, Marco Rodin (inventor of the Rodin Coil) gives us the background.
The annual Melbourne University Puzzle Hunt is back - and this time they need your help fending off villians with your puzzle-solving abilities. Anyone from anywhere in the world can compete in teams of 1 to 10 people (or you can see the puzzles for yourself and play at home). [more inside]
Following in the footsteps of prestigious publications like the Annals of Improbable Research, NCBI ROFL, Rejecta Mathematica, the Journal of Universal Rejection, and the Journal of Unpublished Results, comes the Journal of Are You Fucking Kidding. Previous, previously, and previouslier. h/t to Retraction Watch
The J programming language is kind of like a super calculator (it’s been described as executable mathematical notation). It was developed by Ken Iverson and Roger Hui and is a successor to APL (and there’s no need to buy a new keyboard). The language is free and open source, and works on Windows, Mac, and Linux. A series of books and articles on using J are also available to download. To whet your appetite, here’s an article on using J to find the eighth ten-digit prime number that appears among the digits of pi.
So you're me and you're in math class and you're learning about graph theory, a subject too interesting to be included in most grade school's curricula so maybe you're in some special program or maybe you're in college and were somehow not scarred for life by your grade school math teachers. [more inside]
New math theories reveal the nature of numbers [1,2] - "We prove that partition numbers are 'fractal' for every prime. These numbers, in a way we make precise, are self-similar in a shocking way. Our 'zooming' procedure resolves several open conjectures, and it will change how mathematicians study partitions." (/.|via) [more inside]
Let's say you're me and you're in math class, and you're supposed to be learning about factoring. Trouble is, your teacher is too busy trying to convince you that factoring is a useful skill for the average person to know with real-world applications ranging from passing your state exams all the way to getting a higher SAT score and unfortunately does not have the time to show you why factoring is actually interesting. It's perfectly reasonable for you to get bored in this situation. So like any reasonable person, you start doodling.[more inside]
In today's example of kids smarter than you and I, Wired follows the exploits of two teens competing at the International Olympiad in Informatics.
A Brief History of Mathematics is a BBC series of ten fifteen-minute podcasts by Professor Marcus du Sautoy about the history of mathematics from Newton and Leibniz to Nicolas Bourbaki, the pseudonym of a group of French 20th Century mathematicians. Among those covered by Professor du Sautoy are Euler, Fourier and Poincaré. The podcasts also include short interviews with people such as Brian Eno and Roger Penrose.
Logical literacy is an awareness and understanding of the metalanguage in which propositions, conjectures, lemmas and theorems are written.
Futurama has always been a haven for geek humor, but last week's episode "The Prisoner of Benda" pushed things to the next level. First hinted at in an American Physical Society interview with showrunner David X. Cohen (previously), staff writer and mathematics Ph.D. Ken Keeler devised a novel mathematical proof based on group theory to resolve the logic puzzle spawned by the episode's brain-swapping (but no backsies!) conceit. Curious how it works? Read the proof (in the show or in plain text), then see it in action using this handy chart. Too much math for a lazy Sunday? Then entertain your brain with lengthy clips from the episode -- including two of the funniest moments in the series in the span of two minutes.
The 300th issue of This Week's Finds in Mathematical Physics will be the last. It is not an exaggeration to say that when John Baez started publishing TWF in 1993, he invented the science blog, and an (academic) generation has now grown up reading his thoughts on higher category theory, zeta functions, quantum gravity, crazy pictures of roots of polynomials, science fiction, and everything else that can loosely be called either "mathematical" or "physics." Baez continues to blog actively at n-category cafe and the associated nLab (an intriguingly fermented commune of mathematicians, physicists, and philosophers.) He is now starting a new blog, Azimuth, "centered around the theme of what scientists can do to help save the planet."
I am pleased to announce a proof that P is not equal to NP. In this paper, Vinay Deolalikar (HP Labs) proposes a proof to answer the most important problem in its field of mathematics. [more inside]
Editors of the pop-culture magazine Wired provided the title "iPhone 4’s ‘Retina’ Display Claims Are False Marketing" to a highly critical article about the new iPhone's high-resolution "Retina" display, so-called as the human eye cannot resolve individual pixels when viewing it. A technician who worked on the Hubble telescope disagreed with the Wired editors' choice of rhetoric in very strong technical terms and issued less stringent disagreement with Raymond Soneira, the writer of the piece. Neuroscientist and photographer Bryan Jones published his own highly readable technical analysis of the display's pixel arrangement, that helped him decide whether Apple's claims were truthful or not.
The great[pdf] Russian mathematican Vladimir Igorevich Arnol'd, foremost modern practitioner of classical mechanics, influential teacher, namesake of a minor planet, and semi-nude cross-country skier has died.
"Gary Foshee, a collector and designer of puzzles from Issaquah near Seattle walked to the lectern to present his talk. It consisted of the following three sentences: "I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"" [more inside]
Plus magazine has compiled all their articles on mathematics and the arts into one handy-dandy page full of highly enjoyable articles ranging from limericks and screeching violins to the restoration of frescoes.
Dan Meyer is a high school math teacher with a clever idea: make math about the real world. On his blog, he writes about classroom management, the real skills of teaching, labels, information design, and assessment.
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.
Mathematician Barbara Shipman speculates that a honey bee's sense of the quantum world could be as important to their perception of the world as sight, sound or smell: "the mathematics implies that bees are doing something with quarks."
Every number from 1 to 9,999 has a special meaning. (much mathematical terminology, scrolling)
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.
Does a group of indigenous South Americans hold the key to our relationship with maths? Still, I thought it odd that numbers larger than five did not crop up at all in Amazonian daily life. What if you ask a Munduruku with six children how many kids they have? "He will say, 'I don't know,'" Pica said. "It is impossible to express."
Grigori Perelman has refused one million dollars from the Clay Mathematics Institute for his solution to the Poincaré conjecture. Despite some pressure to take the money and give it to one party or another, Perelman insists "I am not a hero of mathematics. I am not successful at all, and I do not want to be observed by everyone." Perelman previously refused the Fields Medal, mathematics' highest honor. (Previously.)
Nature by Numbers is a new animated short film by Cristóbal Vila (previously) inspired by some mathematical constructs found in nature. (via)
The Shannon number? Skewes' number? Graham's number? Please. When you're ready to get serious, here are some truly large numbers. (previously, but with dead links)
Found Functions. An elegant demonstration of beauty in mathematics (and landscape). Nikki Graziano is a math and photography student at Rochester Institute of Technology; some of her photographs were recently featured in Wired. Graziano "overlays graphs and their corresponding equations onto her carefully composed photos. ... Graziano doesn’t go out looking for a specific function but lets one find her instead. Once she’s got an image she likes, Graziano whips up the numbers and tweaks the function until the graph it describes aligns perfectly with the photograph."
"Back in 1993 I was tutoring my sister in algebra. Her quizzes and tests were always made of word problems with a running storyline involving many recurring places and characters. I tied the fate of the main characters to how well she did on the previous quiz, so a good performance brought them good fortune. Unfortunately, one test she completely bombed, and, well, this is a transcription of the quiz she got next." [more inside]
The Unreasonable Effectiveness of Mathematics in the Natural Sciences is a 1960 essay by Eugene Wigner. Via Steve Strogatz.
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]
The Calculus Lifesaver lectures -- videos available here in streaming (Real Player), mp4 and wmv formats -- were originally given as "review sessions for the Princeton introductory calculus courses MAT103 and MAT104 during the 2006/7 academic year". Each lecture is about 2 hours.
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.
Alice's adventures in algebra: Wonderland solved "Outgunned in the specialist press, Dodgson took his mathematics to his fiction. Using a technique familiar from Euclid's proofs, reductio ad absurdum, he picked apart the "semi-logic" of the new abstract mathematics, mocking its weakness by taking these premises to their logical conclusions, with mad results. The outcome is Alice's Adventures in Wonderland."
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 Anatomy of Spiral Arms, shows how galaxies naturally evolve to form grand-design two-arm spirals. The Hubble Ultra Deep Field in 3D. [more inside]