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12:02 AM | “Explore Mathematics: Part II”

I felt like my first venture into “Explore Mathematics!” was so successful last quarter with my Advanced Precalculus kids that I wanted to build upon that. So this is what I’m doing for “Explore Mathematics!: Part II” Students scoured the web and did 5 different mini-explorations which exposed them to all the neat math that exists […]

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11:30 PM | On This Day in Math - April 25

Pure mathematics is the world's best game. It is more absorbing than chess,more of a gamble than poker,and lasts longer than Monopoly. It's free. It can be played anywhere - Archimedes did it in a bathtub.~Richard J. Trudeau, Dots and LinesThe 115th day of the year; 115 is the 26th "Lucky" number. Lucky numbers are produced by a sieve method created by Stan Ulam around 1955. The term was introduced in 1955 in a paper by Gardiner, Lazarus, Metropolis and Ulam. They suggest also calling its […]

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11:15 PM | The Amplituhedron – Now In Poster Form!

Recently there’s been a lot of excitement about the amplituhedron. This wacky new object might just revolutionize our understanding of particle scattering. To help you get your head round it, here’s a poster I made for an outreach competition. Click for the full size JPEG file. If you want a hard copy to impress your […]

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intothecontinuum:
There is something special about rotations of 137.5 degrees.
This is an attempt at replicating Seeds by Jared Tarbell of Levitated and Complexification.
Mathematica code:
d[x_, y_, r_, c_, s_, F_, n_] := {Disk[ RotationTransform[n*2.4][{x*c^n, y}], r*c^n], Table[ {White, Disk[ RotationTransform[k*2 Pi/F, RotationTransform[n*2.4][{x*c^n, y}]] [RotationTransform[n*2.4][{x*c^n, y}] + c^n {r - s, 0}], s*c^n]}, {k, 0, F - 1, 1}]}Manipulate[ ImageCrop[
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11:01 PM | Parametric/Projectile Motion Simulated in Desmos - A Common Core Activity for Algebra/Precalculus

The Desmos activity above is both an investigation of parametric representation and a tutorial for more advanced use of this remarkable WebApp. The The text in the side frames begins with a detailed background of the activity for the instructor and how Desmos can be used to demonstrate projectile motion using both parametric and rectangular coordinates. Some of the uses of slider 'variables' are demonstrated including animation, a powerful feature of Desmos.In addition to showing how to […]

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10:51 PM | Our First Real 3-Act

We tried our first real 3-Act on Monday with Jeff's fourth graders. Motivated by issues of perimeter and scale (which I blogged about here), and a great post by Matt Jones over at The Math Lab @ Rm 27, we started out with this photo:Lots of excitement! First we asked the kids if they knew what they were looking at. We were surprised that so many of them knew right away that it was a photo of our school. In order to orient them, we identified some features together and […]

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This one-day workshop will bring together teachers and administrators to explore Michigan’s new Balanced Assessment system slated for implementation next school year. The Smarter Balanced assessments will be part of our new Balanced Assessment system. Smarter Balanced summative assessments will be used for federal accountability. But, Smarter Balanced offers more than just the required summative assessments. Come explore the additional tools and resources that are being released for use
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10:23 PM | A proof of Roth’s theorem

Roth’s theorem on arithmetic progressions asserts that every subset of the integers of positive upper density contains infinitely many arithmetic progressions of length three. There are many versions and variants of this theorem. Here is one of them: Theorem 1 (Roth’s theorem) Let be a compact abelian group, with Haar probability measure , which is […]

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10:14 PM | AISTATS 2014 [no day #2]

Even though the talks yesterday morning at AISTATS 2014 (day #2) were of the same high quality as the other days, I “had” to skip them to drive my daughter to the airport. Originally, the flight was planned at 7:40, which would have given me plenty of time to get back for Andrew’s talk at […]

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9:27 PM | Foster Parenting, A Teachers Perspective

Had a student in foster care? Heard about parents abusing the system on the news? Generally curious about the process? Great! Continue reading. (There aren't any instructions if you answered no to all of those questions. What's that joke about there being two type of people? Those who can extrapolate from incomplete data and...)I decided that I'm settled enough to finally do what I've been expecting/planning to do since my brother was born - become a parent. I bought a condo with extra space,
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9:25 PM | 25 Aprile

Giova ricordarlo, agli apprendisti stregoni la cui presunzione è inferiore solo alla loro ignoranza."Se voi volete andare in pellegrinaggio nel luogo dove è nata la nostra Costituzione, andate sulle montagne dove caddero i partigiani, nelle carceri dove furono imprigionati, nei campi dove furono impiccati. Dovunque è morto un italiano per riscattare la libertà e la dignità, andate lì, o giovani col pensiero, perché lì è nata la nostra Costituzione."(Piero Calamandrei)Viva il 25 aprile! […]

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9:13 PM | INFORMS Connect Launching in May

One of the projects that has been keeping me busy is getting INFORMS Connect, our latest member benefit, ready for launch. It is a members-only online collaboration space.

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9:08 PM | Environmental impact of power lines

This is to simply document my observation which I've been mulling over for a long time until very recently.
A couple of streets that I daily drive over are lined with trees whose branches seem to exhibit strange growth pattern. While their older branches point unremarkably each other way, the younger ones sprout pretty much verticallyEnvironmental impact of power lines is a post from: CTK Insights

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8:52 PM | Milk Cap Magic Squares

Ready for some fun? Grab a copy of Ben Franklin and His Magic Squares to read aloud. Stop reading after it says, "Now Ben wondered if he could make the numbers [1-9, in a square] add up to 15..."Give each student a set of 9 milk caps (I don't EVER throw them away!) to number, 1-9.Challenge them to make a 3 x 3 array in which every row, column, and diagonal totals 15.If they think they've found the answer, have them scurry off to write it down! (And hide it from everyone else!)Stop periodically […]

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8:21 PM | Great Tasks: Infinity Pizza

Connie Schrock and I recently presented a webinar on Great Tasks: What is a “great task”? How is a great task used effectively in the classroom? Published by the National Council of Supervisors of Mathematics (NCSM) with support from Texas Instruments, NCSM Great Tasks for Mathematics 6-12 provides opportunities for students to explore meaningful mathematics […]

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Jovana Helms just sent me the following:Hi Igor, I am looking for a graduate summer intern with CS background to help on a research project at Sandia National Labs in Livermore, CA. Could you please post the position on Nuit Blanche? Please note that US citizenship is required for this position. https://ws11snlntz.sandia.gov/psp/applicant/EMPLOYEE/HRMS/c/HRS_HRAM.HRS_CE.GBL?Page=HRS_CE_JOB_DTL&Action=A&JobOpeningId=646028&SiteId=1&PostingSeq=1 Thanks,JovanaJovana
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6:54 PM | Fantastic math word problems

Here's a weird/funny/fantastic math problem... But it also kind of highlights the word problems we often see in math books - like some have noted, it's only in math classes that trains travel towards each other on the same track, or someone buys 61 watermelons for himself, or people paint houses at identical speeds all day long, etc. All kinds of unrealistic situations.But, being a curriculum author myself, I know it's hard to make problems that would always perfectly relate to real life. In […]

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6:50 PM | MFM2P - Days 47 & 48

Day 47This will be a short post. We did the last example from the solving by substitution set and then students worked on the review package I put together to prepare for Monday's test. I worked with them in small groups and answered individual questions. Trig is still what they have the most trouble remembering. But they do get it once they are pointed in the right direction. Still, I think I need to do more next time around.Day 48I'm cheating and posting for tomorrow but half of my class will
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From head injury to math genius: On savant syndrome and the possibility of a 'little Rain Man within us all': Victoria Lambert:
For Jason, a father-of-one from Tacoma, in Washington State, the effect of his injury was remarkable, very rare — and strangely fortunate. From college drop-out with a dodgy hair cut — interested in little more than drinking, racing cars and going to the gym — Jason, now 43, woke up the day after he was attacked with an extraordinary ability in mathematics and
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5:35 PM | Commenting on the Blog

Should be working again! Thanks for everyone's patience while we've been having problems with Typepad.

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5:18 PM | skyndimynd frá Íslandi (#3)

Filed under: Kids, Mountains, pictures, Travel Tagged: AISTATS 2014, Arnarstapi, cliffs, Iceland, Snaefell, volcanoes

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In recent years, formal and empirical approaches have become central to study group decision-making. Social network analysis, agent-based modeling and simulation techniques are meanwhile widely used not only in sociology, political science, social psychology, and economics. Also philosophers increasingly point to the potentials of these approaches for addressing questions in political and moral philosophy, formal epistemology, and philosophy of science more generally. Whereas the importance of […]

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4:50 PM | Detailed Map of Baseball Fandom

For the past couple of sports seasons, Facebook mapped the most liked team by county. They did it for football …

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Originally posted on Math Online Tom Circle:Shimura and Tanyama are two Japanese mathematicians first put up the conjecture in 1955, later the French mathematician André Weil re-discovered it in 1967. The British Andrew Wiles proved the conjecture and used…

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4:36 PM | Falling into a black hole: tidal forces

Reference: Moore, Thomas A., A General Relativity Workbook, University Science Books (2013) – Chapter 19; Problem P19.9. Using the Riemann tensor, we can get an idea of the force felt by someone falling into a black hole. Recall the original definition of the Riemann tensor was in terms of the equation of geodesic deviation: where […]

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4:12 PM | The Quick Way To Become A Physicist

So you want to become a physicist, right? Problem is you don’t know much physics. Maybe you did some in high school. You might even have read a few physics blogs. But despite your enthusiasm, the road to the research frontier looks perilously long! But I reckon it can be hiked in less than a […]

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Reference: Moore, Thomas A., A General Relativity Workbook, University Science Books (2013) – Chapter 19; Problem P19.8. The component of a four-vector along a basis vector is given by the dot product of the four-vector with the basis vector. Since the dot product is a scalar, it can be computed in any reference frame. In […]

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A group of authors in China has retracted their December 2013 paper in PLoS ONE after realizing that they’d been studying the wrong cells. The paper, “Up-Regulation of pVHL along with Down-Regulation of HIF-1α by NDRG2 Expression Attenuates Proliferation and Invasion in Renal Cancer Cells,” came from Lei Gao, of the Fourth Military Medical University, […]

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A large chunk of machine learning (although not all of it) is concerned with predictive modeling, usually in the form of designing an algorithm that takes in some data set and returns an algorithm (or sometimes, a description of an algorithm) for making predictions based on future data. In terminology more friendly to the philosophy […]

Bailey, D., Borwein, J., de Prado, M.L. & Zhu, Q. (2014). Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance, Notices of the American Mathematical Society, 61 (5) 458. DOI: 10.1090/noti1105

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Here the monotonicity of the EM algorithm is established. $$ f_{o}(Y_{o}|\theta)=f_{o,m}(Y_{o},Y_{m}|\theta)/f_{m|o}(Y_{m}|Y_{o},\theta)$$ $$ \log L_{o}(\theta)=\log L_{o,m}(\theta)-\log f_{m|o}(Y_{m}|Y_{o},\theta) \label{eq:loglikelihood} $$ where \( L_{o}(\theta)\) is the likelihood under the observed data and \(L_{o,m}(\theta)\) is the likelihood under the complete data. Taking the expectation of the second line with respect to the conditional distribution of
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Ruslan R Salakhutdinov, Sam T Roweis & Zoubin Ghahramani (2012). On the Convergence of Bound Optimization Algorithms, arXiv, arXiv: 1212.2490v1

Wu C.F.J. (1983). On the Convergence Properties of the EM Algorithm, The Annals of Statistics, 11 (1) 95-103. DOI: 10.1214/aos/1176346060

McLachlan G. & Peel D. DOI: 10.1002/0471721182

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by @ulaulaman about #exoplanets #planetary_transit #kepler_mission #nasa #astronomy The search for extrasolar planets (or exoplanets) had its first success in 1991 with the discovery of some planets orbiting around the pulsar PSR1257+12(1, 2, 3), measuring the variations of the radio pulses coming from the star. The second important milestone in exoplanet research takes place in 1995, with the discovery around the star 51 Pegasi (a star like our Sun) of a Jupiter-like planet, found at a […]

Wolszczan, A. & Frail, D. (1992). A planetary system around the millisecond pulsar PSR1257 + 12, Nature, 355 (6356) 145-147. DOI: 10.1038/355145a0

Wolszczan, A. (1994). Confirmation of Earth-Mass Planets Orbiting the Millisecond Pulsar PSR B1257 + 12, Science, 264 (5158) 538-542. DOI: 10.1126/science.264.5158.538

Mayor, M. & Queloz, D. (1995). A Jupiter-mass companion to a solar-type star, Nature, 378 (6555) 355-359. DOI: 10.1038/378355a0

Borucki, W., Koch, D., Basri, G., Batalha, N., Brown, T., Caldwell, D., Caldwell, J., Christensen-Dalsgaard, J., Cochran, W., DeVore, E. & Dunham, E. (2010). Kepler Planet-Detection Mission: Introduction and First Results, Science, 327 (5968) 977-980. DOI: 10.1126/science.1185402

Lissauer, J., Fabrycky, D., Ford, E., Borucki, W., Fressin, F., Marcy, G., Orosz, J., Rowe, J., Torres, G., Welsh, W. & Batalha, N. (2011). A closely packed system of low-mass, low-density planets transiting Kepler-11, Nature, 470 (7332) 53-58. DOI: 10.1038/nature09760

George, S. (2011). Extrasolar planets in the classroom, Physics Education, 46 (4) 403-406. DOI: 10.1088/0031-9120/46/4/004

LoPresto, M. & McKay, R. (2005). An introductory physics exercise using real extrasolar planet data, Physics Education, 40 (1) 46-50. DOI: 10.1088/0031-9120/40/1/003

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Non voglio fare concorrenza alla splendida spiegazione di Amedeo o a quella tecnica di Corrado, ma mia sorella, leggendo il post di pancia scritto nella sera dell'annuncio di BICEP2, ha candidamente confessato di non aver capito cosa era accaduto quel giorno. E allora proviamoci, a raccontarlo. (da The Cartoon History of the Universe #1 di Larry Gonick)C'era una volta un'idea di universo, che era la Terra al centro, quindi il Sole, la Luna e gli altri pianeti e sullo sfondo le stelle fisse,
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Hubble E. (1929). A relation between distance and radial velocity among extra-galactic nebulae, Proceedings of the National Academy of Sciences, 15 (3) 168-173. DOI: 10.1073/pnas.15.3.168

Gamow G. (1948). The Evolution of the Universe, Nature, 162 (4122) 680-682. DOI: 10.1038/162680a0

Alpher R.A. & Herman R. (1948). Evolution of the Universe, Nature, 162 (4124) 774-775. DOI: 10.1038/162774b0

Alpher R., Bethe H. & Gamow G. (1948). The Origin of Chemical Elements, Physical Review, 73 (7) 803-804. DOI: 10.1103/PhysRev.73.803

Peebles P.J.E., Schramm D.N., Turner E.L. & Kron R.G. (1994). The Evolution of the Universe, Scientific American, 271 (4) 52-57. DOI: 10.1038/scientificamerican1094-52

McLeish T.C.B., Bower R.G., Tanner B.K., Smithson H.E., Panti C., Lewis N. & Gasper G.E.M. (2014). History: A medieval multiverse, Nature, 507 (7491) 161-163. DOI: 10.1038/507161a

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Much of my undergrad was spent studying physics, and although I still think that a physics background is great for a theorists in any field, there are some downsides. For example, I used to make jokes like: “soft isn’t the opposite of hard sciences, easy is.” Thankfully, over the years I have started to slowly […]

Lazer, D., Kennedy, R., King, G. & Vespignani, A. (2014). Big data. The parable of Google Flu: traps in big data analysis., Science, 343 (6176) 1203-1205. PMID: 24626916

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mathhombre tweeted: @mathhombre

RT @mpershan: @TracyZager My wife is a first year 4th grade teacher. She's learning a ton about teaching math from teaching through TERC.

2014-04-25 01:34:52

mathhombre tweeted: @mathhombre

2014-04-25 01:30:27

wpgaurav tweeted: @wpgaurav

My mobile number is a prime number http://t.co/tL3aULPD99 http://t.co/IyNR9kszGI

2014-04-25 01:30:13

mathhombre tweeted: @mathhombre

MT @samjshah "Explore Math: Part II" which I just devised and emailed my kids about today > http://t.co/nUWlrGrVpU cc @MrsGallasMath

2014-04-25 01:30:09

freakonometrics tweeted: @freakonometrics

"Take a trip through Kowloon Walled City, once the densest place on earth" http://t.co/wIChbBJyqy see http://t.co/JbyLzRAl2X via @WSJAsia

2014-04-25 01:07:36

MrHonner tweeted: @MrHonner

RT @JohnAllenPaulos: Amazing! RT @pickover Shiver in ecstasy. Expression connects Pi, e, radicals, factorials, and infinite limits. http://…

2014-04-25 00:58:58

simonjob tweeted: @simonjob

RT @merryfwilliams: Anyone have a box & whisker foldable to share? #TooTiredToReinventWheelTonight

2014-04-25 00:37:36

mathfour tweeted: @mathfour

I told @KateCrowder I didn't want a whole glass of water. Only half. She knew contextually that it meant some part. #4yo #earlymathfun

2014-04-25 00:31:26

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