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# Posts

### February 27, 2015

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We’ve been working through some of the challenging proofs in chapter 9 of Art of Problem Solving’s Introduction to Geometry book. As I’ve written, my son’s been finding these proofs to be pretty difficult:   BUT – he’s staying with them and seeming to get a little more out of each one that we go…
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Mi última aportación a la Edición 6.1 es Spock y las matemáticas Un cita homenaje a Leonard Nimoy.
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The great convergence is upon us. From the following paper:The present paper demonstrates the first steps in incorporating deep learned priors into generalized linear problems such as compressed sensing.  Approximate Message Passing with Restricted Boltzmann Machine Priors by Eric W. Tramel, Angélique Drémeau, Florent Krzakala Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework […]
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Martin Handford can spend weeks creating a single Where’s Waldo puzzle hiding a tiny red and white striped character wearing Lennon glasses and a bobble hat among an ocean of cartoon figures that are immersed in amusing activities. Finding Waldo is the puzzle’s objective, so hiding him well, perhaps, is even more challenging. Martin once [...]
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This week in The Numbers, our fearless numerical explorer Jo Craven McGinty dives into sea level measurements. Her finding? Sea levels are hard to pin down. Data collection has been inconsistent. And the physics of the moving world isn't helping things.
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I posted a new video to illustrate the fractions of 7 follow a pattern which makes it possible to remember the decimal representation. If you know this pattern, then no need to read further! I always get a few complaints from people that deem a post or video to be too basic math. For example, […]
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30 new artworks by Regolino Bizzi   http://im-possible.info/english/art/various/odonodo.html#a88   Author - http://odonodo.deviantart.com/
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References: Griffiths, David J. (2007), Introduction to Electrodynamics, 3rd Edition; Pearson Education – Chapter 12, Post 14. The relativistic velocity addition formula is most easily derived from the Lorentz transformations: As usual, system is moving to the right relative to system with velocity . If an object is moving in the system with velocity , […]
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By: Samir Chopra Reading some of the discussion sparked by Peter Railton's Dewey Lecture has prompted me to write this post. In the fall of 1996, I began studying for my Ph.D qualifier exams. I had worked full-time at a non-academic job for the previous year, saving up some money...
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Here are a few links for your weekend reading: I’ve used the Monty Hall Problem in class. I didn’t realize agreeing on the correct solution was so controversial. Leonard Nimoy’s portrayal of Spock “in many ways co-created, helped define geek/nerd personality and interests for millions of future geeks” So true. Sports analytics is great and all that, but […]
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Re: Helmut Raulien Right, the “divisor of” relation signified by is a dyadic relation on the set of positive integers so it can be understood as a subset of the cartesian product   It is an example of a partial … Continue reading →
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This is about parity subgroups and the spaces that (nearly) represent them in homotopy, and … other stuff… but the working tool is Blakers+Massey, in the aspect of connectivity estimates. Here \$P \simeq \mathbb{RP}^2\$ is a mod-2 Moore space. For whatever reason, we are considering the spaces \$[P,\Sigma^a P^{\wedge b}]\$ of pointed maps (appologies, in the unlikely event that anyone following is hoping to find this notation used consistently in earlier tmblpsts. I can’t […]
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Have you every noticed that when you open a box of Smarties, there seems to be a lot of air in there? What is amount of air in each box? What percentage of each box is air? What size would the box be if there was no air? Why do they not make the box that size? How many Smarties can you actually fit in a box? What do you need to figure this out? Clearly we need some boxes of Smarties to begin collecting data.We already know how many Smarties are in each box. Now we need to […]
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There is talk in the news about Smarties boxes changing size to better reflect portion size. The new 45 g box has three compartments, each representing one portion size of 15 g. So if you have three children you only need to buy one box of Smarties which they can easily share! How many Smarties would they each get? What if you have four children? How many Smarties should they each expect to get if they share a 75 g box?There also exists a GIANT holiday box of Smarties that weighs in at 430 […]
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On a set with an operation which has a neutral element, there is an algebraic axiom which is equivalent with both associativity and commutativity of the operation. I call it the shuffle (does it have a name?). It is this one (ab)(cd) = (ac)(bd)  so the middle terms b and c switch their position. Of … Continue reading The shuffle trick, or how to eliminate commutativity and associativity, for the benefit of better self-multiplication →
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Even in this corner of the galaxy, Captain, two plus two equals four.Incluso en este rincón de la galaxia, Capitán, dos más dos es igual a cuatroSeñor SpockEsta es una cita (extraída de Aperiodical) que el Señor Spock pronuncia en el episodio La conciencia del Rey de la serie Star Trek: la serie original.En ella se pone de manifiesto que las matemáticas son universales y que independientemente del lugar en que nos encontremos, siguen siendo ciertas.Tito Eliatron DixitPD: Esta entrada es […]
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I like Math. I like how it makes me question, pull things apart, wonder deeply, think harder than I ever thought I could, feel excited about small successes, and much more. I was asked by the parent of two kids that I am tutoring, one in Algebra I and the other in Algebra II, if […]
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For those readers who understand spoken French (or simply appreciate the musicality of the language) and are interested in the history of mathematics, I warmly recommend listening to the recording of a recent programme of Radio France Internationale entitled “Pourquoi Bourbaki ?” In addition to the dialogue of Sophie Joubert with Michèle Audin and Antoine […]
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References: Griffiths, David J. (2007), Introduction to Electrodynamics, 3rd Edition; Pearson Education – Chapter 12, Post 13. Here’s a simple example of using the Lorentz transformations. Suppose that two events occur simultaneously in the Earth frame, a distance 500 km apart. An observer in a (very fast) plane travelling at along the line joining the […]
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References: Griffiths, David J. (2007), Introduction to Electrodynamics, 3rd Edition; Pearson Education – Chapter 12, Post 12. We can combine the effects of time dilation and length contraction to derive the Lorentz transformations. As usual, we align the two inertial frames and (which moves to the right at speed relative to ) so that the […]
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I wrote last year about the mini-projects I use in my “flagship” course Networks: Structure & Algorithms.  We recently finished the first of these miniprojects: rankmaniac. In rankmaniac, students have to build a system (using Amazon Elastic MapReduce) to compute the nodes of a huge web crawl that have the top 20 pageranks, and to do the […]
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For yesterday‘s winner, I’ll follow the reasoning of Manuel in comments: Popper. We would learn more from falsifying the hypothesis that Popper’s talk is boring than what we would learn from falsifying the hypothesis that Richard Pryor’s talk is uninteresting. And today we have the consensus choice for greatest writer vs. the notorious political philosopher. […] The post William Shakespeare (1) vs. Karl Marx appeared first on Statistical Modeling, Causal Inference, and […]
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I was working in Memorial Library yesterday. Whenever I’m over there, I like to pull a book off the shelf and look at it.  (E.G.) I feel I have some kind of duty to the books — there are so many which will never be taken off the shelf again! Anyway, there has never been […]
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Some years ago, at a rather posh function in a swanky London venue, I got talking to a peer of the realm. By this point I had been drinking my endless glass of wine for some time (they have stealthy waiters at these kinds of dos), and didn’t quite catch his name, but he had been, apparently, head of a large supermarket chain. And his response to me mentioning the word ‘biodiversity’ has stuck with me. “When I took over... Read more
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(Click on the comic if you can't see the full image.) (C)Copyright 2015, C. Burke.A whole branch of math grew from a nut.
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A few months ago, I asked for some input regarding your experience with photocopiers as I prepare for a session on error analysis. Thanks for all your help and input. As I continue my preparation, I asked Twitter to share three things you noticed about these three pics.With over 70 responses, the results have been fun to look at. My session is about effectively using error analysis. One small part I'm curious about is if we can make any generalizations about spotting things that seem out […]
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Here’s another installment of PubPeer Selections: Citation, schmitation: “This paper cites two papers of mine, that happen to be completely unrelated to the topic discussed, as far as I can see.” “I hope this settles; practice makes perfect, and the samples would have probably been ordered better on the gel had it was run today, […]The post PubPeer Selections: Odd citations, “practice makes perfect,” a Nature update appeared first on Retraction Watch.
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It would appear that there’s a substantial academic literature on social groupings amongst adolescents at schools. I learned about this while attending a seminar by Robert Akerlof on Social norm formation: the role of esteem. The paper considers a simplified model of social interaction between adoloscents1 in which (in a 2-player version) each player makes 3 choices: effort at 2 activities (academic achievement versus rock music), which one to value, and whether to interact with the other […]