The world's favorite number is seven, at least if the result of a poll conducted by Alex Bellos is to be believed. Some people like it because it is prime, some because they have a lot of sevens in...  Read more on ScientificAmerican.com
Math

Most Topular Stories

Another Reason to Love the Number Seven
Scientific American  Math29 Sep 2014  5:30 am 
Math Storytelling Day: The Hospital Floor
Let's Play Math!24 Sep 2014  6:14 am[Feature photo above by Christiaan Triebert via flickr (CC BY 2.0).] Have you ever heard of Math Storytelling Day? On September 25, people around the world celebrate mathematics by telling stories together. The stories can be real — like my story below — or fictional like the tale of Wizard Mathys from Fantasia and his crystal ball communication system. Check out these posts for more information: Happy Math Storytelling Day Math Storytelling Day resources Moebius Noodles: Math Storytelling Day archive My Math Story My story begins with an unexpected adventure in pain. Appendicitis… 
Extrapolation Gone Wrong: the Case of the Fermat Primes
Scientific American  Math26 Sep 2014  5:00 amSamuel Arbesman recently wrote about incorrect mathematical conjectures. I wanted to add one of my favorites, which came up in my math history class a couple weeks ago.  Read more on ScientificAmerican.com 
Adding uncertainty to improve mathematical models
Mathematics News  ScienceDaily29 Sep 2014  3:05 pmMathematicians have introduced a new element of uncertainty into an equation used to describe the behavior of fluid flows. While being as certain as possible is generally the stock and trade of mathematics, the researchers hope this new formulation might ultimately lead to mathematical models that better reflect the inherent uncertainties of the natural world. 
Nonassociative Algebras
Ars Mathematica30 Dec 2013  2:00 pmI periodically feel like I should learn more about nonassociative algebra. (I’ve studied Lie algebras, and technically Lie algebras are nonassociative, but they’re pretty atypical of nonassociative algebras.) There’s a mysterious circle of “exceptional” examples that are all related — the octonions, the five exceptional Lie algebras, the exceptional Jordan algebra — that I would like to understand better. John Baez has an article about the direct connection that I post about before, but what I don’t understand about the general theory is how…

Search for "math OR mathematics"

KISD students improve ACT scores but college readiness lags
1 Oct 2014  11:39 amKeller School District high school students continue to gain ground in scores and participation on the ACT test but more work is needed to ensure college readiness, officials said. "Keller is among a very small number of districts that enjoy a positive curve in ACT, with an increase in the number of students and maintaining a positive trend in scores," said Charles Carroll, chief academic officer. 
7 Ways to Deal with Family and Friends Who Don't Get it
1 Oct 2014  11:39 amIf "I believe you" are the three most powerful words you can say to someone with an invisible illness. Four of the hardest or most painful words to absorb  whether they are said directly or communicated indirectly through insensitive behavior  are "I don't believe you." 
FCC dangles $45 billion in front of TV stations, hoping to jumpstart ...
1 Oct 2014  11:38 amFCC Chairman Tom Wheeler is making the hard sell to TV broadcasters, enticing them with the possibility of big payouts if they fork over their airwaves for auction. The Federal Communications Commission is trying to convince local TV stations across the country that giving up their broadcast airwaves is in their own best interests. 
Common Core Back In The News
1 Oct 2014  11:36 amCommon core continues to make headlines both locally and statewide. According to the state's education commissioner work is underway on a possible replacement for the controversial curriculum. 
California Winners of the 2014 National Blue Ribbon Schools Award
1 Oct 2014  11:35 amState Superintendent of Public Instruction Tom Torlakson today congratulated 24 California public schools that are being recognized as 2014 National Blue Ribbon Schools. The California schools, which are either high achieving or made significant academic improvement, are among 337 schools in 47 states287 public schools and 50 private schoolsannounced this morning by U.S. Secretary of Education Arne Duncan.

Mathematics News  ScienceDaily

Adding uncertainty to improve mathematical models
29 Sep 2014  3:05 pmMathematicians have introduced a new element of uncertainty into an equation used to describe the behavior of fluid flows. While being as certain as possible is generally the stock and trade of mathematics, the researchers hope this new formulation might ultimately lead to mathematical models that better reflect the inherent uncertainties of the natural world. 
At the interface of math and science: Using mathematics to advance problems in the sciences
29 Sep 2014  3:03 pmIn popular culture, mathematics is often deemed inaccessible or esoteric. Yet in the modern world, it plays an ever more important role in our daily lives and a decisive role in the discovery and development of new ideas  often behind the scenes. In new research, scientists have developed new mathematical approaches to gain insights into how proteins move around within lipid bilayer membranes. 
Taking advantage of graphene defects: Security screening
24 Sep 2014  5:51 amScientists have discovered a potential application for graphene in security screening. A new theoretical model estimates electric current rectification in graphene. Electronic transport in graphene contributes to its characteristics. Now, a Russian scientist proposes a new theoretical approach to describe graphene with defectsin the form of artificial triangular holesresulting in the rectification of the electric current within the material. Specifically, the study provides an analytical and numerical theory of the socalled ratchet effect. 
Recreating the stripe patterns found in animals by engineering synthetic gene networks
23 Sep 2014  8:07 amResearchers are trying to understand how networks of genes work together to create specific patterns like stripes. They have gone beyond studying individual networks and have created computational and synthetic mechanisms for a whole 'design space' of networks in the bacteria Escherichia coli. The system proves to be more efficient and powerful than building networks onebyone, they report. 
Could suburban sprawl be good for segregation?
23 Sep 2014  7:17 amRacially and economically mixed cities are more likely to stay integrated if the density of households stays low, finds a new analysis of a nowfamous model of segregation. By simulating the movement of families between neighborhoods in a virtual 'city,' mathematicians show that cities are more likely to become segregated along racial, ethnic or other lines when the proportion of occupied sites rises above a certain critical threshold  as low as 25 percent.

Scientific American  Math

Another Reason to Love the Number Seven
29 Sep 2014  5:30 amThe world's favorite number is seven, at least if the result of a poll conducted by Alex Bellos is to be believed. Some people like it because it is prime, some because they have a lot of sevens in...  Read more on ScientificAmerican.com 
Extrapolation Gone Wrong: the Case of the Fermat Primes
26 Sep 2014  5:00 amSamuel Arbesman recently wrote about incorrect mathematical conjectures. I wanted to add one of my favorites, which came up in my math history class a couple weeks ago.  Read more on ScientificAmerican.com 
A Computer Scientist Tells Mathematicians How To Write Proofs
24 Sep 2014  12:04 pmBelieve it or not, I do have friends who would describe themselves as not liking math, and every so often one of them will share this meme on Facebook: And then Satan said, "Put the alphabet in...  Read more on ScientificAmerican.com 
Tools for evaluating scholarly journals
24 Sep 2014  8:33 amIn an informationrich age, one of my main functions as a librarian isn't helping people find material, but helping them evaluate the material they find.  Read more on ScientificAmerican.com 
Ig Nobel Prizes Make You Laugh, Then Think
23 Sep 2014  8:04 amCAMBRIDGE, Mass.—What happens in the brains of people who see Jesus in a piece of toast? What are the physics of slipping on a banana peel?  Read more on ScientificAmerican.com

NYT > Mathematics

The Odds, Continually Updated
29 Sep 2014  9:00 pmIn Bayesian statistics, new data is used to shape assumptions, the opposite of the frequentist (classical) approach. 
MacArthur Awards Go to 21 Diverse Fellows
16 Sep 2014  9:00 pmStipends will be awarded to a psychologist studying racial perceptions in crimes, the maker of the film “The Act of Killing” and a law professor seeking to help American Indian women, among others. 
Incentives Aid A.P. Science and Math Scores
1 Sep 2014  9:00 pmA Pittsburgh high school took part in an initiative to raise its performance in math and science, but did its results match the high expectations? 
From a Compound in the Brazilian Hills, Excellence in Math Emerges
27 Aug 2014  9:00 pmThe National Institute for Pure and Applied Mathematics in Rio is gaining attention as a hidden gem in a country with few worldrenowned educational institutions. 
Top Math Prize Has Its First Female Winner
12 Aug 2014  9:00 pmA professor at Stanford who made an important discovery about dynamical systems joined three other mathematicians in accepting the Fields Medal.

Ars Mathematica

Arguesian Lattices
23 Sep 2014  12:46 pmAs is wellknown, the lattice of submodules of a module is modular. What I did not know is that the converse is not true, and that lattices of submodules must satisfy a stronger property, the arguesian law. The Arguesian law is a latticetheoretic analogue of Desargues’ theorem in projective geometry. I read the statement of the theorem several times and I have no intuition about what it means. There is a kind of converse to this result: a complemented lattice can be embedded into the lattice of submodules of a module if and only if it is arguesian. (I found the result in… 
K2, not the mountain
20 Mar 2014  2:18 pmChandan Singh Dalawat has a nice survey article about K2. It just gives the highlights of the theory, without proofs, so it’s closer to a teaser trailer than it is to fulllength movie. But sometimes you just want a teaser trailer to tell you if you want to invest the time in the movie. 
Cayley Bacharach Theorem through History
10 Feb 2014  3:04 pmI came across this terrific article that describes a sequence of results beginning with Pappas’ theorem through the CayleyBacharach theorem to modern formulations in terms of the Gorenstein (!) condition. The connection between classical topics in algebraic geometry and modern techniques is fascinating. 
Nonassociative Algebras
30 Dec 2013  2:00 pmI periodically feel like I should learn more about nonassociative algebra. (I’ve studied Lie algebras, and technically Lie algebras are nonassociative, but they’re pretty atypical of nonassociative algebras.) There’s a mysterious circle of “exceptional” examples that are all related — the octonions, the five exceptional Lie algebras, the exceptional Jordan algebra — that I would like to understand better. John Baez has an article about the direct connection that I post about before, but what I don’t understand about the general theory is how… 
Determinacy
30 Nov 2013  1:27 pmOne of my ambitions in life is to understand projective determinacy. Fortunately, Tim Gowers has written a series of posts to explain Martin’s proof that Borel sets are determined. The main source of interest in determinacy is that results suggest that it is the strongest regularity property that a set can have, in that it it tends to imply other nice properties such as Lebesgue measurability. Here is a short proof by Martin that determinacy implies Lebesgue measurability. Justin Palumbo has a nice set of lecture notes that relate determinacy to other regularity properties. (One nuance…

Loren on the Art of MATLAB

Symbolic Math Solves a Linear Algebra Conundrum
24 Sep 2014  5:49 amI'd like to introduce this week's guest blogger Alan Weiss. Alan writes documentation for mathematical toolboxes here at MathWorks.An economist I know (well, he's my son) asked me a question the other day. I was able to answer him quickly by using Symbolic Math Toolbox™ calculations. You might find the steps to be an interesting case of a somewhat nonstandard use of symbolic mathematicsContentsA Linear Algebra QuestionA Symbolic ApproachFeedbackA Linear Algebra QuestionMy son was working through a paper that described a computational algorithm. He got stuck on one step of the… 
Analyzing Uber Ride Sharing GPS Data
6 Sep 2014  12:25 pmMany of us carry around smartphones that can track our GPS positions and that's an interesting source of data. How can we analyze GPS data in MATLAB?Today's guest blogger, Toshi Takeuchi, would like to share an analysis of a public GPS dataset from a popular ride sharing service Uber.ContentsIntroductionUber anonymized GPS logsDoes the usage change over time?Where do they go during the weekend?Visualizing the traffic patterns with GephiSummaryIntroductionUber is a ride sharing service that connects passengers with private drivers through a mobile app and takes care of payment. They are in… 
Age is No Barrier to Exploring Ideas and Concepts in MATLAB and Simulink
25 Aug 2014  11:24 amAge is No Barrier to Exploring Ideas and Concepts in MATLAB and SimulinkI’d like to introduce you to this week’s guest blogger, Graham Dudgeon. Graham is with our Industry Marketing Team at MathWorks, and focuses on the Utilities & Energy Industry. In this blog, Graham shares a story about age being no barrier to exploring ideas and concepts in MATLAB and Simulink.Hi Everyone, and thank you Loren for inviting me to be a guest blogger. This story begins with my dog, waiting patiently at the patio door expecting either of my two sons to let her in. She was out of luck. I am no… 
Ever Needed to Move a Figure?
11 Aug 2014  8:53 amHave you ever needed to move a figure? Perhaps because it is offscreen>? Or at least the menus or close box are not visible? This happens to me from time to time when I get code from someone else who is programming specifically to the size of their display. Working on a laptop, I often have fewer available pixels. What to do?ContentsHow to Find my Figure?Degrees of FreedomHave You Needed Help Locating Something?How to Find my Figure?I used the Function Browser to search for "move figure" and found movegui. It might be just the ticket for you.Degrees of FreedomAs you can see from the… 
Write Once, Deploy Anywhere
28 Jul 2014  8:03 amGuest blogger Peter Webb returns with another in an occasional series of postings about application deployment.ContentsDeployment TargetsDeploying to MATLABDeploying to the DesktopDeploying to a Java ApplicationReuse, Don't RewriteDeployment TargetsI've written a MATLAB application that reports on the presence of contaminants in surface water, using a publically available database of water quality observations maintained by the United States Geological Survey and the Environmental Protection Agency. Many groups of people might be interested in this kind of information. MATLAB made it easy to…

Homeschool Math Blog

Timed tests
22 Sep 2014  4:15 pmI wrote a new piece outlining some of the dangers of using timed tests in math, such as how they promote math anxiety and cause children to be afraid of making mistakes in math classes.Should you use timed tests for math facts?Go check it out! 
The farmer and his three sons
18 Sep 2014  4:36 pmHere's an interesting story problem that I received in an email!A farmer died leaving his 17 horses to his three sons. When his sons opened up the will it read: Photo by www.flickr.com/photos/iceninejonMy eldest son should get 1/2 (half) of total horses;My middle son should be given 1/3rd (onethird) of the total horses;My youngest son should be given 1/9th (oneninth) of the total horses. As it's impossible to divide 17 into half or 17 by 3 or 17 by 9, the three sons started to fight with each other. So, they decided to go to a farmer friend who they considered… 
Evaluation of a math assessment test  example
15 Sep 2014  5:12 amYou might already know that the placement tests on my site work equally well as generic math assessment tests.I also evaluate the test results for free. Now you can see an example of one student's test results and my evaluation here.Many students need to take two or even more tests in order to get a full picture of the gaps they have in their skills and knowledge. That was the case with this student also: she actually took three tests, grade 6, 5, and 4. I posted two of the tests and my evaluation at MathMammoth.com site. I hope it's helpful! 
Number talks
4 Sep 2014  2:39 pmNumber talks are short discussions among a teacher and students about how to solve a particular mental math problem. The focus is not on the correct answer, but on all the possible methods of finding the answer.Each student has a chance to explain their method, and everyone else will learn from other people's methods!To start a number talk, the teacher gives the students a SHORT math problem to solve — but the students are not allowed to use a calculator or paper & pencil. The idea is to solve it in one's head! For example, you could ask students to solve 5 × 18 using mental math.Read… 
Math Mammoth Grade 7A is here!
29 Aug 2014  2:46 pmI know it's Labor Day weekend, but... Math Mammoth Grade 7A is here! Please note: Only part 7A is available for now (as of August 2014). Part B is expected to be ready sometime in early 2015.Math Mammoth Grade 7A is the first half of the prealgebra curriculum from Math Mammoth. Part A worktext deals with:introduction to basic algebra conceptsintegers and their operationssolving onestep equations, including with negative numbersoperations with negative rational numberssolving linear equations and writing equations for word problemsgraphing linear equations and an introduction to the…

Let's Play Math!

Math Storytelling Day: The Hospital Floor
24 Sep 2014  6:14 am[Feature photo above by Christiaan Triebert via flickr (CC BY 2.0).] Have you ever heard of Math Storytelling Day? On September 25, people around the world celebrate mathematics by telling stories together. The stories can be real — like my story below — or fictional like the tale of Wizard Mathys from Fantasia and his crystal ball communication system. Check out these posts for more information: Happy Math Storytelling Day Math Storytelling Day resources Moebius Noodles: Math Storytelling Day archive My Math Story My story begins with an unexpected adventure in pain. Appendicitis… 
Math Teachers at Play #78 via 1001 Math Problems
23 Sep 2014  12:35 pmMath Teachers at Play is a traveling collection of math tidbits — games, lesson ideas, and more — from around the Internet. It moves around from month to month, and the September edition is now posted at 1001 Math Problems blog. What a fun list of math posts to browse! Special Blog Carnival Edition of 1001 Math Problems Welcome to the 78th edition of the Math Teachers At Play math education blog carnival, which I am thrilled to be hosting this month in celebration of my soontobereleased book, Camp Logic. What is the blog carnival? It is a monthly snapshot of some interesting… 
Calling All Math Teacher Bloggers and Homeschoolers: Carnival Time!
15 Sep 2014  3:01 pmby Bob Jagendorf via flickr The monthly Math Teachers at Play (MTaP) math education blog carnival is almost here. If you’ve written a blog post about math, we’d love to have you join us! Each of us can help others learn, so in a sense we are all teachers. Posts must be relevant to students or teachers of schoollevel mathematics (that is, anything from preschool up to firstyear calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival. Click here to submit your blog post. Browse all the past editions of the Math Teachers at Play… 
Quotable: I Do Hate Sums
29 Aug 2014  10:51 amI’ve been looking for quotes to put at the beginning of each chapter in my math games books. I found a delightful one by Mrs. LaTouche on the Mathematical Quotations Server, but when I looked up the original source, it was even better: I am nearly driven wild with the Dorcas accounts, and by Mrs. Wakefield’s orders they are to be done now. I do hate sums. There is no greater mistake than to call arithmetic an exact science. There are Permutations and Aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden… 
Math Teachers at Play # 77 via Math = Love
26 Aug 2014  3:10 pmMath Teachers at Play is a traveling collection of math tidbits — games, lesson ideas, and more — from around the Internet. It moves around from month to month, and the August edition is now posted at Math = Love blog. What a fun list of math posts to browse! Math Teachers At Play: Blog Carnival Edition # 77 Welcome to the 77th edition of the Math Teachers at Play Blog Carnival! I’m super excited to be hosting this carnival because I’ve been reading it for years! Yes, I am that crazy person who started reading math teacher blogs as a high school junior. I think you are…

Basic mathematics blog

Counting money worksheets
26 Sep 2014  7:11 pmCounting money worksheets teachers print for free to help students in first grade count money 
Counting worksheets
25 Aug 2014  11:28 amCounting worksheets teachers can use for students in preschool or first grade. Available to print for free. Help your students to count 
Common mistakes in math
19 Aug 2014  2:30 pmSome common mistakes in math and how to avoid them when doing your math problems 
Volume of irregular shapes
28 Jul 2014  1:28 pmLearn to calculate the volume of irregular shapes using commonly used volume formulas 
Geometry word problems
28 Jul 2014  5:40 amA collection of geometry word problems to help you practice a wide variety of concepts in geometry. All problems come with the solution

ChapterZero

Algebra: it matters
15 Sep 2014  4:42 pmI’m looking at two different models for learning polynomial functions, and trying to determine if they are equivalent. After a couple days of thinking, I’ve reduced the question to the following: Can every symmetric polynomial of degree \(r\) in \(d\) variables that has no constant term be written as a sum of the \(r\)th powers of linear polynomials in \(d\) degrees and a homogeneous polynomial of degree \(r\) each of whose monomials involves at most \(d1\) variables? 
Julia, once more
9 Aug 2014  12:43 pmJulia + PyCall + CCall + Gadfly or PyPlot (+ Julia Studio ?) looks delicious. The only feature that absolutely needs to be added is shared memory parallelism (why wasn’t this an initial core feature of the language?), but I’m extremely excited by the current awesomeness of the Julia ecosystem. I recommend you get into it now, if you’re a scientific computation person. Update: Julia has experimental support for sharedmemory arrays on Unix, which is really all that I need at this point. Great! 
a bit on word embeddings
25 Jul 2014  9:31 pmLately I’ve been working almost exclusively on continuous word representations, with the goal of finding vectorial representations of words which expose semantic and/or syntactic relationships between words. As is typical for any interesting machine learning problem, there are a glut of clever models based on various assumptions (sparsity, hierarchical sparsity, lowrankedness, etc.) that yield respectable embeddings. Arguably, however, the most well known of these representations are the word2vec models due to Mikolov et al., which are part of a larger class of neural networkbased… 
Installing Hadoop on Ubuntu (works for Ubuntu 12.04 and Hadoop 2.4.1)
18 Jul 2014  4:11 pmI’m trying to use LDA on a large amount of data. A quick recap: Tried vowpal wabbit … it’s fast, I’ll give it that, but it’s also useless: the output is dubious (what I think are the topics look like they haven’t changed very much from the prior) *and* I have no idea how it maps onto topics and documents (the documentation is AWFUL, and the dimensions of the output files are WONKY). Tried two implementations of SCVB0, a stochastic collapsed variational bayes LDA algorithm: one doesn’t work at all (as in, it stalls on any amount of data — so… 
Sharing numpy arrays between processes using multiprocessing and ctypes
1 May 2014  4:32 pmBecause of its global interpreter lock, Python doesn’t support multithreading. To me, this is a ridiculous limitation that should be gotten rid of posthaste: a programming language is not modern unless it support multithreading. Python supports multiprocessing, but the straightforward manner of using multiprocessing requires you to pass data between processes using pickling/unpickling rather than sharing memory. Needless to say, this slows down execution when large amounts of data need to be shared by processes. In my case, I’ve been using multiprocessing to speed up the training…

Computational Complexity

Dagstuhl on Algebra in Computational Complexity
30 Sep 2014  9:17 am(Reminder Theory day at UMCP: here is the link. ) There was a Dagstuhl on Algebra in Computational Complexity Sept 2226. I learned stuff in the talks, over meals, and even in my room alone at night. 1) Recall that a while back Ryan Williams (the theorist, not the AmericanFootball player) showed that NEXP is not in ACC. His proof involved MANY things but one of the core things was an ALGORITHM for a version of SAT (I think SuccinctSAT) that was eversoslightly better than brute force. So one lesson is that people in complexity theory should know some algorithms. At Dagstuhl… 
MikeFest
27 Sep 2014  6:38 amI rarely highlight individual events on the blog, but one's advisor only turns sixty once. We will honor Michael Sipser at MIT on Sunday, October 26 with a oneday symposium full of great speakers in complexity. As one of Sipser's PhD students, I'm helping to organize the event and serving as emcee for the dinner speeches. Please send me any funny or embarrassing stories or pictures of Sipser through the decades. Many of you know Sipser from his popular textbook Introduction to the Theory of Computation. Sipser was one of the driving forces in complexity in the 70's and 80's. Sipser… 
Typecasting in Dagstuhl
24 Sep 2014  1:36 pmAfter this prerecorded typecast, we learned of the tragic death of Alexey Chervonenkis, the C of VC dimension, a huge loss to the learning community. We’ll have a proper obit soon. Now onto the typecast. Lance: Hello and welcome to Dagstuhl for our first typecast since the 2014 Complexity Conference. Howdy Bill. Bill: Hi Lance. Are you enjoying Dagstuhl? Lance: I always have fun at Dagstuhl especially when you are here Bill. Bill: I have not seen you at many talks. Lance: So maybe you should go to more talks Bill. Bill: Never mind. As you told me Scott is writing a blog book. Should we… 
Goodbye MSRSVC
22 Sep 2014  10:51 amThis week I'm back at Dagstuhl for the Workshop on Algebra in Complexity Theory. Bill is here as well and we hope to have a typecast for you later this week. The big discussion is the closing of Microsoft Research in Silicon Valley last week. The 50 researchers at MSRSVC included 15 in a strong theory group. Luckily I captured the page last night as Microsoft has eliminated all mention of the lab from its web site. Just like the novel 1984: Microsoft doesn't have a research lab in Silicon Valley. Microsoft never had a research lab in Silicon Valley. I visited MSRSVC a couple of times, once… 
Gentry and Lurie and Zhang can say they are geniuses without bragin' MacArthur Geniuses
18 Sep 2014  9:12 pm(If I mispell anything in this post, well, that"s why I'm not a MacArthur Genius, or any other kind of Genius.) Craig Gentry, of homomorphic encryption fame, won a 2014 MacArthur Genius award. here is an article about it and a description of his work, which is understandable to most nongenius's. It is great work and I am glad to see the work and him honored. Have other computer scientists won it? Yes. Have other CS theorists won it? Yes. Here is a list, though it may be incomplete: Peter Shor (1999), Erik Demaine (2003), Jon Kleinberg (2005), Daniel Spielman (2012). Jacob Lurie…

IMA Journal of Applied Mathematics  current issue

A theory for deformation dependent evolution of continuous fibre distribution applicable to collagen remodelling
19 Sep 2014  8:36 amThis work explores the implications of a constitutive framework that introduces a particular remodelling process for materials having a continuous distribution of fibre directions. It is assumed that the matrix constituent is unaffected and that fibres remodel by a process of dissolution and reassembly. Dissolution results from a time dependent chemical kinetic process that is influenced by fibre stretch. Two possibilities for the reassembly of the fibres are considered: (1) fibres reassemble in a stressfree state or (2) fibres assemble in a prestrained state matching that of the… 
Orthotropic cyclic stresssoftening model for pure shear during repeated loading and unloading
19 Sep 2014  8:36 amWe derive an orthotropic model to describe the cyclic stress softening of a carbonfilled rubber vulcanizate through multiple stress–strain cycles with increasing values of the maximum strain. We specialize the deformation to pure shear loading. As a result of straininduced anisotropy following on from initial primary loading, the material may subsequently be described as orthotropic because in pure shear there are three different principal stretches so that the straininduced anisotropy of the stress response is different in each of these three directions. We derive nonlinear… 
A polyconvex formulation of isotropic elastoplasticity theory
19 Sep 2014  8:36 amA model of finitedeformation elastoplasticity theory that accommodates finite elastic strain is discussed. This is based on a polyconvex extension of the classical Hookean relation between stress and elastic strain. A framework for the description of scale effects associated with strain hardening is also developed, based on the theory of materially uniform bodies with inhomogeneities. 
Foreword to Special Issue celebrating Professor Ray Ogden's 70th birthday
19 Sep 2014  8:36 am 
Mechanics of contact between bimaterial elastic solids perturbed by a flexible interface
19 Sep 2014  8:36 amThis paper generalizes the classical result of R.D. Mindlin for the axisymmetric problem related to the action of a concentrated force at the interior of an isotropic elastic halfspace to include a bimaterial region that is perturbed by an interface exhibiting flexural behaviour. The flexural behaviour of the interface is described by a Germain–Poisson–Kirchhoff thin plate theory. A Hankel integral transform technique is used to obtain an explicit result for the deflection of the flexural interface. The reduction of the solution to conventional results associated with both…

WordPress Tag: Mathematics

"Chronology"
30 Sep 2014  9:43 am“Chronology” From precognitive dreams, where the future is recognizably predicted before it happens, we can infer that time is other than what ordinarily we think it is. From the way philosophers have sometimes talked, mathematicians and physicists too on occasion, and theologians fairly often, we can gather that there is a dimension of reality where the hands of the clock don’t measure anything. That dimension is called “eternity.” Bracketing out eternity, the poet says, … at my back I always hear Time’s wingèd chariot hurrying near. What is he trying to say to “his coy… 
Étienne de Condillac and the Importance of Language in Logical Reasoning
30 Sep 2014  9:34 amRead More at http://ift.tt/1rB1Pkz 
Lost Partition
30 Sep 2014  9:29 am 
Uncertain Math Might Be Better Math
30 Sep 2014  7:59 amPrecision almost seems like part of the definition of math. The realm of numbers and symbols and methods seems to be one in which vagueness is an outcast. http://motherboard.vice.com/read/howuncertainmathmightbebettermath 
Fantasm
30 Sep 2014  7:52 amIn the wake of failure I dreamed of fantasy. I fell headfirst from the pages of my linear algebra textbook into another classroom. It reminded me of calculus, but was of no building I’ve ever stepped foot in: the walls were white and discolored at the edges, darker greys and burnt yellows that made the corners stretch into oblivion. Low white tables sat in clusters of four or five around the room, but I was the only student held between its four walls. And hanging at its front, two large projector screens hung, covered in a PowerPoint slide as simple as text and a link. But I said I…

Mr. L's Math

Visual Pattern Site by Fawn Nguyen
26 Sep 2014  2:06 pmpattern no. 155 from Fawn Nguyen’s site visualpatterns.org When I taught 7th grade for six years visual patterns were used to start the school year because they did so many great things for students. They were engaging to the students, visually stimulating, allowed all students easy entry to the math involved, worked great for student projects, and addressed many math standards. Here’s a site with a lot of patterns you can use in your classroom, along with commentary for teacher use. As of the date of this post (Sept 2014) there are 145 patterns, along with the Equation… 
Malin ChristerssonDigital Math for GeoGebra Enthusiasts
25 Sep 2014  5:46 pmMalin Christersson’s site, Digital Mathematics, is a great place to spend some time for GeoGebra enthusiasts. It has some of the best tutorials on the web, organized into seven clusters. Malin provides clear and detailed explanations, some with embedded videos, that help the new as well as experienced user to get more out of GeoGebra. Malin also has provided further work in the areas of NonEuclidean Geometry, Latex/LyX, Geometry, Functions, Trigonometry, Calculus, Statistics, Linear Algebra, and Fractals. From the site: “This is a collection of material that I have used when… 
Circle Dissection PuzzleFour Equal Curved Areas
24 Sep 2014  4:30 pmDissect the circle into four parts of equal area by drawing three curved lines of equal length. – idea from Arithmetrics, by Jerome S. Meyer, pg 88 Move slider halfway to reveal a hint if you’re stuck. Questions for you or your students: 1 Why are the 3 curved lines of equal length? 2 How do you show that the 3 curved lines make equal areas? The downloadable file can be found here. My other GeoGebraTube apps can be found here. here. 
Van Aubel’s Theorem for Triangles
23 Sep 2014  2:47 pmVan Aubel’s Theorem describes a relationship between squares constructed on the sides of a quadrilateral. In Martin Gardner’s “Mathematical Circus,” pg 179, he shows generalizations of this theorem. This one is for triangles. Starting with a triangle, construct a square on each side. In this case Van Aubel’s Theorem says that the line segment between the centers of two of the squares and the line segment between a vertex of the triangle and the center of its opposite square are of equal lengths and are at right angles to one another. Draggable points are colored red. The… 
Yin and Yang Extended
23 Sep 2014  11:36 amHere’s the familiar yinyang figure in a circle of radius 1. If you continue subdividing the diameter of the large circle into semicircles, this wavy line approaches the diameter as a limit. It’s tempting to say that this wavy line then has a length of 2, but of course, its length is still π. Starting at the top and moving downward, any path (mix and match) also has length π. – idea from “Wheels, Life and other Mathematical Amusements“, by Martin Gardner, pg 54 The downloadable file can be found here. My other GeoGebraTube apps can be found here.

MathNotations

Implement The Core: A Variation on a Classic Rate Problem
28 Sep 2014  5:07 amTwitter Problem 92814 (twitter.com/dmarain) Trip to work took 90 min including stopping b/c of accident for x min. Avg'd 30 mph overall; apart from delay, avg'd 50 mph. x=? Answer: 36 min Solution?? REFLECTIONS Do ratetimedistance problems still appear on SAT and other standardized tests? Yes! Do our students get enough practice with these? In Prealgebra? Algebra 1? Do you view these as applied problems? 3 days left for halfprice subscription for detailed solutions to all Twitter problems. See right sidebar... VISIT ME DAILY ON TWITTER AT twitter.com/dmarain 
Implement The Core: Mean of 3 scores=90%,Range=30%,Median??
26 Sep 2014  6:05 amA little more detail from the Twitter Math Problem 92614 (twitter.com/dmarain)Mean of 3 tests:90 Range:30 Explain why median must be 100.Note: Assume all tests are based on 100 pts. The % info could be misleading, aka wrong!REFLECTIONS... 1) Emphasis here is on explanation/reasoning rather than giving a numerical answer. That's why the problem is different from the title. This is at the "core" of the Mathematical Practices of the Common Core. 2) As any dedicated professional knows: Finding challenging problems to promote collaboration and maximize participation is a daunting task. But isn't… 
Least positive integer with 2014 factors  Detailed Solution
25 Sep 2014  5:00 amActual Twitter Problem from 92314 had additional restrictions which didn't fit in the title:Explain why (3^52)(7^18)(11) is the smallest positive integer with 2014 factors and which doesn't end in 5 or an even digit.Before the solution, a fewREFLECTIONS...1) This is not an SAT or typical Common Core Problem. It's more challenging than that. But it does apply a fundamental principle of arithmetic which is often overlooked.2) The solution below is more detailed than most but these are the kinds of solutions I will be emailing to you when you subscribe. See details at top of sidebar to the… 
The sum of 2 pos int is 216, gcf=24  PUFM and Common Core
24 Sep 2014  2:56 pmThe sum of 2 positive integers is 216 and their gcf is 24. Find all possibilities.Parents/Teachers/Students... Want higherorder thinking questions (with detailed solutions/strategies) like this sent to your inbox almost every day for the 201415 school year? Just subscribe to MathNotations Twitter problems. Details and ordering instructions at top right of sidebar. Special pricing ends 93014.REFLECTIONS To solve the problem above without GuessTestRevise requires a more (P)rofound (U)nderstanding of (F)undamental (M)athematics  thus the acronym in the title. (Research Liping Ma for more… 
Which one of these might be on your child's math HW tonight? IMPLEMENTING THE CORE...
24 Sep 2014  4:49 amFrom my Twitter feed today... (twitter.com/dmarain) And I'm not talking about that socalled Challenge Problem at the bottom of the worksheet. The one where your child says, "Oh, we don't have to do that one!" 1) Remainder when 999 is ÷ by 30? 2) Largest multiple of 30 less than 1000? 3) Largest 3digit integer div by 2,3 &5? Which of these require more reasoning and conceptual understanding? Mathematical Practices and Core Reflections... 1) How often do we just throw a challenge problem at a class knowing that only a couple will actually try it. You know, the…

mathrecreation

A year of tinkering
29 Sep 2014  6:37 pmYou really should take advantage of the free until August 2015 license that is currently being offered with a fresh download TinkerPlots. Almost a year of tinkering  would that it were freely available in perpetuity without condition.If you are a middle school teacher, then this is designed for you and yours. If, like me, you are not, you may find it fun to play with anyway. Here is something I was playing with recently:An elementary school number sense activityIn the JUMP math curriculum for grades 3 and 4, there are lessons where students investigate the patterns formed when… 
modular tables
17 Sep 2014  7:13 pmNo, not a post about IKEA furniture. A while ago I put up a post on colouring multiplication tables by assigning ranges of numbers a colour value. You end up with something that looks like a rainbow.This image was made in Tinkerplots, so it was easy to go from a 10 x 10 table to a 50 x 50 table (removing the numbers and just keeping the colours, and shrinking each cell down a bit):Inspired by the "Zn Multiplication visualizer" found here and mentioned here, and thinking about modular arithmetic from the last post, I decided to make a few more images.If you take the values in this… 
squashing multiples
15 Sep 2014  7:21 pmAn elementary school exercise leads to writing a simple program, a little proof by contradiction, and learning about some mostlyforgotten calculation tricks: just some of the fun that can be had when playing with simple math. Sound good? It all starts with squashing numbers...No doubt you've noticed some patterns in the nonzero multiples of 9: 9, 18, 27, 36, 45,... One thing to notice is that if you (repeatedly) add up all the digits of a multiple of 9, you always get 9 as your answer.This works immediately for many multiples of 9, like 9*14 = 126 (1 + 2 + 6 = 9), for others you need to… 
parallel coordinates
20 Jun 2014  7:17 pmWhat's going on with these?Playing around with parallel coordinates. 
origami workshop
28 May 2014  7:28 pmI mentioned in the previous post that I was considering doing some modular Sonobe origami in an upcoming workshop for middle school students. Wondering if this is a good idea, and thinking that I had better have some backup plans, I decided to make a list of origami models that I have used in school workshops in the past.Simple TrianglesThese simple models are nice for the very young and for beginners. Start with a triangle made from cutting standard origami paper along a diagonal.A bit of playing around with the triangles should be enough for you to figure out how to fold examples like the…

MathFour

How to Tell the Difference between 0.3 and 0.33 – Visually
26 Sep 2014  4:39 amA student was working on this problem the other day: Find the volume of a cone with radius 2.5 units and height 5 units. Of course we all remember the formula as So she plugged in her numbers and got 29.45 cubic units. She checked the back of the book and was disappointed to see the answer listed as 32.72 cubic units. Turns out she was using 0.3 instead of 1/3! What’s wrong with the answer? I asked her to calculate with 0.33 instead. She got 32.39 – far closer to the answer from the book. Then I asked her to use 0.333. This yielded 32.69. She was amazed at how adding another 3 got… 
Teaching Math to Special Needs Children
16 Sep 2014  7:38 pmI’m out of my depth. Like 3 bazillion leagues out of my depth. I took a math teaching position at a school for kids with neurological differences. I knew it would be hard. But I didn’t think it would be this hard. Lesson 1: Everything you know is wrong. It’s a Weird Al song, but it also applies to teaching kids with special needs. I gave this great math artwork activity that I thought would be perfect. My students are all 1219 years old. They can communicate, be polite and follow instructions. And they are all listed as over 2nd grade in abilities. So this should have be a… 
How Much Weight Does Wet Hair Add?
21 Aug 2014  3:47 amHave you heard that saying, “She weighs 115 pounds, soaking wet”? That saying hit me this morning while stepping out of the shower. I’m doing Weight Watchers and so I’m a bit hyperfocused on weight right now. So I thought I’d do an experiment. With math of course. Do I weigh more soaking wet? I weighed myself before I dried my hair. And then I weighed again, after it was dry. I didn’t do anything else – no consuming or, ahem, evacuating. I kept the same state of clothing. I didn’t move too much for fear I’d lose weight through energy. 
All About the Benjamin – How Math Saves Lives
15 Aug 2014  8:51 amThis is the story of how a 67% tip on a sushi bill saved a teenager’s life. Okay, that’s a bit of a hyperbole. But roll with me for a bit. The Back Story This summer I started teaching at a small school for kids with neurological differences 2.5 miles from my house. This was the perfect distance to start run commuting – running to work to get back into my old prekid running shape. During inservice for the fall, I attended a two day class on Reasoning Mind’s RMCity with a new colleague, Stephanie. Turns out Stephanie is pretty cool and she’s a runner. A twice… 
Even and Odd Numbers – Basic, but Not Easy to Learn
2 Aug 2014  3:32 amYou know about even and odd numbers, right? I was visiting with my sister yesterday and she was excited that her 8 year old son had finally grasped the idea. “I know, it’s a pretty basic concept, “ she told me, “but I’m just so excited he finally got it.” Which made me consider it. Are the concepts of even and odd basic? Basic but Not Easy Okay, yes. Even and odd numbers are considered a basic concept. Everyone over the age of 15 or so should have a general idea of which numbers are even and which numbers are odd. But evenness and oddness are NOT easy concepts. Think about it:…

CSE Blog  quant, math, computer science puzzles

Balancing Act Puzzle
19 Sep 2014  1:21 amSource: Australian Mathematical Society Gazette Puzzle Corner 35 Problem:There are some weights on the two sides of a balance scale. The mass of each weight is an integer number of grams, but no two weights on the same side of the scale share the same mass. At the moment, the scale is perfectly balanced, with each side weighing a totalof W grams. Suppose W is less than the number of weights on the left multiplied by the number of weights on the right.Is it always true that we can remove some, but not all, of the weights from each side and still keep the two sides balanced? 
"Flawless Harmony" Puzzle
26 Aug 2014  2:40 amSource: AUSTMS Puzzle Corner 35 Problem: Call a ninedigit number flawless if it has all the digits from 1 to 9 in some order. An unordered pair of flawless numbers is called harmonious if they sum to 987654321. Note that (a, b) and (b, a) are considered to be the same unordered pair.Without resorting to an exhaustive search, prove that the number of harmonious pairs is odd. 
Minimum sum of numbers in an array
10 Aug 2014  10:21 pmSource: Asked to me on quora ( cseblog.quora.com ) Problem: Given an array of n positive numbers (n ~ 100000), what is the algorithmic approach to find the minimum possible sum (>=0) by using all the numbers in an array? Example 1: 1 2 2 3 4 Answer : 0 (1+223+4) Example 2: 2 3 4 7 13 Answer: 1 (+2347+13) 
Caterer's Problem
5 Aug 2014  10:07 pmSource: Puzzle Toad CMU Problem: You are organizing a conference, with a festive dinner on the first day. The catering service has 1024 different dinner choices they know how to make, out of which you need to choose 10 to be in the dinner menu (each participant will choose one of these during the dinner). You send an email to the 6875 participants of the conference, with the list of all 1024 choices, asking them to rank the choices in linear order from their favorite to their unfavorite. You want to find a list L of 10 choices, such that for any dinner choice d not in the list L, if we run a… 
3D Tic Tac Toe Puzzle
10 Jul 2014  12:19 pmSource: Shared by Alok Mittal (Cannan Partners) Problem: A 3x3 tic tac toe has 8 "winning lines" (3 horizontal, 3 vertical and 2 diagonals). How many "winning lines" does the 3x3x3 3D tictactoe have? There is a brute force solution, and then there is the aha! solution.

Math for all Grade blog

Sep 24, Coordinategeometry
24 Sep 2014  4:52 amCoordinategeometry 
Sep 23, Statistics Help
23 Sep 2014  2:21 amStatisticshelp 
Sep 23, Math Formulas
23 Sep 2014  12:10 amMath Formulas 
Sep 23, The quadratic formula
23 Sep 2014  12:10 amThe quadratic formula is to solve for x in the general quadratic equation, when factoring fails. 
Sep 23, Binomial Theorem Formulas
22 Sep 2014  10:14 pmBinomial Theorem Formulas