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http://ift.tt/2EuEpd7 In Januari’s issue of the Notices of the AMS there’s a paper by Mohammad Ghomi Dürer’s Unfolding Problem for Convex Polyhedra . Here are the opening lines: “Convex polyhedra are among the oldest mathematical objects. Indeed the five platonic solids, which constitute the climax of Euclid’s books, were already known to the ancient people of Scotland some 4,000 years ago; see Figure 1.” It sure would make a good story, the (ancient) Scotts outsmarting the Greek in discovering the five Platonic solids. Sadly, the truth is different. Once again, hat tip to +David Roberts on Google+ for commenting on the AMS announcement and for linking to a post by John Baez and a couple of older posts here refuting this claim. Perhaps the most readable of the two posts is: Scottish solids, final(?) comments in which I tell the story of the original post and its aftermath. The bottom-line is this: Summarizing : the Challifour photograph is not taken at the Ashmolean

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http://ift.tt/2Fsy7tv The Bulletin of the AMS just made this paper by Julia Mueller available online: “On the genesis of Robert P. Langlands’ conjectures and his letter to Andre Weil” (hat tip +ChandanDalawat and +DavidRoberts on Google+). It recounts the story of the early years of Langlands and the first years of his mathematical career (1960-1966)leading up to his letter to Andre Weil in which he outlines his conjectures, which would become known as the Langlands program . Langlands letter to Weil is available from the IAS . The Langlands program is a vast net of conjectures. For example, it conjectures that there is a correspondence between – $n$-dimensional representations of the absolute Galois group $Gal(\overline{\mathbb{Q}}/\mathbb{Q})$, and – specific data coming from an adelic quotient-space $GL_n(\mathbb{A}_{\mathbb{Q}})/GL_n(\mathbb{Q})$. For $n=1$ this is essentially class field theory with the correspondence given by Artin’s reciprocity law . Here we hav

Students, Alumni Watch As Michigan State Tries To Restore Its Reputation The university grapples with the aftermath of the Larry Nassar sex abuse scandal that's left students, faculty, alumni and donors wondering what's next, and bracing for civil suits against the school. Read more on NPR

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In D.C., 34 Percent Of Graduates Received A Diploma Against District Policy Following the WAMU/NPR investigation into policy violations at Ballou High School, a new report shows that more than 900 students districtwide graduated against policy. Read more on NPR

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Nearly 9,000 DACA Teachers Face An Uncertain Future Classroom teachers covered by the federal immigration program could lose their jobs and face deportation unless Congress and the Trump administration reach agreement on protecting them. Read more on NPR

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http://ift.tt/2Bzv1Bz The monstrous moonshine picture is the finite piece of Conway’s Big Picture needed to understand the 171 moonshine groups associated to conjugacy classes of the monster. Last time I claimed that there were exactly 7 types of local behaviour, but I missed one. The forgotten type is centered at the number lattice $84$. Locally around it the moonshine picture looks like this \[ \xymatrix{42 \ar@{-}[dr] & 28 \frac{1}{3} \ar@[red]@{-}[d] & 41 \frac{1}{2} \ar@{-}[ld] \\ 28 \ar@[red]@{-}[r] & \color{grey}{84} \ar@[red]@{-}[r] \ar@[red]@{-}[d] \ar@{-}[rd] & 28 \frac{2}{3} \\ & 252 & 168} \] and it involves all square roots of unity ($42$, $42 \frac{1}{2}$ and $168$) and $3$-rd roots of unity ($28$, $28 \frac{1}{3}$, $28 \frac{2}{3}$ and $252$) centered at $84$. No, I’m not hallucinating, there are indeed $3$ square roots of unity and $4$ third roots of unity as they come in two families , depending on which of the two canonical forms to

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School Shootings Are Sad, But No Longer Surprising The school shooting in Kentucky that killed two students and injured 16 others was the 11th of 2018 in the U.S. NPR's Scott Simon wonders if school shootings have lost the power to shock and sober us. Read more on NPR

http://ift.tt/eA8V8J In The Da Vinci Code , Dan Brown feels he need to bring in a French cryptologist, Sophie Neveu, to explain the mystery behind this series of numbers: 13 – 3 – 2 – 21 – 1 – 1 – 8 – 5 The Fibonacci sequence , 1-1-2-3-5-8-13-21-34-55-89-144-… is such that any number in it is the sum of the two previous numbers. It is the most famous of all integral linear recursive sequences , that is, a sequence of integers \[ a = (a_0,a_1,a_2,a_3,\dots) \] such that there is a monic polynomial with integral coefficients of a certain degree $n$ \[ f(x) = x^n + b_1 x^{n-1} + b_2 x^{n-2} + \dots + b_{n-1} x + b_n \] such that for every integer $m$ we have that \[ a_{m+n} + b_1 a_{m+n-1} + b_2 a_{m+n-2} + \dots + b_{n-1} a_{m+1} + a_m = 0 \] For the Fibonacci series $F=(F_0,F_1,F_2,\dots)$, this polynomial can be taken to be $x^2-x-1$ because \[ F_{m+2} = F_{m+1}+F_m \] The set of all integral linear recursive sequences, let’s call it $\Re(\mathbb{Z})$, is a beautifu

Olympic Scandal Hits Michigan State University; DeVos Calls Students 'Unprepared' Plus, students getting their money back in bankruptcy, and more in the weekly education roundup. Read more on NPR

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Teach Students To Use Social Media (The Right Way) And The Possibilities Are Endless Social media can be a big part of students' lives, and teachers across the country are finding ways to use popular platforms as teaching tools. Read more on NPR

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http://ift.tt/eA8V8J Do we know why the monster exists and why there’s moonshine around it? The answer depends on whether or not you believe that vertex operator algebras are natural, elegant and inescapable objects. the monster Simple groups often arise from symmetries of exceptionally nice mathematical objects. The smallest of them all, $A_5$, gives us the rotation symmetries of the icosahedron . The next one, Klein’s simple group $L_2(7)$, comes from the Klein quartic . The smallest sporadic groups, the Mathieu groups , come from Steiner systems , and the Conway groups from the 24-dimensional Leech lattice . What about the largest sporadic simple, the monster $\mathbb{M}$? In his paper What is … the monster? Richard Borcherds writes (among other characterisations of $\mathbb{M}$): “3. It is the automorphism group of the monster vertex algebra . (This is probably the best answer.)” But, even Borcherds adds: “Unfortunately none of these definitions is completely sati

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http://ift.tt/eA8V8J CRANFORD, NJ – Cranford Public Schools will host a mathematics and reading information session for parents of children in kindergarten through second grade. The session will be ran by math coach Debra Shriner and literacy coach Lorraine Madden. The two will provide tips , activities, ideas and ... via Math Tips

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http://ift.tt/2Fbfjir If you take two Fischer involutions in the monster (elements of conjugacy class 2A) and multiply them, the resulting element surprisingly belongs to one of just 9 conjugacy classes: 1A,2A,2B,3A,3C,4A,4B,5A or 6A The orders of these elements are exactly the dimensions of the fundamental root for the extended $E_8$ Dynkin diagram. This is the content of John McKay’s E(8)-observation : there should be a precise relation between the nodes of the extended Dynkin diagram and these 9 conjugacy classes in such a way that the order of the class corresponds to the component of the fundamental root. More precisely, one conjectures the following correspondence: John Duncan found such a connection by considering carefully the corresponding moonshine groups and their inter-relation. For more on this, look at the old post E8 from moonshine groups . The extended Dynkin diagram with these moonshine groups as vertices is: Duncan does this by assigning numbers to moonshine

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http://ift.tt/eA8V8J Felton's students showed 20% growth from 2015 to 2016 in Partnership for Assessment of Readiness for College and Careers (PARCC) year-end assessments for Algebra I. She works equally well with both high- and low-performing students: In the three years Felton has taught AP Calculus at AHS, ... from Algebra

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Laptops And Phones In The Classroom: Yea, Nay Or A Third Way? We asked teachers, professors, a psychiatrist and a technologist for their thoughts, and we heard a range of opinions on one of the most "weirdly divisive" issues in education. Read more on NPR

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http://ift.tt/2DNWy57 The monstrous moonshine picture is the subgraph of Conway’s big picture consisting of all lattices needed to describe the 171 moonshine groups. It consists of: – exactly 218 vertices (that is, lattices), out of which – 97 are number-lattices (that is of the form $M$ with $M$ a positive integer), and – 121 are proper number-like lattices (that is of the form $M \frac{g}{h}$ with $M$ a positive integer, $h$ a divisor of $24$ and $1 \leq g \leq h$ with $(g,h)=1$). The $97$ number lattices are closed under taking divisors , and the corresponding Hasse diagram has the following shape Here, number-lattices have the same colour if they have the same local structure in the moonshine picture (that is, have a similar neighbourhood of proper number-like lattices). There are 7 different types of local behaviour: The white numbered lattices have no proper number-like neighbours in the picture. The yellow number lattices (2,10,14,18,22,26,32,34,40,68,80,88,90,112

What Do Asthma, Heart Disease And Cancer Have In Common? Maybe Childhood Trauma Toxic stress in childhood can lead to a lifetime of health problems and, ultimately, a shorter life. Here's what schools can do to help. Read more on NPR

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http://ift.tt/2EZYBTa (image credit: Joe Blitzstein via Twitter ) Smullyan’s Knights and Knaves problems are classics. On an island all inhabitants are either Knights (who only tell true things) and Knaves (who always lie). You have to determine their nature from a few statements. Here’s a very simple problem: “Abercrombie met just two inhabitants, A and B. A made the following statement: “Both of us are Knaves.” What is A and what is B?” Now, this one is simple enough to solve, but for more complicated problems a generic way to solve the puzzles is to use propositional calculas, as explained in Smullyan’s Logical Labyrinths” , chapter 8 “Liars, truth-tellers and propositional logic’. If an inhabitants $A$ asserts a proposition $P$, and if $k_A$ is the assertion ‘$A$ is a Knight’, then the statement can be rephrased as \[ k_A \Leftrightarrow P \] for if $A$ is a Knight, $P$ must be true and if $A$ is a Knave $P$ must be false. Usually, one can express $P$ as a propositional

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http://ift.tt/eA8V8J My students need to interact with algebra concepts in a tactile way. I teach creative students with limited resources to display their talent. I teach freshman at an urban high school in Columbus, OH. My students live in poverty; we have 100% free and reduced... from Algebra

http://ift.tt/2rmxAHC SNORT , invented by Simon NORTon is a map-coloring game, similar to COL. Only, this time, neighbours may not be coloured differently. SNORTgo, similar to COLgo , is SNORT played with go-stones on a go-board. That is, adjacent stones must have the same colour. SNORT is a ‘hot’ game, meaning that each player is eager to move as most moves will improve your position. In COL players are reluctant to move, because a move limits your next moves. For this reason, SNORT positions are much harder to evaluate, and one needs the full force of Conways’s ONAG . Here’s a SNORTgo endgame. Who has a winning strategy? , and what is the first move in that strategy? The method to approach such an endgame is similar to that in COLgo . First we remove all dead spots from the board. What remains, are a 4 spots available only to Right (white) and 5 spots available only to Left (bLack). Further, there a 3 ‘live’ regions: the upper righthand corner and the two lower corners. The

http://ift.tt/eA8V8J Get now : http://ift.tt/2DsKkSw DOWNLOAD PDF GMAT Algebra Strategy Guide (Manhattan Prep GMAT Strategy Guides),GMAT Algebra Strategy Guide (Manhattan Prep GMAT Strategy Guides) ebook download,GMAT Algebra Strategy Guide (Manhattan Prep GMAT Strategy ... from Algebra

http://ift.tt/2mUMEqb At a seminar at the College de France in 1975, Tits wrote down the order of the monster group \[ \# \mathbb{M} = 2^{46}.3^{20}.5^9.7^6.11^2.13^3.17·19·23·29·31·41·47·59·71 \] Andrew Ogg , who attended the talk, noticed that the prime divisors are precisely the primes $p$ for which the characteristic $p$ super-singular $j$-invariants are all defined over $\mathbb{F}_p$. Here’s Ogg’s paper on this: Automorphismes de courbes modulaires , Séminaire Delange-Pisot-Poitou. Théorie des nombres, tome 16, no 1 (1974-1975). Ogg offered a bottle of Jack Daniels for an explanation of this coincidence. Even Richard Borcherds didn’t claim the bottle of Jack Daniels, though his proof of the monstrous moonshine conjecture is believed to be the best explanation, at present. A few years ago, John Duncan and Ken Ono posted a paper “The Jack Daniels Problem” , in which they prove that monstrous moonshine implies that if $p$ is not one of Ogg’s primes it cannot be a diviso

DeVos: 'Common Core Is Dead'; A Large Online Charter School Is Shut Down School-to-prison pipeline, foster youth transportation, and more education news of the week. Read more on NPR

http://ift.tt/eA8V8J WARSAW — The BEST Center at Genesee Community College has released its SAT prep course schedule. The SAT prep course is designed to prepare students for the English and math components of the SAT exam. It familiarizes students with the exam format and uses practice questions similar to ... from Algebra

http://ift.tt/eA8V8J For my program individuals were required to have a high school diploma with first year algebra . I developed a screening test which tested comprehension levels of listening and reading English, basic math, and simple algebra (E=I x R). In a class of 32 students, 5 flunked my screening test. When asked ... from Algebra

http://ift.tt/eA8V8J Ever since she was told by an algebra teacher that she'd never succeed, Ashley McBryde has had a fire in her heart to prove them wrong. The Arkansas native is readying herself for that revelation with the announcement of her highly-anticipated debut album, Girl Going Nowhere. The triumphant project ... from Algebra

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http://ift.tt/eA8V8J Consider a study conducted in the Chicago high schools. Students who had failed algebra were randomly assigned either to online or to face-to-face recovery courses. The results were clear: Students in the online algebra courses learned much less than those who worked with a teacher in a classroom. from Algebra

http://ift.tt/2DNWy57 Time to wrap up my calculations on the moonshine picture , which is the subgraph of Conway’s Big Picture needed to describe all 171 moonshine groups . No doubt I’ve made mistakes. All corrections are welcome. The starting point is the list of 171 moonshine groups which are in the original Monstrous Moonshine paper . The backbone is given by the $97$ number lattices, which are closed under taking divisors and were found by looking at all divisors of the numbers $N=n \times h$ for the 171 moonshine groups of the form $N+e,f,\dots$ or $(n|h)+e,f,\dots$. The Hasse-diagram of this poset (under division) is here (click on the image to get a larger version) There are seven types of coloured numbers, each corresponding to number-lattices which have the same local structure in the moonshine picture, as in the previous post . The white numbered lattices have no further edges in the picture. The yellow number lattices (2,10,14,18,22,26,32,34,40,68,80,88,90,112,126

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http://ift.tt/eA8V8J They will be taking algebra 1 and algebra 2. They will be taking geometry,” says Palfry. Palfry adds that all of the teachers on staff are certified with teaching licenses which offers an another level of competency and guarantee for a higher quality of education. According to the Gorlich family, their kids are ... from Algebra

http://ift.tt/eA8V8J Mississippi had planned to pay to create an Algebra II exam and administer it in high school to students who take Algebra I in eighth grade. But Oakley said federal officials now say Mississippi can continue with its current practice of giving both the eighth-grade math test and the Algebra I exam to those ... from Algebra