The collapse of forprofit giant Corinthian Colleges, a chain felled by charges of fraud and predatory lending, left students fighting to have their federal loans discharged under a littleknown law meant for people just like them. But instead of a clear path to debt relief, many found themselves in an overwhelmly complex process.


Most Popular Stories

New federal rules could make it easier to have student loans forgiven
Search for "math OR mathematics"27 Oct 2016  9:52 pm 
Finding patterns in corrupted data
Mathematics News  ScienceDaily26 Oct 2016  7:47 amA new modelfitting technique is efficient even for data sets with hundreds of variables, say researchers. 
U.S. Students Improve in Sciencebut Just Barely
Scientific American  Math27 Oct 2016  5:45 amFourth and eighthgraders score better than before, but weak gains and overall poor marks hint at long way to go  Read more on ScientificAmerican.com 
Ian Stewart: Calculating the Cosmos
Mathematics24 Oct 2016  10:00 amA calculation challenge by the mathematician Ian Stewart, author of the newly released “Calculating the Cosmos: How Mathematics Unveils the Universe.” 
MATLAB arithmetic expands in R2016b
Loren on the Art of MATLAB24 Oct 2016  6:32 amWith pleasure, I introduce today's guest blogger, my colleague, S teve Eddins. He has been heavily involved in image processing capabilities in our tools and more recently has also contributed substantially to designing additions and improvements to the MATLAB language.Earlier this summer, I was writing some colorspace conversion code. At one point in the code, I had a Px3 matrix called RGB, which contained P colors, one per row. I also had a 1x3 vector, v. I needed to multiply each column of RGB by the corresponding element of v, like this:RGB_c = [RGB(:,1)*v(1) RGB(:,2)*v(2)…




Search for "math OR mathematics"

New federal rules could make it easier to have student loans forgiven
27 Oct 2016  9:52 pmThe collapse of forprofit giant Corinthian Colleges, a chain felled by charges of fraud and predatory lending, left students fighting to have their federal loans discharged under a littleknown law meant for people just like them. But instead of a clear path to debt relief, many found themselves in an overwhelmly complex process. 
Graduation: Educators have other goals to achieve
27 Oct 2016  9:49 pmWest Virginia students, parents and teachers have reason to be proud they are now achieving a high school graduation rate of nearly 90 percent  fastapproaching the goal set for the year 2020. But outgoing State Superintendent of Schools Michael Martirano is wrong about what that means. 
Child of Refugees Tries to Achieve the American Dream
27 Oct 2016  9:46 pmIn the United States, the children of refugees often grow up disadvantaged as their parents struggle to adapt to a new life and support a family. That is Xiao Hoa Michelle Ching's story. 
Beaumont Child in Dallas for Recovery from Mystery Illness
27 Oct 2016  9:46 pmA rare and mysterious illness called acute flaccid myelitis, is paralyzing some children across the country and here in North Texas. A rare and mysterious illness called acute flaccid myelitis is paralyzing some children across the country and here in North Texas. 
Dual immersion can improve learning ability
27 Oct 2016  9:42 pmIt would allow school districts to create dual immersion programs. Proposition 58 would replace Proposition 227, which currently mandates that English is the only language allowed to be used in classrooms, besides foreign language courses.



Mathematics News  ScienceDaily

Finding patterns in corrupted data
26 Oct 2016  7:47 amA new modelfitting technique is efficient even for data sets with hundreds of variables, say researchers. 
Breakthrough in quantifying belief system dynamics
24 Oct 2016  10:27 amIt's no secret humans are social creatures with beliefs that are, literally, all over the map. What wasn't known was how those beliefs are influenced by our social interactions. Now sociologists have developed a mathematical model that describes the relationship between belief systems and interpersonal influence, and what happens when underlying beliefs change. 
Mathematical analysis reveals architecture of the human genome
20 Oct 2016  11:26 amMathematical analysis has led researchers to a formula that can describe the movement of DNA inside living human cells. Using these calculations, researchers may be able to reveal the 3D architecture of the human genome. In the future, these results may allow scientists to understand in detail how DNA is organized and accessed by essential cellular machinery. 
Army of agents to tackle corrupt officials, tax evaders, terrorists, and botnets as game theory gears up for the chaos of the modern world
20 Oct 2016  9:07 amMany of the world's major problems are spawned not from monolithic blocks of selfinterest, but from a vast array of single entities making highly individual choices: from lone wolf terrorists to corrupt officials, tax evaders, isolated hackers or even armies of botnets and packages of malware. Game theory needs to catch up, and new research by mathematicians has just found the way to do that by giving game theory calculations an enormous army of 'agents'. 
Study solves 50yearold puzzle tied to enigmatic, lone wolf waves
4 Oct 2016  8:17 amSolitary waves called solitons are one of nature’s great curiosities. In a new paper, a team of mathematicians, physicists and engineers tackles a famous, 50yearold problem tied to these enigmatic entities.



Scientific American  Math

U.S. Students Improve in Sciencebut Just Barely
27 Oct 2016  5:45 amFourth and eighthgraders score better than before, but weak gains and overall poor marks hint at long way to go  Read more on ScientificAmerican.com 
Math Puts a New Twist on Solving a Rubik's Cube with the Fewest Moves
26 Oct 2016  12:30 pmFor this puzzle with over 43 quintillion permutations, author Ian Scheffler explains how players have found the most efficient route to resolving a Rubik’s cube.  Read more on ScientificAmerican.com 
How to Use Statistics to Understand Poll Results
26 Oct 2016  7:00 amLearn how to use statistics to understand the significance of the latest political polling results and to keep yourself from being duped by misleading information  Read more on ScientificAmerican.com 
Solving the Rubik's Equation
24 Oct 2016  12:30 pmAuthor and “Speedcuber” Ian Scheffler reveals some of the math behind how you could solve the Rubik’s cube puzzle.  Read more on ScientificAmerican.com 
Why Math Education in the U.S. Doesn't Add Up
24 Oct 2016  4:30 amResearch shows that an emphasis on memorization, rote procedures and speed impairs learning and achievement  Read more on ScientificAmerican.com



Mathematics

Ian Stewart: Calculating the Cosmos
24 Oct 2016  10:00 amA calculation challenge by the mathematician Ian Stewart, author of the newly released “Calculating the Cosmos: How Mathematics Unveils the Universe.” 
What Your Brain Looks Like When It Solves a Math Problem
28 Jul 2016  9:26 amResearchers demonstrated a method for reconstructing how the brain moves from understanding a problem to solving it. 
Howard Raiffa, Mathematician Who Studied Decision Making, Dies at 92
13 Jul 2016  7:24 pmHe was cofounder of the Kennedy School of Government at Harvard and a professor at the university for 37 years who pioneered decision science. 
Letters to the Editor
27 Jun 2016  10:30 amReaders react to articles in Science Times. 
Uncovering a Tale of Rocket Science, Race and the ’60s
20 May 2016  12:51 pmTaraji P. Henson and Octavia Spencer star in “Hidden Figures,” a largely untold story of AfricanAmerican mathematicians in the space program.



Loren on the Art of MATLAB

MATLAB arithmetic expands in R2016b
24 Oct 2016  6:32 amWith pleasure, I introduce today's guest blogger, my colleague, S<ol> teve Eddins. He has been heavily involved in image processing capabilities in our tools and more recently has also contributed substantially to designing additions and improvements to the MATLAB language.Earlier this summer, I was writing some colorspace conversion code. At one point in the code, I had a Px3 matrix called RGB, which contained P colors, one per row. I also had a 1x3 vector, v. I needed to multiply each column of RGB by the corresponding element of v, like this:RGB_c = [RGB(:,1)*v(1) RGB(:,2)*v(2) RGB(:,3)*v(3)];But since I was using an internal developer build of MATLAB R2016 (released on September 14), I didn't type the...</ol> 
MultiArmed Bandit Problem and Exploration vs. Exploitation Tradeoff
10 Oct 2016  6:59 amCasino slot machines have a playful nickname  "onearmed bandit"  because of the single lever it has and our tendency to lose money when we play them. They also inspire the creativity of researchers. Today's guest blogger, Toshi Takeuchi, will introduce an interesting thought experiment known as multiarmed bandits. image sourceOrdinary slot machines have only one lever. What if you had multiple levers to pull, each with different payout. This is a multiarmed bandit. You don't know which lever has the highest payout  you just have to try different levers to see which one works best, but for how long? If you keep pulling the low payout lever, you forego more rewards, but you won't know which lever is... 
Indexing with Curly Braces
26 Sep 2016  6:57 amI have talked about indexing a bunch of times in the past, including my last post. Recently I have visited quite a few customers who still get tripped up a bit sometimes. So I thought I'd try again.Contents<ul><li>Cell Arrays</li><li>Where People Trip</li><li>How to Extract Contents from a Cell</li><li>What If I Want the Contents from Multiple Cells?</li><li>Tables</li><li>Extra the Data Compatible with Numbers</li><li>Follow Up</li></ul>Cell ArraysWhat are cell arrays? In MATLAB, they are variables that hold, in each "cell", other MATLAB variables. And they are "regular". By that, I mean that they have a uniform layout, equal numbers of elements in each row, each column, each page, etc. as you march along the dimensions. How do you get information into them, and out from... 
Introducing String Arrays
15 Sep 2016  6:02 amToshi is back for today's guest post. You may have seen Toshi's earlier posts about text analytics and he often deals with text in his data analysis. So he is very excited about new string arrays in R2016b. One of the new features I love in R2016b is string arrays, which give you a new way to handle text in MATLAB in addition to the familiar character arrays and cell arrays of character vectors. String arrays are most helpful when dealing with text in your data. In today's post I walk through some practical examples with text data to demonstrate how to use string arrays.Contents<ul><li>Analyzing Baby Name Trends</li><li>String Concatenation</li><li>Combine Files to Create a Single Table</li><li>String Comparison</li><li>Memory Use and Performance of...</li></ul> 
Fifteen Years of MATLAB Central Memories!
6 Sep 2016  5:55 amWow! It's been fifteen years since MATLAB Central was set up for the MATLAB community! What a crazy and wonderful time it's been.Contents<ul><li>The Art of MATLAB</li><li>Favorite Topics</li><li>MATLAB Central is More than Blogs</li><li>Celebrate</li></ul>The Art of MATLABThe first blog to appear was Pick of the Week. As you may know, I have been writing my blog for a fairly long time  I started in December 2005. I chose to call it the Art of MATLAB because that expresses my feelings about programming. There are often many ways to say the same thing. It's an art to say what you want and say it well. I hope I've accomplished that most of the time.I know I've messed up sometimes, and thankfully, with smart and generous readers as you are, I am...



Homeschool Math Blog

Quilting and math  patterns!
25 Oct 2016  3:01 pmMathematics has been called the science of patterns, and here's another field that is all about patterns: QUILTING. Fascinating patterns and lots of eye candy!Go check out this math teacher's take on a visit to a quilt show with tons of beautiful pictures. Enjoy! 
Number sense
24 Oct 2016  6:47 amA short video on NUMBER SENSE  the ability to work flexibly with numbers.We want to encourage this with our children! The example she uses is a multiplication problem, but developing number sense starts earlier, with addition. For example, you can encourage your students/children to solve 8 + 9 using several different strategies, such as: 9trick: The nine wants to become ten, so it takes one from the eight. Thinking this way, 8 + 9 becomes 7 + 10 which is an easier problem. doubles: 8 + 9 is really close to 8 + 8. If the child remembers that 8 + 8 = 16, then 8 + 9 is just one more. Similarly, 8 + 9 is just one less than 9 + 9.The same type of strategies can then be used in solving more complex addition... 
Angle theorems reference page
22 Oct 2016  12:22 pmI found a neat reference page about the important angle theorems, with visuals AND interactive versions: Includes for example such basics as angles around a point add up to 360 degrees; vertical angles are equal; corresponding angles are equal; and results about the angle sum of a triangle, a quadrilateral, polygons; plus a few more.Go check it out! I feel not only teachers, but students also might enjoy browsing through the page. 
In my room
17 Oct 2016  1:14 pmReading the news day after day in these times can be so troubling... I love this peaceful song and the thoughts in it... 
Video lessons for 6th grade
12 Oct 2016  12:46 pmAny 6th graders?Here's a handy index or list of my video lessons specifically meant for 6th grade. You'll find topics such as percent, decimals, ratios, statistics, beginning algebra topics, and more.



DeniseGaskins.com

Number Game Printables
27 Oct 2016  4:32 amOne step closer to getting my longawaited Multiplication & Fraction Games book out — I finished the printables file! At least, I hope I’ve finished. Sometimes it seems like whackatypo never ends… You have permission to copy and use these game boards and worksheets in your own local classroom, home school, math circle, coop class, etc. But you may not post them on your own website or sell them. If you’re not sure how copyright works on the Internet, check out Daniel Scocco’s Copyright Law: 12 Dos and Don’ts. Multiplication & Fraction Printables Click here to download the Multiplication & Fraction Printables, featuring mathematical model cards, hundred charts, and game boards to accompany the upcoming... 
Playful Math Carnival #101 at Arithmophobia No More
26 Oct 2016  2:17 pmCheck out the new carnival of playful math for all ages at Arithmophobia No More blog. You’re sure to enjoy this great collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun. <ul> <li>Math Teachers At Play Blog Carnival 101</li> </ul> The carnival features prime numbers, multiplication, arithmetic puzzles, magic, word problems, picture puzzles, games, mathematical conversations, and much more. Click here to go read the carnival blog! Past carnivals are still full of mathy treasure. Check them out: <ul> <li>Browse all the past editions of the Math Teachers at Play blog carnival</li> </ul> Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales... 
Math Teachers and Homeschool Bloggers: We Want You!
17 Oct 2016  9:10 amNOTE: After a couple of months in which personal/family issues combined with technical difficulties to sabotage our bestlaid plans, the MTaP is back on track. We WILL have a mathed blog carnival this month, so please submit your favorite blog post today! [Photo by Olga Berrios via flickr.] Do you have a favorite blog post about math activities, games, lessons, or handson fun? The Math Teachers at Play (MTaP) math education blog carnival would love to feature your article! We welcome math topics from preschool through the first year of 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 Don’t procrastinate: The... 
If You Read Fiction, Check This Out
1 Sep 2016  7:54 amI love reading fiction, especially when I find a good story by a newtome author. And that’s why I LOVE the Fiction River anthology series. I’ve been reading it for the last three years, and I just signed up for a twoyear subscription renewal. If you like pageturning, heartwrenching, uplifting (mostly) stories that cross and transcend genre, check it out: <ul> <li>Fiction River Kickstarter Campaign</li> </ul> I’m not the only one who enjoys Fiction River — the Kickstarter drive met its funding goal in only 23 hours. Wow! But there’s still plenty of time to get in on the fun… Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other... 
Making Sense of Arithmetic
29 Aug 2016  12:34 pmHomeschoolers have an advantage in teaching math: As our students grow, our own understanding of math grows with them because we see how the ideas build on each other. This is especially true for those of us with large families. We pass through the progression of concepts with each student, and every pass lays down another layer in our own minds. If you’d like to shortcut that process, check out Graham Fletcher’s Making Sense of Elementary Math video series. He’ll walk you through the topics, showing how manipulatives help build early concepts and gradually give way to abstract calculations. “Understanding the vertical progression of mathematics is really important in the conceptual development of...



Basic mathematics blog

Proof of the Law of Sines
24 Oct 2016  3:10 pmStraightforward proof of the law of sines. Easy to follow and understand 
Ambiguous Case of the Law of Sines
24 Oct 2016  8:10 amExplanation of the ambiguous case of the law of sines. 
Two Beautiful Law of Sines Problems
17 Oct 2016  4:37 pmTwo great law of sines problems that will show you how to use the law of sines to solve real life problems 
Law of Sines
17 Oct 2016  7:05 amWhat is the law of sines? How do I use it to find missing lengths in a triangle? 
A TwoDigit Number
10 Oct 2016  9:33 amSomething interesting about a twodigit number and the algebra behind it.



Computational Complexity

Get Ready
27 Oct 2016  4:29 amMy daughters, now in college, never knew a time when they couldn't communicate with anyone instantaneously. Molly, now 18, takes pride having the same birth year as Google. They have never in their memory seen a true technological change that so dramatically affects the world they live in. But they are about to. The 50's and 60's saw a transportation revolution. The Interstate highway system made local and national car and truck travel feasible. The jet engine allowed short trips to faraway places. The shipping container made transporting a good, made anywhere in the world, cheaper than producing it. We could have national and worldwide academic conferences. China became a superpower by shipping us... 
Exaggeration is one thing but this is....
24 Oct 2016  3:20 pmThiswebsite is about the history of math and lists famous mathematicians. The ones from the 20th century are biased towards logic, but you should go there yourself and see who you think they left out. There entry on Paul Cohen is... odd. Itshere. I quote from it:  His findings were as revolutionary as Gödel’s own. Since that time, mathematicians have built up two different mathematical worlds, one in which the continuum hypothesis applies and one in which it does not, and modern mathematical proofs must insert a statement declaring whether or not the result depends on the continuum hypothesis.  When was the last time you had... 
Alternate Histories
20 Oct 2016  5:07 amImagine if we had a machine that let us change some earlier moment in history and see what developed. We wouldn't actually change historythat would lead to paradoxes and other disasters, but we could see what would develop. Suppose Archduke Ferdinand was never assassinated. How would that have changed 20th century history and beyond? The same could be said for an academic field. Science flows like a story, with building results from other results, "standing on the shoulders of giants" so to say. But not all theorems are dependent on earlier ones and suppose that things happened in a different order. How would that have changed our field? Points to ponder: Suppose Gauss was alive today instead of two... 
This university does not discriminate based on....
18 Oct 2016  7:46 amI recently came across the following (I delete the name of the school) and also add my own comments in caps as they relate to UMCP hiring of professors. XUniversity, located in YZ, in hiring professors does not discriminate on the basis of race color . COULD AN HBCU DISCRIMINATE AGAINST WHITE PROFESSORS? religious HAS NEVER COME UP. COULD A RELIGIOUS SCHOOL DISCRIMINATE ON THIS BASIS? creed I LOOKED UP HOW IT DIFFERS FROM RELIGIONS CREED COULD BE ANY SET OF BELIEFS. WHAT IF ONE OF CANDIDATES BELIEVES ARE REPREHENSIBLE BUT WOULD NOT INTERFERE WITH THEIR JOB? JUST ASKING. age WHAT IF YOU WANT SOMEONE THERE LONGTERM? gender. COULD A WOMEN'S (MEN'S) SCHOOL DISCRIMINATE AGAINST MEN... 
2016 Fall Jobs Post
13 Oct 2016  3:44 amThe weather cools down, the leaves change color and you start thinking about what you plan to do after you graduate. As a public service every year about this time, we offer up links and advice for the job search for PhDs in theoretical computer science. For computer science faculty positions best to look at the ads from theCRAand theACM. For theoretical computer science specific postdoc and faculty positions check out TCS Jobs and Theory Announcements. If you have jobs to announce, please post to the above and/or feel free to leave a comment on this post. It never hurts to check out the webpages of departments or to contact people to see if positions are available. Even if theory is not listed as a...



Mathematics and Computation

Five stages of accepting constructive mathematics
10 Oct 2016  8:27 amIn 2013 I gave a talk about constructive mathematics “Five stages of accepting constructive mathematics” (video) at the Institute for Advanced Study. I turned the talk into a paper, polished it up a bit, added things here and there, and finally it has now been published in the Bulletin of the American Mathematical Society. It is not quite a survey paper, but it is not very technical either. I hope you will enjoy reading it. Free access to the paper: Five stages of accepting constructive mathematics (PDF) 
The new and improved Programming languages zoo
7 Sep 2016  1:39 amIt is my pleasure to announce the new and improved Programming languages Zoo, a potpourri of miniature but fully functioning programming language implementations. The new zoo has a decent web site, it is now hosted on GitHub, and the source code was cleaned up. Many thanks to Matija Pretnar for all the work. The purpose of the zoo is to demonstrate design and implementation techniques, from dirty practical details to lofty theoretical considerations: <ul> <li>functional, declarative, objectoriented, and procedural languages</li> <li>source code parsing with a parser generator</li> <li>recording of source code positions</li> <li>prettyprinting of values</li> <li>interactive shell (REPL) and noninteractive file processing</li> <li>untyped, statically and...</li></ul> 
Formal proofs are not just deduction steps
30 Aug 2016  8:08 amI have participated in a couple of lengthy discussions about formal proofs. I realized that an old misconception is creeping in. Let me expose it. In traditional mathematical logic (by which I mean firstorder logic, as established by Hilbert, Ackermann, Skolem, Gödel and others) the concepts of logical formula and formal proof are the central notions. This is so because the main goal of traditional logic is the metamathematical study of provability, i.e., what can be proved in principle. Other concerns, such as what can be computed in principle, are relegated to other disciplines, such as computability theory. It is too easy to forget that mathematical logic is only an idealization of what... 
What is a formal proof?
9 Aug 2016  5:28 amMike Shulman just wrote a very nice blog post on what is a formal proof. I much agree with what he says, but I would like to offer my own perspective. I started writing it as a comment to Mike’s post and then realized that it is too long, and that I would like to have it recorded independently as well. Please read Mike’s blog post first. Just as Mike, I am discussing here formal proofs from the point of view of proof assistants, i.e., what criteria need to be satisfied by the things we call “formal proofs” for them to serve their intended purpose, which is: to convince machines (and indirectly humans) of mathematical truths. Just as Mike, I shall call a (formal) proof a complete derivation tree in a... 
Hask is not a category
6 Aug 2016  1:36 pmThis post is going to draw an angry Haskell mob, but I just have to say it out loud: I have never seen a definition of the socalled category Hask and I do not actually believe there is one until someone does some serious work. Let us look at the matter a bit closer. The Haskell wiki page on Hask says: The objects of Hask are Haskell types, and the morphisms from objects A to B are Haskell functions of type A > B. The identity morphism for object A is id :: A > A, and the composition of morphisms f and g is f . g = \x > f (g x). Presumably “function” here means “closed expression”. It is then immediately noticed that there is a problem because the supposed identity morphisms do not actually work...



IMA Journal of Applied Mathematics  current issue

On the weakly competitive case in a twospecies chemotaxis model
30 Sep 2016  9:51 pmIn this article we investigate a parabolic–parabolicelliptic twospecies chemotaxis system with weak competition and show global asymptotic stability of the coexistence steady state under a smallness condition on the chemotactic strengths, which seems more natural than the condition previously known. For the proof we rely on the method of eventual comparison, which thereby is shown to be a useful tool even in the presence of chemotactic terms. 
Exact solutions describing the injectiondriven growth of a doublyperiodic fluid region in a HeleShaw cell
30 Sep 2016  9:51 pmWe construct a timedependent conformal map parameterizing a growing, doublyperiodic blob of viscous fluid of infinite connectivity formed by injection into an initially empty Hele–Shaw cell through an array of point sources, assuming zerosurface tension along the free boundaries of the blob. The map is from a preimage circular domain. It is identified as a function that is quasiautomorphic with respect to an associated secondary Schottky group and then constructed explicitly in terms of the Schottky–Klein prime function. A key role in this construction is played by the Schwarz function of the free boundary. Additional possible applications of these results include Hele–Shaw flows in the interior of... 
Wave stability in anisotropic generalized temperatureratedependent thermoelasticity
30 Sep 2016  9:51 pmTemperatureratedependent thermoelasticity is a theory of thermoelasticity in which two relaxation times are introduced into the equations of classical thermoelasticity. An important consequence of this theory is that heat now travels at a finite speed rather than the infinite speed implied by the diffusion equation. In an anisotropic temperatureratedependent thermoelastic material, it is found that four plane harmonic waves may propagate in any direction, all dispersive and attenuated, yet all are stable in the sense that their amplitudes remain bounded. An alternative theory that forces heat to travel at finite speed is generalized thermoelasticity in which the rate of change of heat flux also appears... 
Upscaling of a triphase phasefield model for precipitation in porous media
30 Sep 2016  9:51 pmWe consider a porous medium with a pore space that is completely filled by three different phases: two immiscible fluids (say water and oil) and a solid phase. One fluid phase contains dissolved ions, which can precipitate at the pore boundary to form the solid phase. The reverse process of dissolution, is also possible. Consequently, the solid phase changes in time; its variation is not known a priori. The second fluid contains no solute and has no interaction with the solid phase. Starting from a standard sharp interface model for the porescale dynamics we develop a diffuse interface approach that accounts for the timedependent spatial distribution of the three species and the overall concentration of... 
Adapting the Kärger model to account for finite diffusionencoding pulses in diffusion MRI
30 Sep 2016  9:51 pmDiffusion magnetic resonance imaging (dMRI) is an imaging modality that probes the diffusion characteristics of a sample via the application of magnetic field gradient pulses. If the imaging voxel can be divided into different Gaussian diffusion compartments with intercompartment exchange governed by linear kinetics, then the dMRI signal can be described by the Kärger model, which is a wellknown model in Nuclear Magnetic Resonance. However, the Kärger model is limited to the case when the duration of the diffusionencoding gradient pulses is short compared to the time delay between the start of the pulses. Under this assumption, the time at which to evaluate the Kärger model to obtain the dMRI signal...



The Math Less Traveled

Primitive roots of unity
20 Oct 2016  4:15 amSo we have now seen that there are always different complex th roots of unity, that is, complex numbers whose th power is equal to , equally spaced around the circumference of the unit circle. Consider the first th root around the circle from the positive axis (i.e. the darkest blue dot in the picture above). Let’s call this number . For example, in a previous post we saw that . Then the other dots around the circle—the other th roots of 1—are obtained by taking powers of . The next dot is , the next is , … and finally . In my original post that kicked off this series, I drew circles with dots on only some of the spokes, like this: I explained one way to think about this: in the circle with ... 
Complex multiplication: proof
18 Oct 2016  3:24 amIn my previous post, I claimed that when multiplying two complex numbers, their lengths multiply and their angles add, like this: In particular, this means that there are always different complex numbers whose th power is equal to : they are equally spaced around the circumference of the unit circle. For example, here are the twelve th roots of : Did you figure out why? Here’s one way to understand it. If a complex number is at distance away from the origin, and makes an angle with the positive axis, then will be at distance from the origin (since lengths multiply), and will make an angle with the positive axis (since angles add). First of all, for all the complex numbers on the unit... 
Complex multiplication and roots of unity
14 Oct 2016  11:25 amIf played around with the question from my previous post, you probably found something like the following: That is, as the powers of we get , , and with all possible sign combinations. Of course, since , if we continue taking higher powers after that we will just get the same values repeated. Remember that is the complex number corresponding to the end of the first spoke on a circle. If we plot its powers, we find that they are exactly the other spokes of the circle! Every time we multiply by , we seem to rotate around the circle of the way. What’s going on? As it turns out, there’s nothing magical about these particular values—this is just how complex multiplication works! Plot any complex... 
Complexifying our dots
11 Oct 2016  8:16 pmIt’s time to up our game a bit. Previously we have considered some cool pictures with dots and bespoked circles, looking for patterns, without really considering what sort of mathematical objects these circles might represent. In fact, they turn out to have a close connection to complex numbers. Recall that a complex numbers are built from real numbers together with the “imaginary unit” (which is just as real as real numbers!) which has the property that . A complex number is of the form for real numbers and , and we can think of complex numbers as living in a twodimensional plane, where we usually think of real numbers as the horizontal axis, and imaginary numbers as the vertical axis. So the... 
Totient sums
7 Oct 2016  12:31 pmI took a bit of a break to travel to Japan for a conference, but I’m back now to continue the series I started with Post Without Words #10, a followup post, and Post Without Words #11. Recall that we have dots on circles with spokes, like this: Circle has a dot on spoke if and only if (the spokes are numbered from zero). In PWW #11, I showed some pictures like this: We have here the circles with , , , , , and spokes—one for each divisor of . The colors highlight the fact that if we take all these circles and superimpose them on each other, we get exactly one dot at the end of each spoke. Does this always happen? In fact, it does. First, as I explained in a previous post, a spoke in a...



eon

If there is some good inflammable stuff it will catch fire
21 Oct 2016  8:06 pmDo not try to satisfy your vanity by teaching them great many things. Awake their curiosity. It is enough to open the minds, do not overload them. Put there just a spark. If there is some good inflammable stuff it will catch fire. The quote appears at the end of chapter 14 of Polya’s Mathematical Discovery. Polya attributes the quote to Anatole France from Le jardin d’Epicure. Perhaps he translated the French into English. He further adds: There is a great temptation to paraphrase this passage: “Do not try to satisfy your vanity by teaching high school kids a lot of … just because you wish to make people believer that you understand it yourself …” Yet les us resist temptation.... 
Catalan numbers
20 Oct 2016  5:22 pmI really enjoyed reading Federico Ardila’s article in the Mathematical Intelligencer. Apparently there was a vote of 3030 members at an assembly of CUP (Not Cambridge University Press but the Candidatura d’Unitat Popular). The vote had to do with forming an alliance with another party and ultimately related to the independence of Catalonia. The amazing thing that happened was that the vote came out 1515 Yes and 1515 No. The probability that a YESNO vote of 2m persons ends up in a tie is [tex] \binom{2m}{m}/2^{2m} [/tex], closely related to the Catalan number [tex] \binom{2m}{m}/(m+1) [/tex]. I love the dual connections and of course Ardila did not fail to mention Stanley’s Enumerative Combinatorics. What... 
Truncatable Primes
27 Sep 2016  7:06 pmA colleague asked about sequences of primes a(n) such that a(n+1) is obtained by appending a single digit (in base 10) to the right of a(n). For example: 3, 31, 311 … Some thinking lead to the conjecture that such sequences are of finite length and that it is possible to use an exhaustive search to find all of them. A natural question would be what is the longest possible sequence but I was unable to find any conclusive answer on the web. So I decided to write a simple (and not very efficient) recursion in maple to search for all such primes. Here’s my ugly code: cat3prime:= proc(n) local d, s, i; s:=n; d:=irem(n,10); if isprime(s) then print(s); return(cat3prime(10*s+1)); else for i from d to 7 by 2 do ... 
Twin corrections
19 Sep 2016  5:41 pmToday is the 20th anniversary of the passing of Erdős and I would like to make two corrections. I had always thought the accent on Erdős’ name was ö , html code ö but it is actually Hungarian, html code ő. The second is the coffee quote which I had attributed to him. I realised my mistake a number of years ago but never got a chance to correct it online. Both errors were perpetuated in this post from 2004. Here is a quote from Erdős’ paper “Child Prodigies” In Hungary, many mathematicians drink strong coffee, in fact Rényi once said “a mathematician is a machine which turns coffee into theorems.” Correction done but sadly I am still not quite sure how to pronounce his name... 
Bollobas on solving problems
24 Aug 2016  6:24 pmWhat you should be terrified of is a blank sheet in front of you after having thought about a problem for a little while. If after a session your wastepaper basket is full of notes of failed attempts, you may still be doing very well. Avoid pedestrian approaches, but always be happy to put in work. In particular, doing the simplest cases of a problem is unlikely to be a waste of time and may well turn out to be very useful. Bela Bollobas, from Advice to Young Mathematicians



WordPress Tag: Mathematics

Historical Math Facts And Information
27 Oct 2016  9:26 pmThe symbols used for subtraction and addition have been around for many years; however, it was not until the 16th century that most mathematical symbols were invented. Math equations before were written in words. Interesting Math Facts As far back as 3000 BC, it is believed that Ancient Egyptians made use of complex mathematics like arithmetic, geometry and algebra. This was proven by the use of equations to approximate the area of circles. Around the 11th century BC, Chinese mathematics was developed. And this included some significant concepts related to decimals, geometry, algebra, and negative numbers. Greek mathematics, on the other hand, was developed around the 7th century BC. This produced plenty of... 
Mathematics
27 Oct 2016  8:32 pmLearn more about different types of ways to learn m the depths of mathematics. 
Interactive early childhood teaching resource: Transport Sort  Readilearn
27 Oct 2016  5:21 pmSorting is a very important skill. We sort things every day without even thinking about it. We sort 
Generalized heaps
27 Oct 2016  4:06 pmMinmax heaps were introduced in [ASSS86] as an efficient way to support heap operations for both mi 
Easy as Pi... Well, As Easy as Coffee, Anyway
27 Oct 2016  12:15 pmWant to remember the value of Pi (3.1415926) in easy way? You can do it by counting each word



Institute for Mathematics and Computer Science

IMACS Success Spotlight: Fiona Brady
12 Oct 2016  10:00 pmCongratulations to IMACS graduate Fiona Brady who is beginning her studies at the University of Chicago. Fiona first attended IMACS HiTech Summer Camp when she was ten. Over the next eight years, she went on to complete IMACS’ universitylevel courses in University Computer Science, AP Computer Science: Java Programming, and Logic for Mathematics. Homeschooled since fifth grade, Fiona was awarded a National Merit Scholarship, named an AP Scholar with Distinction, and scored 2360 on the SAT. She is also a second degree black belt in Taekwondo and won a bronze medal at the 2013 AAU Junior Olympic Games. As a high school student, Fiona studied four years of undergraduate, advanced undergraduate, and... 
IMACS Success Spotlight: Zachary Farnsworth
19 Sep 2016  10:00 pmCongratulations to IMACS graduate Zachary Farnsworth who is beginning his sophomore year at Stanford. Zac began taking IMACS classes in first grade. Nine years later, he had completed all of IMACS Mathematics Enrichment and Computer Enrichment and IMACS UniversityLevel Computer Science. Zac graduated valedictorian of St. Thomas Aquinas High School, but not before being founder and captain of the Robotics Club and the Programming Team, earning the rank of Eagle Scout, and being named a National Merit Scholar Finalist and National AP Scholar. Having scored 2350 on the SAT, 800 on the SAT Math II Subject Test and 5′s on the AP Calculus AB, AP Computer Science, AP Calculus BC, and AP Statistics exams,... 
Gifted Math Program in Silicon Valley Has Roots in Owner’s Childhood
5 Sep 2016  10:00 pmThibault de Chatellus, President of IMACS California, and Assistant Director Debby Jensen are excited to bring IMACS' unique, logicbased enrichment program to families in Silicon Valley. The Institute for Mathematics and Computer Science (IMACS) has a new location in Silicon Valley! In today's IMACS Blog, we get to meet the President of IMACS California, Thibault de Chatellus (pronounced teebo), whose passion for making a positive impact led him to a new career in education. Thibault de Chatellus grew up in Boulogne, France, the second of four children whose parents made education a priority. Math education is very important in France and is used as a selection tool for admission to the most... 
Online Gifted Math Program to Grow to Several Hundred Students in Broward County Public Schools
3 Aug 2016  10:00 pmCorbin Diaz, a rising seventh grader in the BCPS/EMF program, is excited about learning advanced mathematics. Broward County Public Schools (BCPS) is increasing the number of middle school students enrolled in the Elements of Mathematics: Foundations (EMF) curriculum from 40 to several hundred students over the next several years. EMF was created for mathematically talented children by the Institute for Mathematics and Computer Science (IMACS), an independent teaching and educational research institute based in South Florida. EMF is an online curriculum that teaches prealgebra through precalculus plus several more advanced subjects in just three years. Graduates will be ready to study Advanced... 
The Multiplied Foundation and IMACS Provide Over $10,000 in Scholarships for HiTech Summer Camps
27 Jul 2016  10:00 pmPeyton Robertson visits with one of the scholarship recipients he is helping to sponsor at IMACS HiTech Summer Camp. The Institute For Mathematics and Computer Science (IMACS) has received a grant of $5,000 from the Multiplied Foundation Fund of the Community Foundation of Broward to provide full scholarships worth over $10,000 for 20 students to enroll in IMACS' 2016 HiTech Summer Camp. The Multiplied Foundation was founded by 14year old IMACS student, Peyton Robertson, with the mission of supporting and expanding STEM (science, technology, engineering and math) education. Peyton has a deep appreciation for how early exposure to enriching STEM activities can motivate a young person. At 11 years...



mathrecreation

notes for a spirolateral bestiary
25 Oct 2016  7:12 pmThe simple rules for creating generalized spirolaterals produce a surprisingly diverse menagerie of paths which trace out some familiar and lessfamiliar shapes, including regular polygons, star polygons, tangles, wreaths and infinitely long springs.some spirolaterals (graph here)In the formula below, a represents the angle that you turn by at each step, and m represents the maximum length of the sides that you count up to before repeating. If m = 1, all sides are length 1, if m = 2, then the sides alternate between length 1 and length 2, for m = 3, the lengths of the sides form the repeating squence 1, 2, 3, 1, 2, 3... etc.If the angle that you turn by is a rational multiple of 2pi, then the first... 
more familiar spirals in Desmos: spirolaterals
20 Oct 2016  7:45 pmAfter thelast post about how to draw some types of spirals using Desmos, I was pointed to a treasure trove of spiral and Desmos goodness in the twitter microblogging of@Veganmathbeagleand @GHSMaths. I haven't yet had the chance to dig too deeply yet, but looking forward to it.Also,@Desmos kindly improved upon one set of spirals: the "polygonal numbers on quadratic spiral" family, showing how to connect the dots and link up the points of the spiral (the improved graph is here). The technique: use the functions for x and y to create a family of parametrically defined line segments. To create a line segment between two points A and B, you can introduce a parameter t which moves you from A to B as t varies... 
some familiar spirals in Desmos
13 Oct 2016  9:23 pmI am revisiting some favorite spirals, plotting them in Desmos  for each below, try following the link to play with the graph yourself.start with a circleThe basic approach to drawing these spirals (and other things, like these curves), is to start with a circle defined using parametric equations. (graph here)By playing with this simple equation, often by just adjusting the r and t values, we can make a number of spirals. In many cases we are going to make spirals out of points, so we'll just be replacing r and t with integer sequences.Phyllotaxisish spiralsThese spirals are easy to create, and are a perennial favorite (pun intended: the sunflower connection). I've plotted these in Fathom/Tinkerplots,... 
understanding transformed functions with arrows
11 Oct 2016  7:33 pmI am taking a stroll down memory lane, helping a student with "Grade 11 Functions" (Ontario, MCR3U). An early topic is "introduction to functions." Here is a sample question that students are answering by the end of the unit:I find that questions like this, and many others, are best answered by drawing simple arrow diagrams. Here's what we would draw in this case:Which gives us the image point as (5/4, 10).Look interesting? You can start using these diagrams pretty quickly, after getting used to a few things.basic arrowsWe can write basic operations between two variables as an arrow diagram. For example b = a+ 2 can be written like this:This is instructing us: when you follow the arrow to get a b from an... 
brain and propeller fractals using Desmos
4 Oct 2016  7:28 pmI have been playing around with Desmos  it's very nice. The support for parametric formulas means we can play around curves defined by equations like these:The plus/minus sign in the expression for y means that you are going to have to make a choice in your formula for whether you want to have a plus or a minus sign for a particular term. We might choose to leave out all negatives and only pluses. This gives us "the brain fractal," Desmos version is shared here:If we choose to alternate plus and minus signs, we end up with something that looks like a propeller, Desmos version shared here:Modifying the formula slightly you can explore other members of the curve family, like this one:or this one:UpdateAfter...



Maths Tips From Maths InsiderMaths Tips From Maths Insider

Sumaze Math App – Perfect for all Ages
1 Oct 2016  7:15 amSumaze! is a cool problemsolving app that helps kids and adults build an intuitive approach to math. I’ve been playing it for for past week and it really is kind of addictive! What I also love about it is that it’s low stakes – no timers and no negative audio sounds when you get the puzzle wrong, so it’s perfect for nervous young mathematicians! Sumaze’s puzzles involve arithmetic, inequalities, the modulus function, indices, logarithms and primes and players don’t need ANY previous knowledge of these topics in order to play. This app was created by the UK organization Mathematics in Education and Industry (MEI) and the Sigma network who provide support for excellence in mathematics and... 
8 Things to Love About Tabtor Math
1 Sep 2016  10:50 pmBy far the most popular post on Maths insider is my post, 8 Things to Hate About Kumon! As a former Kumon instructor who now works as an instructor with Tabtor (a play on the words Tablet and Tutor!) I’m writing this post to give a unique perspective as someone who has worked for both companies. At Tabtor I look after many, many exKumon students including a family with 4 kids who switched from Kumon so that their children could explore the wider curriculum that Tabtor offers. So whether your kids are currently doing Kumon, another math program or you’re just starting to look into math programs to support your child’s math, let me share with you the 8 things to love about Tabtor. 1. Tabtor is... 
12 Brain Building Math Board Games for Curious Kids
31 May 2016  6:02 amWith summer coming up, I’m on the lookout for a new game or two to liven up quiet afternoons. It’s an added bonus if I can sneak a little math practice in without anyone noticing what I’m up to. Here are my top twelve picks for fun games with math skills at the core. Take a look at this previous post on math board games for even more inspiration. 1. SmashUp Game Aliens, Ninjas, Pirates, Dinosaurs and more battle to smash more bases than the opposing team. Eight different factions and dozens of combinations to try. ‘It’s really fast setup, it’s really fast play … It’s easy to pick up the rules.’ 24 players, recommended for age 13+. 2. Melissa & Doug ShutTheBox A deceptively... 
15 More Cool, Beautiful and Inspiring Math Quotes
20 May 2016  4:16 amMath Quote Inspiration Are you looking for some cool and beautiful math inspiration? Check out the Math Quote GIF’s below that highlight the eternal beauty of math. For more math inspiration check out my post 13 Cool, Beautiful and Inspirational Math Quotes. Enjoy! “Wherever there is number, there is beauty.” Proclus “The book of nature is written in the language of Mathematic” Galileo “Mathemathics is the queen of the science” – Carl Friedrich Gauss “The advancement and perfection of Mathematics are intimately connected with the prosperity of the State” Napoleon “A Mathematician who is not also something of a poet will never be a complete mathematician” Karl Weierstrass “The mathematician does... 
How to Help Your Child with Math – Even If You’re Not a “Math” Person
19 May 2016  7:57 pmHave you ever found yourself going round and round in circles when trying to help your child with math? Believe it or not – I’ve been there! Yes – I’m a math teacher – a lover of math Hello, this is Caroline from www.mathsinsider.com and I’m going to talk today about a question that a Maths insider reader asked which was,” How can I help my child with their maths if I’m not a math person?” I understand where you’re coming from So to start off, I’d just like to say that I obviously…I really like maths, I love sciences, I like geography, history I like most of the subjects, but one of the subjects that I don’t feel completely confident in supporting my kids in is English or Language Arts. I kind...



Math ∞ Blog

Data Science Boot Camps II
17 Oct 2016  6:03 pmNOTE: I will be posting to and administering the Math Blog while Antonio and his family recover from the fire at his home. Inc. recently ran an article: The Strange and Sudden Disappearance of a Coding Bootcamp Founder For months, Jim O’Kelly taught students how to code via Slack and video lectures. On September 27, he suddenly vanished. And with him, students say, was $100,000 in tuition money. This sad story of dashed hopes and possible international crime reminded me of my cautionary October 23, 2015 post Data Science Boot Camps In a difficult economy that continues to limp eight years after the crash in 2008, where international trade and other factors continue to eliminate stable, well paying middle... 
A fire destroyed everything I own. Math Blog will be on a hiatus.
16 Oct 2016  10:05 pmI regret to inform you that Math Blog will be on hold for a while due to tragic personal circumstances. On the evening of Thursday, October 13, 2016, an 18 year old girl having a domestic dispute with her mother allegedly set her own house on fire. The fire spread quickly to the whole fourplex, which included our townhome. The girl has been arrested by the police. My wife and I managed to rescue our dog, Annie, in the process. She came close to dying, but she is doing okay and is expected to recover. Despite trying for several minutes in pitch black acrid smoke, we simply couldn’t find our beloved cat of 8 years, Stella, anywhere in the house and she is sadly presumed dead in the fire at this point. We... 
Ronald Fisher and Maximum Likelihood Estimation Video and Slides
23 Aug 2016  7:20 am“Ronald Fisher and Maximum Likelihood Estimation” is a presentation that I gave to the Bay Area Entrepreneurs in Statistics (BAES) on August 20, 2016 at Symation in Richmond, CA — just north of Berkeley. BAES is a Meetup Group for people interested in the application of statistics to entrepreneurial ventures. A video and slides from the presentation are now online: https://youtu.be/biXQ1Z_NsDM Ronald Fisher and Maximum Likelihood Estimation BAES Presentation Maximum Likelihood Estimation (MLE) is one of the major foundational methods of parameter estimation and statistical inference. It is used in many fields from experimental particle physics, where it is regularly used to detect and measure the... 
Giveaway: Elements of Mathematics: From Euclid to Gödel
18 Aug 2016  12:00 amThis week we’re giving away a hardcover copy of Elements of Mathematics: From Euclid to Gödel. To enter Math Blog’s August giveaway, please follow the instructions below. PRIZE DETAILS Elements of Mathematics: From Euclid to Gödel by John Stillwell is a great dim sum, so to speak, of various mathematical areas. The topics covered are “elementary” and the clear explanations, as per the author’s admission, don’t assume mathematical knowledge beyond a high school level. Presented this way, the book would appear to be quite basic. In reality, I would expect most undergraduate students to be challenged at times while reading it. I’ll go further and say that despite being an extremely approachable book, I’m... 
July 2016 Noteworthy Math Books
11 Aug 2016  3:28 pmA bit late in the month, but here we are with July’s list of noteworthy math book releases. Should you want to receive these updates more often (on a weekly basis), consider signing up with Any New Books, my service for new book notifications. GENERAL AND POPULAR MATHEMATICS BOOKS Idea Makers: Personal Perspectives on the Lives & Ideas of Some Notable People Stores: USA  UK  Canada  Italy  Kindle  UK Kindle By Stephen Wolfram ISBN: 1579550037 Publisher: Wolfram Media, Inc. Publication date: July 7, 2016 Binding: Hardcover Estimated price: $13.86 Share this book on Twitter  Facebook  Google+ Overcomplicated:...



MathFour

I’m the New Secretary of Education
11 Oct 2016  5:01 amToday’s Breakfast Club 5:30 tweet chat topic is, “The new President appoints you Sec. of Education. What’s the first thing you do?” As a “I’m queen of the world,” question, it’s easy. I’d quadruple the salaries of teachers. As a “this is real” question, it’s not so easy. Because I’d have to figure out the budgetary requirements for quadrupling the salaries of teachers. Regardless, I think the extreme salary bump could do the trick. Teacher Salaries x 4 Why I think it will work… I know that teacher salaries in other (more successful) countries is super high. Higher than engineers, for instance. Which gives us indication that it may work. Apart from that, let’s consider what happens... 
Remembering Great Teachers
24 Aug 2016  12:10 pmI cried this morning. Kate is attending her last day of Kindergarten. That’s typical, right? My baby is growing up. I’m sensitive. But that’s not it at all. I’m going to miss her teachers so much! What makes good teachers? That’s a tough question. When I try to answer it, I rewind to all the good (and great) teachers I’ve had through the years. I’ve integrated a piece of each of them into my own teaching style: Miss Soap – 4th grade – taught us a standingatyourdesk dance to the Copa Cabana. From her I learned that being a freakish fan about people like Barry Manilow and Earl Campbell gets you remembered. (I’m a freakish fan of Weird Al and Matt Mullenweg. And I still sing and dance in... 
Math Teachers Have a Dirty Little Secret
15 Aug 2016  1:17 pmWhen a math teacher presents a problem in front of a class it goes something like this: <ol> <li>The teacher grabs her notes.</li> <li>She walks to the board.</li> <li>She writes a problem on the board.</li> <li>She explains the stepbystep solution with precision and elegance.</li> <li>She repeats the steps above a few times, then assigns the homework.</li> </ol> And based on this, students perceive that math is done just this way. They think math teachers can look at a problem and just KNOW how to do it, automatically. Here’s what happens before the classroom lesson: <ol> <li>The teacher sits down at home with the textbook and paper.</li> <li>She opens the book to the lesson’s topic.</li> <li>She works through an example problem.</li> <li>She gets confused, and reworks it.</li> <li>She figures out...</li></ol> 
Benjamin Franklin’s 13 Virtues for the Next 45 Years
9 Jul 2016  6:02 amI just turned 45 years old. Like, 2 hours ago. Some birthdays cause you more pause than others. This is one of those for me. I’m feeling like I’m at the midpoint of my life. Age 50 should be the middle, right? But I can’t help but think I’m past halfway. Will I live to be 90 years old? Looks like there’s a 2/3 chance I’m over halfway to death. According to the Society of Actuaries’ life expectancy calculator, I have only about 1/3 chance of living to age 90. I don’t know much about actuarial stuff. But I do know it’s based on averages. Which means about 2/3 of my sameaged peers will be dead in 45 years. Two out of three of us won’t be around. Goodness! What should I do with the second half of... 
Fact Family – Truth Mafia or Math Term?
26 Apr 2016  6:55 amHave you heard of a fact family? Does it make you think of the math mob? Or the truth police? Here’s what it is, really. “What the heck is a fact family?” I asked the first time I read the term. And the second, third, fourth and fifth times. “Fact families” – both the term and the families – seem to be everywhere these days. So what IS a fact family? Well, it’s a family of facts. But not parents or cousins. More like siblings. Here’s a nice one I’ve known for years: And here’s another one I’m fond of: Is that a real thing in math? The short answer is “no.” When you look it up on WolframAlpha.com, you don’t get a definition. It gives you the definition of “family.” And according to that definition,...



Motion Math

Factors of Learning – a new tool for personalization
20 Oct 2016  11:43 amWe’re excited to announce a new tool in the Motion Math teacher dashboard – Factors of Learning. This new report offers innovative data to help you build a student’s learning mindset – a... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
New game content…update your apps!
22 Sep 2016  10:38 amWe’re encouraging all Motion Math subscribers to update your apps, or politely ask your local IT guru to do so. (Even better, turn on “Automatic app updates” on your iPads.) Why?... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
The Loan Shark
22 Sep 2016  10:00 amWe’ve just added a new feature to the latest version of our economics simulation game Cupcake: the loan shark. Loans and debt are a significant economic and lifeskill issue worth discussing with... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
More ways to Match – new levels!
20 Sep 2016  5:26 pmHello Motion Math Educators! We hope your school year is off to a great start. We’ve been working hard to improve the Motion Math experience for administrators, teachers, and of course,... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
Top 7 Criteria of a Great Learning Game
17 May 2016  9:52 pmAccording to a 2015 study by Project Tomorrow, 62% of elementary school teachers use games in the classroom. At Motion Math, we’re positively thrilled that more and more teachers recognize gaming’s... [[ This is a content summary only. Visit my website for full links, other content, and more! ]]



Math for all Grade blog

Oct 22, Factoring Trinomials
22 Oct 2016  6:22 amfactoring trinomials which are perfect square trinomial and others. 
Jul 30, Math Help
30 Jul 2016  12:43 amMathhelp 
Jul 30, Geometryhelp
30 Jul 2016  12:43 amGeometryhelp 
Jul 30, Geometry Formulas
30 Jul 2016  12:43 amGeometry Formulas 
Jul 30, geometry problems
30 Jul 2016  12:43 amgeometry problems in angles, triangles, circles, quadrilaterals, three dimensional shapes.



MIND Research Institute Blog

JiJi Visits Medieval Times
26 Oct 2016  9:00 amWhy does math matter? A powerful way to answer this question is by exploring the impact of math on civilizations throughout history. At the Math Fairnext Saturday in Orange County, CA,you’ll get a chance to play ancient math games from Africa and explore the math behind the historical trade of blacksmithing, to name a few handson experiences. Understanding the origins of mathematical conceptscan help create deeper learning experiences that bring math to life. Take this example from the Middle Ages: We don't often think of the Middle Ages as a time of great mathematical achievement. However, one of the most important shifts in how we represent numbers occurred during the Middle Ages, and... 
Born for Math
25 Oct 2016  9:00 amPicture a proud lioness stalking the plains of the Serengeti, slinking silently towards an unsuspecting hyena. Suddenly, another one appears out of the brush. Unfazed, the lioness stalks on, confident in her strength and abilities. But then another hyena appears, and another. This gives her pause. Feeling outnumbered, our lioness silently slinks away, living to hunt another day. Although few would call this math in the conventional sense, this lioness is actually performing a quantity comparison in her head, comparing the number of hyenas she sees with some internal representation of what she considers to be “too many.” And it’s not just lions who possess this innate ability. Monkeys know how to... 
Advancing Equity in Education Through Wifi
20 Oct 2016  9:00 amWhat does equal access to high quality education look like? Today, the internet plays a central role. Students need online access to conduct research projects, use educational apps and access homework, while parents need to receive important communication from their school and teachers through the web. Students without reliable access to the internet face a distinct disadvantage in their education. And yet 31.4% of families (nearly 1 in 3) earning less than $50,000 still do not have internet access at home, according to Pew Research. Source:Pew Research Center For schools, this creates a serious conundrum: equity in education is no longer something confined to the resources within their walls. The... 
Math Fair Sneak Peek: Math Mystery Theater
18 Oct 2016  6:00 amWhat if we could change the perception of math from being an enigma to being a part of our everyday lives? Registration is filling up fast for the thirdannual Math Faira free, familyfun event that will excite young minds as they interact with mathematicallythemed activities, games, exhibits and performances. This year’s Math Fair will take place on Saturday, November 5th at the OC Fair & Event Center in Costa Mesa, CA. Perfect for all ages, Math Fair visitors will experience the beauty and power of mathematics while problemsolving. The Audience Solves the Mysteries at Math Mystery Theater The stage will be set for pure mathematical genius! The Math Mystery Theater’s talented performers... 
Behind the Scenes: How Math Fair Comes to Life
13 Oct 2016  9:00 amHow does a “popup” math museum come to life? For the third year in a row, MIND Research Institute is holding a free, community Math Fair, complete with mathematicallyinspired exhibits, performances, workshops and more. But how do we make the Math Fair happen? Let’s take a peek behind the scenes at the Math Fair. A lot of key strategies come into play when considering the exhibit experiences for the Fair, including interactivity, mobility, accessibility, deep learning opportunities and of course,fun! Here are just a few strategies to create a great learning event. 1. Build A Team First and foremost, gather together those who will contribute. At MIND, we call on our math content specialists and...



Ash Tutors

List of favourite resources for exam preparation
21 Oct 2016  1:18 amExams coming up or do you want to help someone with their studying? It's important to know how to prepare properly and set aside time for studying. With this in mind we have put together a collection of some of the best online resources for exam preparation. However, before we get to the resources, we would like to share 3 top tips to help you on the way to achieving your study goals: Tips for study success 1Knowing how to prepare for exams is one of the key ways to manage exam stress. Bear in mind, as well as good exam preparation, always believe in yourself and remember that if you have prepared for your exams properly in advance you should do fine. 2Start your revision early and don't leave it until... 
Top 10 things to do with kids in North West England
16 Oct 2016  3:58 amThere is no shortage of fun and interesting things to do with the family in North West England and in no particular order we have listed the top 10 things to do come rain or shine in this wonderful part of the country. 1Turbary Woods Owl and Bird of Prey Sanctuary in Preston is home to a unique collection of more than 90 birds of prey including falcons, owls, hawks and eagles as well as a few more unusual bird species. This is a fabulous day out for all the family and well worth the small admission charge. Try to catch the flying displays which take place daily weather permitting. Check the website for more details and times. Do bear in mind Turbary Woods is run by volunteers and is non profit making... 
How to help children fall in love with books
29 Sep 2016  5:51 amSome children are obsessive readers, while others are more than reluctant to even pick up a book. The question is, how can we get children interested in books in the first place? Here are 5 proven techniques to help children love books and become greater readers: 1 Join the local library. The library is not only a great place to encourage children to love books, it also teaches them to become responsible and treat things that don't belong to them with care. As well as a huge range of books and many opportunities for children to develop as readers, libraries also offer free story time sessions which promote literacy and social development.Go home and open a book! 2Let children read what they... 
Banish That Poor Handwriting Scrawl For good!
25 May 2016  2:56 amBanish that scrawl for good!  9 Handwriting Best Practices So, dear reader, you’re pushed for time  I can see that. So either scroll down a bit for the article, or download it for later.What’s your preference for ‘consuming’ content? Do you want to get a beautiful infographic / poster for your child’s bedroom wall? Download '9 Handwriting best practices' Infographic 
GCSE English  A Modern Parent's Survival Guide! (Year 11s too!)
14 Mar 2016  8:05 amGCSE English Language and English Literature Exams A Modern Parents’ Survival Guide! By Rachael (Ash Tutors ref: 181), Secondary School English Teacher “Help!” I hear you cry, “Why is GCSE English so much different, harder, confusing, befuddling and downright mindboggling compared to when I was at school?”



StudyPug

How to Deal With a Drop in Grades
14 Oct 2016  3:18 pmAs parents, you love your children and want them to succeed in everything they undertake. When it comes to school that generally translates to expecting them to bring home good grades — or grades in line with their natural abilities. When your child has been working up to the level of his or her ability and, all of a sudden, grades drop, it’s not surprising that you will worry. However, before you react strongly and try to try to rectify the situation, it’s important to take a deep breath and evaluate what is going wrong. Try not to be accusatory. By using “what” questions, rather than “why” questions, you’ll get more facts, and your child won’t be tempted to avoid blame by making... 
Study Skills for High School 101
23 Sep 2016  4:51 pmAs you begin your high school career, all of a sudden, grades become very important. Not only do they show your mastery of a subject and bring you pride; they have direct bearing on your opportunities to attend prestigious colleges and universities. College may still seem like it’s a long way off, but students who learn how to study and earn good grades early in their high school careers will have an easier time achieving the successes they want later. Not only will they gain entrance to the best postsecondary institutions; they will also have learned the discipline and focus necessary to success in many walks of life. You, too, can be one of the successful students whose report card features lots of... 
Study Tips for University Exams
9 Sep 2016  1:42 pmThe academic year is off and running, with papers and assignments looming large on each university course syllabus. As a student, you may find it challenging at first to budget your time accordingly to meet these homework deadlines; it is an adjustment to realize that no one but you is monitoring your work habits and output and that you alone are responsible for meeting deadlines. As you turn your attention to these projects, exams probably aren’t top of mind. After all, they happen later in the semester, so why worry about them now? However, if you don’t want to find yourself putting in an allnight study session prior to each of your exams, it’s worth considering your approach to preparing for them... 
Your US College Application – a Checklist
30 Aug 2016  1:46 amThe school year is upon us once again. For students graduating from high school next spring, it’s an exciting time: they are “top dogs” in their high schools and are looking toward a future filled with opportunities. Many students are planning to attend college next fall and have been working toward that goal for four years. They have studied hard and earned good grades; they have participated in extracurricular activities and done volunteer work to round out their studies; and they have earned solid scores on college entrance examinations. Now, it’s time to put the final piece of the puzzle in place: the college application. Before you, the student, dive into the guts of the application, it’s... 
Starting the School Year Off the Right Way
23 Aug 2016  2:33 pmAs the summer draws to a close, both children and their parents begin to think about preparing for the school year ahead. There are always supplies and clothes to be purchased and plans to make for a successful academic experience. After all, the slate I clean – no matter what the past year brought in terms of classes and grades, this year offers the promise of being equally good or better. Students, Take Note Students can help themselves, setting a positive tone for the year, by following a few tips set forth by Gabrielle Flank, writing for the Huffington Post. <ul> <li>Be organized. Ensure that you have the notebooks and writing implements you need to get your work done and stay organized.</li> <li>Plan ahead....</li></ul>
