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Desmos | Beautiful, Free Math
"Our mission is to help every student learn math and love learning math. We accomplish that goal by building products and partnerships. First, we built our best-in-class HTML5 Desmos graphing calculator, which millions of students around the world use for free, including students who are blind or visually-impaired. Our partners have also embedded the calculator in digital curricula and on digital assessments so students spend less time worrying about technology and more time thinking about math. More recently, we've built hundreds of digital activities, covering grades 6-12 and expanding quickly to other areas of math. Those activities take advantage of everything that makes computers special. They invite students to create their own mathematical ideas, rather than just consuming ours. They encourage students to share their creations with each other, rather than with a grading algorithm. We distribute those activities for free on our website and through partnerships with curriculum publishers."
mathematics  education  pedagogy  online  tool 
4 weeks ago by tsuomela
MPSOpenData
"Funded by the National Science Foundation, this workshop series will generate discipline-specific responses from the Mathematical and Physical Sciences research communities to the federal policy requiring open data and the recently-released NSF policy statement on open data. In order to decide how and what to preserve for public consumption, and in what manner the data will be stored and accessed, a series of dialogues is required. Discussions within individual disciplines must reach a consensus on data preservation procedures and data access guidelines consistent with discipline-specific expectations for data re-use, access policies, and the level of burden implied by conservation that is placed on the individual investigator."
open-data  open-research  mathematics  science  physical  workshops  report 
september 2017 by tsuomela
The Paradox of the Proof | Project Wordsworth
"On August 31, 2012, Japanese mathematician Shinichi Mochizuki posted four papers on the Internet. The titles were inscrutable. The volume was daunting: 512 pages in total. The claim was audacious: he said he had proved the ABC Conjecture, a famed, beguilingly simple number theory problem that had stumped mathematicians for decades. Then Mochizuki walked away. He did not send his work to the Annals of Mathematics. Nor did he leave a message on any of the online forums frequented by mathematicians around the world. He just posted the papers, and waited."
mathematics  proof  warrant  community  peer-review  sociology  fame  prestige 
may 2013 by tsuomela
Yitang Zhang Proves 'Landmark' Theorem in Distribution of Prime Numbers | Simons Foundation
"On April 17, a paper arrived in the inbox of Annals of Mathematics, one of the discipline’s preeminent journals. Written by a mathematician virtually unknown to the experts in his field — a 50-something lecturer at the University of New Hampshire named Yitang Zhang — the paper claimed to have taken a huge step forward in understanding one of mathematics’ oldest problems, the twin primes conjecture. Editors of prominent mathematics journals are used to fielding grandiose claims from obscure authors, but this paper was different. Written with crystalline clarity and a total command of the topic’s current state of the art, it was evidently a serious piece of work, and the Annals editors decided to put it on the fast track."
mathematics  proof  warrant  community  peer-review  sociology  fame  prestige 
may 2013 by tsuomela
[1304.3480] Friendship Paradox Redux: Your Friends Are More Interesting Than You
"Feld's friendship paradox states that "your friends have more friends than you, on average." This paradox arises because extremely popular people, despite being rare, are overrepresented when averaging over friends. Using a sample of the Twitter firehose, we confirm that the friendship paradox holds for >98% of Twitter users. Because of the directed nature of the follower graph on Twitter, we are further able to confirm more detailed forms of the friendship paradox: everyone you follow or who follows you has more friends and followers than you. This is likely caused by a correlation we demonstrate between Twitter activity, number of friends, and number of followers. In addition, we discover two new paradoxes: the virality paradox that states "your friends receive more viral content than you, on average," and the activity paradox, which states "your friends are more active than you, on average." The latter paradox is important in regulating online communication. It may result in users having difficulty maintaining optimal incoming information rates, because following additional users causes the volume of incoming tweets to increase super-linearly. While users may compensate for increased information flow by increasing their own activity, users become information overloaded when they receive more information than they are able or willing to process. We compare the average size of cascades that are sent and received by overloaded and underloaded users. And we show that overloaded users post and receive larger cascades and they are poor detector of small cascades."
social-networks  friendship  connection  community  twitter  mathematics 
april 2013 by tsuomela
Bonacich, P. and Lu, P.: Introduction to Mathematical Sociology.
"Mathematical models and computer simulations of complex social systems have become everyday tools in sociology. Yet until now, students had no up-to-date textbook from which to learn these techniques. Introduction to Mathematical Sociology fills this gap, providing undergraduates with a comprehensive, self-contained primer on the mathematical tools and applications that sociologists use to understand social behavior."
sociology  mathematics  modeling 
march 2013 by tsuomela
Math journal accepts computer-generated nonsense paper - Boing Boing
"This is a nice follow-on from the Sokal hoax, wherein a humanities journal was tricked into accepting a nonsense paper on postmodernism. Goes to show that an inability to distinguish nonsense from scholarship exists in both of the two cultures."
hoax  mathematics  two-cultures 
october 2012 by tsuomela
Nutonian Inc.
We develop advanced scientific data mining technologies that uncover deep mathematical relationships hidden in your data. Whether your goal is deeper insight, better prediction, or faster optimization, formulize your data to discover its underlying hidden patterns.
science  mathematics  modeling  statistics  regression  software  cloud  windows 
june 2012 by tsuomela
EYH Home - Expanding Your Horizons
Expanding Your Horizons in Science and Mathematics™ conferences nurture girls' interest in science and math courses to encourage them to consider careers in science, technology, engineering, and math
science  mathematics  feminism  gender  STEM  education 
may 2012 by tsuomela
Stephen Pinker is a member of the intellectual elite « Quomodocumque
Is lack of statistics education really the pressing problem for higher education?

"Go around saying “Society can get along fine without the study of literature” and you’re a hard-nosed realist willing to make tough choices in hard times. Try it with “Society can get along fine without scientists and engineers” and you’re laughed out of town."
via:cshalizi  innumeracy  statistics  humanities  two-cultures  intellectuals  history  mathematics  education  elites 
october 2011 by tsuomela
Economics Debunked: Chapter Two for Sixth Graders « naked capitalism
"That means one way to figure out whether mainstream economics makes sense is to see what the assumptions are, and to try to decide whether those assumptions make sense. For example, what were Samuelson’s assumptions? What were Arrow and Debreu’s assumptions?

Samuelson had one big assumption, that economists call ergodicity.

[Teacher pauses to give kids time to stumble over the word.]

When they say ergodicity, they mean that no matter what happens in the world, in the end, everything will reach a point whether things stop changing. That point is called the “equilibrium.” At the equilibrium, everyone will end up with a certain amount of money. The amount of money that everybody gets at the equilibrium depends on how talented they are, and not on anything that happened before. So if you rob a bank, it won’t matter because when you get to the equilibrium, if you’re stupid, you will still have the same amount of money you would have had if you didn’t rob the bank."
economics  history  story  mathematics  modeling  scientism  sts 
september 2011 by tsuomela
Economics Debunked: Chapter Two for Sixth Graders « naked capitalism
"That means one way to figure out whether mainstream economics makes sense is to see what the assumptions are, and to try to decide whether those assumptions make sense. For example, what were Samuelson’s assumptions? What were Arrow and Debreu’s assumptions?

Samuelson had one big assumption, that economists call ergodicity.

[Teacher pauses to give kids time to stumble over the word.]

When they say ergodicity, they mean that no matter what happens in the world, in the end, everything will reach a point whether things stop changing. That point is called the “equilibrium.” At the equilibrium, everyone will end up with a certain amount of money. The amount of money that everybody gets at the equilibrium depends on how talented they are, and not on anything that happened before. So if you rob a bank, it won’t matter because when you get to the equilibrium, if you’re stupid, you will still have the same amount of money you would have had if you didn’t rob the bank."
economics  history  story  mathematics  modeling  scientism  sts 
september 2011 by tsuomela
The Tyranny of Scales - PhilSci-Archive
"This paper examines a fundamental problem in applied mathematics. How can one model the behavior of materials that display radically different, dominant behaviors at different length scales. Although we have good models for material behaviors at small and large scales, it is often hard to relate these scale-based models to one another."
philosophy  mathematics  modeling  scale  via:cshalizi 
july 2011 by tsuomela
Quantum computing for the determined | Michael Nielsen
"I’ve posted to YouTube a series of 22 short videos giving an introduction to quantum computing. Here’s the first video:

Below I list the remaining 21 videos, which cover subjects including the basic model of quantum computing, entanglement, superdense coding, and quantum teleportation.

To work through the videos you need to be comfortable with basic linear algebra, and with assimilating new mathematical terminology. If you’re not, working through the videos will be arduous at best! Apart from that background, the main prerequisite is determination, and the willingness to work more than once over material you don’t fully understand."
video  quantum  computing  science  education  mathematics  physics  open-access 
june 2011 by tsuomela
The Second Pass
Review of On Growth and Form by D'Arcy Thompson
book  review  evolution  mathematics  history  sts  science 
june 2011 by tsuomela
Mathematical Platonism | Philosophy Now
If one ‘goes Platonic’ with math, one has to face several important philosophical consequences, perhaps the major one being that the notion of physicalism goes out the window.
philosophy  mathematics  objects  metaphysics  physical 
june 2011 by tsuomela
News: 'Loving and Hating Mathematics' - Inside Higher Ed
"A new book, Loving and Hating Mathematics: Challenging the Myths of Mathematical Life (Princeton University Press) takes a look at some of the most common (mis)conceptions about mathematics and mathematicians, addressing their origins and assessing their truth value in a somewhat unexpected fashion. Rather than amassing data on PISA and SAT scores, analyzing the race and gender breakdowns of degrees awarded or tenure and promotion rates, or perhaps administering Enneagram tests to math majors, authors Reuben Hersh and Vera John-Steiner focus on the lives and experiences of mathematicians, past and present."
book  interview  mathematics  education  learning  pedagogy  calculus 
may 2011 by tsuomela
Study Hacks » Blog Archive » On Becoming a Math Whiz: My Advice to a New MIT Student
"But this isn’t about natural aptitude, it’s about practice. That other student has more practice. You can catch-up, but you have to put in the hours, which brings me back to my original advice: keep working even after you get stuck.

That’s where you make up ground."
talent  success  school  academic  mathematics  practice  deliberate 
may 2011 by tsuomela
M-Phi
blog dedicated to mathematical philosophy.
weblog-group  philosophy  mathematics 
april 2011 by tsuomela
David Bressoud's Launchings
"One point of agreement between us is that a singular view of high school mathematics as preparation for calculus has created serious problems. This is particularly damaging when combined with the belief that, if at all possible, students must get through calculus while still in high school, and if they cannot get through it, then, at the least, they have to learn its tricks before they get to college. "
mathematics  education  curriculum  algebra  calculus  STEM  high-school  college 
march 2011 by tsuomela
Endless Algebra—the Deadly Pathway from High School Mathematics to College Mathematics
"I constantly ask myself two questions: (1) Are we really offering our secondary students an appropriate mathematics experience? (2) What can we do to provide students with relevant, coherent mathematical options on the pathway throughout high school and as they move into college? Or to put it another way: (1) Is the “layer cake” of algebra-dominated mathematics that pervades our U.S. secondary schools still relevant? (2) Is calculus the be-all and end-all goal for the preparation of students for a successful transition to college? My answer is, I think not."
mathematics  education  curriculum  algebra  calculus  STEM  high-school  college 
march 2011 by tsuomela
A frequentist interpretation of probability for model-based inductive inference
"The main objective of the paper is to propose a frequentist interpretation of probability in the context of model-based induction, anchored on the Strong Law of Large Numbers (SLLN) and justifiable on empirical grounds."
statistics  probability  frequentist  interpretation  mathematics  via:cshalizi 
march 2011 by tsuomela
PLoS ONE: Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities
" Typically, linear per capita indicators are used to characterize and rank cities. However, these implicitly ignore the fundamental role of nonlinear agglomeration integral to the life history of cities. As such, per capita indicators conflate general nonlinear effects, common to all cities, with local dynamics, specific to each city, failing to provide direct measures of the impact of local events and policy. Agglomeration nonlinearities are explicitly manifested by the superlinear power law scaling of most urban socioeconomic indicators with population size, all with similar exponents (1.15). As a result larger cities are disproportionally the centers of innovation, wealth and crime, all to approximately the same degree. We use these general urban laws to develop new urban metrics that disentangle dynamics at different scales and provide true measures of local urban performance. "
cities  urban  economics  statistics  powerlaw  growth  model  mathematics  econometrics  research  complexity 
january 2011 by tsuomela
Outstanding, Superlinear Cities - Science News
"In an article this month in PLoS ONE, Bettencourt and his team created a way to measure how exceptional cities are by comparing their characteristics with what mathematics would predict for their size. The team then ranked the exceptionality of 300 U.S. cities based on personal incomes, gross metropolitan product (GMP), number of patents and number of violent crimes. "
cities  urban  economics  statistics  econometrics  mathematics  model  growth  powerlaw 
january 2011 by tsuomela
What's stats got to do with it? - Expression Patterns Blog | Nature Publishing Group
"I realized I wasn't scared of stats: just bored and annoyed and wondering, indeed, what they had to do with various things. Keeping track of lots of data makes for pretty graphs and useful trends. Those kinds of stats are cool. But statistical analysis of data doesn't always make sense to the people using it. Not just because it's complicated, but because it's not always informative of what they're looking at. It has to make sense in context. You have to be able to actually answer the question "what's stats go to do with it?", and not just use it rhetorically like I did in most of this post. "
statistics  mathematics  graphs  data  understanding  significance 
january 2011 by tsuomela
Verbal vs. mathematical aptitude in academics | Gene Expression | Discover Magazine
"- Philosophers are the smartest humanists, physicists the smartest scientists, economists the smartest social scientists."
testing  graduate-school  gre  standard  verbal  mathematics 
december 2010 by tsuomela
The Philosopher's Stone: MARX'S ECONOMICS IN MODERN DRESS
In the thirty years or so after Sraffa's little book appeared, an extraordinary world-wide theoretical discussion arose among well-trained theoretical economists who were sympathetic to the classical and Marxian programme, and were disenchanted with the General Equilibrium models then all the rage.
marxism  economics  mathematics 
december 2010 by tsuomela
What correlates with problem solving skill? | Casting Out Nines
What all this suggests is that there is a stronger relationship between conceptual knowledge and mechanics, and between conceptual knowledge and problem solving skill, than there is between mechanical mastery and problem solving skill....
If this relationship holds in general — and I think that it does, and I’m not the only one — then clearly the environment most likely to teach calculus students how to be effective problem solvers is not the classroom primarily focused on computation. A healthy, interacting mixture of conceptual and mechanical work — with a primary emphasis on conceptual understanding — would seem to be what we need instead. The fact that this kind of environment stands in stark contrast to the typical calculus experience (both in the way we run our classes and the pedagogy implied in the books we choose) is something well worth considering.
education  pedagogy  mathematics  calculus 
december 2010 by tsuomela
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