Each month, we will be recognizing one male and one female US Youth Soccer Player of the Month, whose accomplishments on and off the field stick out among the rest. While great performances in the game of soccer are appreciated, it's important to note that accomplishments off the field are valued just as much as those achieved on the field.


Most Popular Stories

300x250 Pom Usys
Search for "math OR mathematics"22 Jul 2017  11:31 pm 
Mathematics World Mourns Maryam Mirzakhani, Only Woman to Win Fields Medal
Scientific American  Math17 Jul 2017  11:45 amThe brilliant Stanford professor, killed by breast cancer at 40, worked with shapes unconstrained by the real world  Read more on ScientificAmerican.com 
Maryam Mirzakhani, Only Woman to Win a Fields Medal, Dies at 40
Mathematics16 Jul 2017  10:31 amDr. Mirzakhani, a mathematician at Stanford University, was the only woman and only Iranian ever to win what is often described as the Nobel Prize of mathematics. 
30th 5Star Review This Year—and It’s ONLY July!
Blog – DreamBox Learning20 Jul 2017  8:00 amIn 1985, actress Sally Fields delivered one of the mostquoted (and often misquoted) Oscar acceptance speeches of all time. After recounting that, more than anything else, she wanted the respect of her peers, Fields gushed, “You like me … you like me!” And, 30+ years later it’s still the stuff memes and gifs are made of—although it’s usually misquoted as, “…you like me, you REALLY like me!” Either way, respect from our peers on Facebook has us all feeling like Sally Fields today. Since January of this year, 40 DreamBox users have taken the time to post on our Facebook… 
Web Scraping and Mining Unstructured Data with MATLAB
Loren on the Art of MATLAB10 Jul 2017  8:39 amA lot of information is shared on the web and a lot of people are interested in taking advantage of it. It can be used to enrich the existing data, for example. However, information is buries in HTML tags and it is not easy to extract useful information. Today's guest blogger, Toshi Takeuchi shows us how he uses MATLAB for web scraping to harvest useful data from the web and then uses fuzzy string match to enrich existing data.ContentsNIPS 2015 PapersScraping Data from a Web PageMatching Scraped Data to Database TableFuzzy String MatchingValidating Fuzzy Match ResultsUpdating Missing Values…




Search for "math OR mathematics"

300x250 Pom Usys
22 Jul 2017  11:31 pmEach month, we will be recognizing one male and one female US Youth Soccer Player of the Month, whose accomplishments on and off the field stick out among the rest. While great performances in the game of soccer are appreciated, it's important to note that accomplishments off the field are valued just as much as those achieved on the field. 
Student learning, unified efforts are focus of new administrators
22 Jul 2017  11:25 pmRecent retirements, resignations and position reshufflings at the central office of Jefferson City Public Schools created the openings for Brian Shindorf to become the district's chief of learning, Lorie Rost, to have Shindorf's previous job of assistant to the superintendent of elementary education and Gary Verslues to be the district's assistant to the superintendent of secondary education, among other new administrative hires. In their positions, the three will be part of conversations at district Board of Education meetings, so it seemed timely to ask them to remind people of what they do and what they're looking forward to in their new positions as the school year approaches. 
Savvy Shopper: Priceless information courses available on internet
22 Jul 2017  10:55 pmFor example, when television was invented, there were many who thought the quantum leap in information flow placed our society at the cusp of a more enlightened age. Considering that my TV is tuned in to the Kardashians as I write this, it seems safe to say that these forecasts were a little optimistic. 
Everybody has a voice now and so we have stopped listening: Devdutt Pattanaik
22 Jul 2017  10:52 pm"Whenever I get a negative feeling, I turn to the Hanuman Chalisa. There's something about the Ramayana, and, Hanuman, especially, in the Ramayana, that calms you down," says the author. 
Breadfruit snack heading overseas  JP starts shipping in August, others ramp up fruit production
22 Jul 2017  10:50 pmBreadfruit hang from a tree in Bartons, St Catherine. Jamaica Producers Group will be exporting breadfruit chips for the first time, starting August 2017.



Scientific American  Math

Mathematics World Mourns Maryam Mirzakhani, Only Woman to Win Fields Medal
17 Jul 2017  11:45 amThe brilliant Stanford professor, killed by breast cancer at 40, worked with shapes unconstrained by the real world  Read more on ScientificAmerican.com 
What Are Mixed Fractions?
8 Jul 2017  5:00 amHow do they work? And how can you turn them into improper fractions? Keep on reading to find out!  Read more on ScientificAmerican.com 
Review: Remembering Sofya Kovalevskaya
3 Jul 2017  10:00 amMichle Audin’s book about Sofya Kovalevskaya is a fascinating combination of biography, personal reflections, and fictional digressions  Read more on ScientificAmerican.com 
4 More FAQs about Percentages
28 Jun 2017  7:00 amHow do you quickly calculate 25 percentof a number? Or 33 percentof a number? And how can you quickly calculate percentage increases?  Read more on ScientificAmerican.com 
Nil Communication: How to Send a Message without Sending Anything at All
27 Jun 2017  5:00 amPhysicists have exploited the laws of quantum mechanics to send information without transmitting a signal. But have they, really?  Read more on ScientificAmerican.com



Mathematics

Maryam Mirzakhani, Only Woman to Win a Fields Medal, Dies at 40
16 Jul 2017  10:31 amDr. Mirzakhani, a mathematician at Stanford University, was the only woman and only Iranian ever to win what is often described as the Nobel Prize of mathematics. 
Questions for: ‘Ending the Curse of Remedial Math’
13 Jun 2017  1:45 amWhat strategies does the CUNY Start program use to serve as a model for remedial students at the college level? 
YearEnd Roundup, 201617  All Our Lesson Plans, All in One Place
7 Jun 2017  6:07 amA Learning Network lesson plan directory, covering all academic subjects from this past year. 
Math Problem
16 May 2017  12:02 amHow long will it take you to figure out a problem that it took this boy less than a second to solve? 
Math Champion Wins With Answer About Pecking Chicks
15 May 2017  12:02 pmA 13yearold boy from Texas took less than a second to answer the word problem in the Raytheon Mathcounts National Competition.



Blog – DreamBox Learning

30th 5Star Review This Year—and It’s ONLY July!
20 Jul 2017  8:00 amIn 1985, actress Sally Fields delivered one of the mostquoted (and often misquoted) Oscar acceptance speeches of all time. After recounting that, more than anything else, she wanted the respect of her peers, Fields gushed, “You like me … you like me!” And, 30+ years later it’s still the stuff memes and gifs are made of—although it’s usually misquoted as, “…you like me, you REALLY like me!” Either way, respect from our peers on Facebook has us all feeling like Sally Fields today. Since January of this year, 40 DreamBox users have taken the time to post on our Facebook page, and 30 of them rated DreamBox Learning® Math 5 stars—the highest rating available! Now as mathematicians we love... 
It’s Here! Professional Development that Gives Teachers a Choice and a Voice!
18 Jul 2017  5:00 amBy now DreamBox blog readers, conference attendees, and members of DreamBox Nation have heard the buzz about an exciting, new, selfpaced professional development program that corresponds directly to what students are learning in the classroom. Today, the promise of truly personalized PD is finally a reality for DreamBox subscribers across the U.S. and Canada. DreamBox is pleased to unveil—a revolutionary new solution for professional development that empowers teachers to learn more about math concepts on an asneeded basis to improve differentiation and grow student achievement. Now teachers can finally get the coaching they need at a time and place that’s right for them—on demand and directly... 
What’s New in DreamBox Learning
13 Jul 2017  1:22 amWe are continuously innovating and working hard to create a stellar experience for our administrators, teachers, students and families. From on demand PD based on student achievement to streamlined navigation and resources, there are several enhancements to the DreamBox Insight Dashboard that will leave teachers cheering this back to school season. Data driven, relevant, and actionable PD within DreamBox. Available on demand and directly from within DreamBox, MyFlexPD uses student achievement data to surface corresponding professional development options that will empower educators to guide student success based on what students are learning. Teachers can access PD courses wherever they see the blue PD icon... 
25 School Districts Achieve Million Lessons Milestone
11 Jul 2017  6:00 amAccording to financial journalist Monica Mehta, “the more times you succeed at something, the longer your brain stores the information that allowed you to do so well in the first place.” If that’s true—and Mehta has neuroscience and researchers at MIT’s Picower Institute for Learning and Memory on her side—then completing one million DreamBox lessons bodes well for students in the topperforming districts across the United States and Canada. DreamBox Learning recently announced that 25 school districts each completed more than one million DreamBox math lessons during the 20162017 school year. To complete just one DreamBox lesson is to succeed. To complete over a million suggests that a... 
Math was Made for “Aha Moments”
6 Jul 2017  5:00 amFive years ago, the good folks at Miriam Webster added the phrase “aha moment” to the 2012 edition of their dictionary. They credited Oprah Winfrey with coining and popularizing the expression, which they define as “a moment of sudden realization, inspiration, insight, recognition, or comprehension.” Fortunately, you don’t have to be a billionaire media giant to have an aha moment. We recently asked DreamBox Nation teachers to share their flashes of insight. In reading their responses, we experienced an aha moment of our own. Math, by its very nature, is revelatory. Think about the time you first recognized a pattern, identified a relationship, or solved a particularly challenging problem … Aha! Am...



Loren on the Art of MATLAB

Web Scraping and Mining Unstructured Data with MATLAB
10 Jul 2017  8:39 amA lot of information is shared on the web and a lot of people are interested in taking advantage of it. It can be used to enrich the existing data, for example. However, information is buries in HTML tags and it is not easy to extract useful information. Today's guest blogger, Toshi Takeuchi shows us how he uses MATLAB for web scraping to harvest useful data from the web and then uses fuzzy string match to enrich existing data. Contents<ul><li>NIPS 2015 Papers</li><li>Scraping Data from a Web Page</li><li>Matching Scraped Data to Database Table</li><li>Fuzzy String Matching</li><li>Validating Fuzzy Match Results</li><li>Updating Missing Values with Fuzzy Match Result</li><li>Reviewing Unmatched</li><li>Substring Match</li><li>Updating Missing Values with Substring Match...</li></ul> 
MATLAB and the 2017 Eclipse – Part 2: Training the Volunteers
27 Jun 2017  7:34 amToday our guest blogger, David Garrison, will continue his series on MathWorks involvement in the 2017 solar eclipse.<ul><li>Part 1: The Citizen CATE Experiment</li><li>Part 2: Training the Volunteers</li><li>Part 3: Rehearsing for the Eclipse</li><li>Part 4: Imaging the Eclipse Here is Part 1 of the Series.</li></ul>Here is Part 2 of the Series.Contents<ul><li>Recap of Part 1</li><li>The Project Volunteers</li><li>The Equipment</li><li>Training the Volunteers</li><li>Any Questions?</li><li>Next Up: Practicing for the Eclipse</li></ul>Recap of Part 1In Part 1 of this series I discussed the total solar eclipse that will occur on August 21, 2017 where the path of totality will pass over the continental United States. The National Solar Observatory is running a citizen science project called the Citizen CATE... 
Customer Blog, a Great Resource, Especially for Earth Sciences
12 Jun 2017  5:21 amCustomer Blog, a Great Resource, Especially for Earth SciencesI recently started following a new blog by Martin Trauth, called MATLAB Recipes for Earth Sciences. Even if you are not an earth scientist (which, by the way, is part of my scientific lineage), you may find many useful nuggets there.Martin is a geoscience professor at University of Potsdam. He's written wellregarded textbooks, one with the same title as his blog (which he currently posts to at a very healthy pace, one I cannot sustain!). Martin's post cover a huge range of topics, many of which are not at all specific to, though helpful to, geoscientists. Some notable titles I read recently include:<ul><li>Missing Version History of MATLAB...</li></ul> 
MATLAB and the 2017 Eclipse – Part 1: The Citizen CATE Experiment
31 May 2017  6:43 amToday I’d like to introduce a guest blogger, David Garrison, who is a MATLAB Product Manager here at MathWorks. This is the first in a series of blogs over the next few months describing MathWorks involvement in an exciting project related to the 2017 solar eclipse.<ul><li>Part 1: The Citizen CATE Experiment</li><li>Part 2: Training the Volunteers</li><li>Part 3: Rehearsing for the Eclipse</li><li>Part 4: Imaging the Eclipse Here is Part 1 of the Series.</li></ul>Here is Part 1 of the Series.Contents<ul><li>The 2017 Solar Eclipse</li><li>The Citizen CATE Experiment</li><li>MathWorks Involvement in the Project</li><li>What are Your Plans for the Eclipse?</li><li>Next Up: Training the Volunteers</li></ul>The 2017 Solar EclipseAs many of you know, a total solar eclipse will occur on August 21, 2017 where... 
How to win ALL marbles in Mancala on your first move, with MATLAB!
22 May 2017  7:02 amToday's guest blogger is Anoush Najarian who leads the MATLAB Performance Team at MathWorks. And while she mostly focuses on helping MATLAB run fast, in her spare time, she likes to use MATLAB for hobby projects in robotics, math, and games.Contents<ul><li>Winning at Mancala</li><li>The Rules</li><li>Is There a FirstPlayer Advantage? (You Bet!)</li><li>Alternative Rule Sets</li><li>What's Next?</li></ul>Winning at MancalaLet me tell you what happened when I got tired of losing at Mancala, and decided to write some MATLAB code to play it. Shoutout to my daughter, sixth grader Natalie, for introducing me to the game, and being a partner in these experiments. The RulesNow, there are many ways to play the games in the Mancala family. The rule set we wrote the...



Homeschool Math Blog

Word problems involving "four times as many as"
21 Jul 2017  12:34 pmSomeone asked for help to explain the concepts of multiplicative word problems involving "as many as", like the ones below:1) Haley had four times as many dollars as her sister. Together they had $60. How much money does Haley have?2) Rachel had 5 times as many dollars as her sister, Nora. They had a total of $90. How much money did each of them have?The BAR MODEL is an excellent tool for helping children understand what is going on in these types of word problems.In (1), draw a bar for Haley and another for her sister. Divide Haley's bar into four parts, and make the other bar just one such part long.Haley Sister Now you will see that the TOTAL needs divided into FIVE equal parts —... 
Flash sale for Math Mammoth
13 Jul 2017  6:26 amHomeschool Buyers Coop is running a FLASH SALE for the large Math Mammoth bundles — get them at 40% off! This sale ends on July 17, 2017. 
Graph paper, and those who don't love math
3 Jul 2017  8:35 pmIf you have a few minutes, check outhttp://tjzager.com/2017/06/17/representationsandmanipulativesandtoolsandthings/It's an interesting and encouraging read. Thoughts about technology (no need for it at every turn), and how to teach those who don't love math, and how just a piece of graph paper can lend itself to a powerful learning tool...! 
What age do YOU think is old?
30 Jun 2017  6:33 amI just saw this in the IntMath Newsletter I subscribe to...QUOTEHere's an age equation that's pretty accurate:OldAge = 10 * √NowAgeWhen you're 16, old people are 40. When you're 50, old people are 70, and when you're 100, you know you're old!UNQUOTEHat Tip to Murray fromhttp://www.intmath.com/blog/letters/intmathnewsletterquadraticgraphscymathfoodlearning11234 
A fiveyear old GOT the connection between addition and subtraction
31 May 2017  11:09 amI just got this in from a customer... how PRECIOUS!QUOTELydia, who is not yet five years old, has just started the subtraction section of Math Mammoth 1A. She made an amazing discovery and wanted to tell you about it. A photo of her letter is attached, which a translation here."Dear Math People,I found outWhen you do a subtractionBackwardsIt's addingDid you know about that?Lydia"UNQUOTELydia's mom also said that she feels Lydia is going to be so amazed when the workbook points this out a few pages from now!



Denise Gaskins' Let's Play Math

How to Talk Math With Your Kids
18 Jul 2017  5:47 amA friend shared this video, and I loved it! From Kent Haines, a father who happens to also be a math teacher… “I hope that this video helps parents find new ways of interacting with their kids on math topics.” —Kent Haines More from Kent Haines <ul> <li>My First Math Event: Planning a mathplay party at the local library.</li> <li>What the Kids Made at My First Math Event: Symmetry art and fun with mirrors.</li> <li>Talking to Parents about Math Explorations: Plus a link where you can buy your own mirror book.</li> <li>Ana: An inspirational story about one student who struggled with math — and who still finds math hard, but worth the effort.</li> </ul> Advice and Examples of Talking Math with Kids If you enjoyed Kent’s video, you’ll love... 
Math Teachers and Homeschool Bloggers: We Want You!
17 Jul 2017  9:10 am[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 recent editions of this carnival. Click here to submit your blog post Don’t procrastinate: The deadline for entries is Friday, July 21. The carnival will be posted next week at Three J’s Learning blog. Would You Like to Host the Carnival? Hosting the blog carnival is fun because you get to “meet” new bloggers through their submissions. And there’s a... 
Playful Math Carnival #109 at Math Mama Writes
3 Jul 2017  4:26 amCheck out the new carnival of playful math for all ages at Math Mama Writes blog. Each month’s carnival brings you a great new collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun. <ul> <li>Math Teachers at Play #109 (a blog carnival)</li> </ul> This month’s post features books, animations, puzzles, and games. Early math, high school math, and writing in math class. Probability, statistics, and teaching tips. And much more! Click Here to Read the Carnival Blog Hey, Blogger, Can You Spare a Time? Do you write an education or family blog? Classroom teacher, math coach, homeschooler, parent, college professor, unschooler — anyone interested in helping kids play around with math? Please... 
Let’s Play Math in Korean
22 Jun 2017  9:51 amOoo, look at my shiny new book! Let’s Play Math is now out in Korean. How cool is that? You can find the book at these two major bookstores: And probably in other places where Korean education or parenting books are sold. I’m sorry to say I can’t read Korean — but I did play math there a couple years back. My daughter teaches English through EPIK, and I had a wonderful visit with her in Jeju. If you’re interested, you can see a few of my photos here, and my fractionmath sidewalk puzzle here. And if you know a Koreanspeaking family who wants to play math with their kids, I’d be honored if you share my book. Want to help your kids learn math? Claim your free 24page problemsolving booklet, and sign... 
10 Ways to Play Math with PlayDoh
20 Jun 2017  11:29 amToday we have a guest post from Lucy Ravitch, author of the new Kickstarter picture book Trouble with Monkeys: A math concept story of place value. She’s sharing a few ideas from her Math Activity Thursday (M.a.Th.) video series. Enjoy! Hello, math fans and enthusiasts! Each week I try to give you and your family a fun math activity to try. Two months ago I posted this video with ten ways to turn play dough into an engaging activity for lower and upper elementary math. If you want to make your own dough from scratch here are a few simple recipes. I encourage you to let your children play freely at first, before trying these activities. Below I have identified some of the math concepts that your kids will...



Basic mathematics blog

Find water left in a tank using arithmetic sequences
20 Jul 2017  7:41 pmA water tank is emptied at a constant rate. Initially, 36,000 gallons of water were in the tank. A the end of five hours, 16,000 gallons remained. How 
distance from the mountain
15 Jul 2017  7:45 pmJane drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Jane drove home, there was no traffic 
Price of 3 pens without discount
15 Jul 2017  7:25 pmA stationery store sells a dozen ballpoints pens for $3.84, which represents a 20% discount from the price charged when a dozen pens are bought individually. 
Speed word problem
10 Jul 2017  7:15 pmA truck left a depot at noon traveling an average speed of 40 kilometers per hour. How far from the depot and what time will it overtake another truck, 
A subtraction word problem
10 Jul 2017  7:36 amProblem #1: Peter has 20 dollars in his pocket. He buys a 32 ounces vanilla ice cream for 8 dollars. How much is Peter's change? Solution In this situation,



Computational Complexity

I would call these Galois Games but I can't
20 Jul 2017  2:47 pmHere is a game (Darling says I only blog about nonfun games. This post will NOT prove her wrong.) Let D be a domain, d ≥ 1 and 0 ≠ a0∈ D. There are two players Wanda (for Wants root) and Nora (for No root). One of the players is Player I, the other Player II. (1) Player I and II alternate (with Player I going first) choosing the coefficients in D of a polynomial of degree d with the constant term preset to a0. (2) When they are done, if there is a root in D then Wanda wins, else Nora wins. There is a paper by GasarchWashingtonZbarskyherewhere we determine who wins the game when D is Z,Q (these proofs are elementary), any finite extension of Q (this proof uses hard number theory), R, C... 
89944 Hat Problems
17 Jul 2017  6:26 amI've blogged about different hat problems a few times (seehere). The question arises: How many hat problems are there? The answer is really infinite (literally) but I will list some parameters and bound them reasonably to get an upper bound. Some of the combinations don't make sense, but we'll live with that. (I am also working on a website of hat problem papers. Its nowhere near finished yet and maybe never will be, but itsherefor your benefit. And for mine if there are some obvious papers I've omitted then comment or email me.) First off, what is a hat problem? Ignoring many parameters: There are n people and c different colors of hats and they are put on people's heads and the people have to... 
Solutions to some Hat Problem AND some points of interest.
13 Jul 2017  12:50 pmIn my last bloghereI asked three (known) hat problems since they may be new to you (one of them I just learned last week) and I had a point to make about them. I have WRITTEN UP the proofs heresince html is clumsy with math (or I'm clumsy with htmlmath), so this post is mostly about the points to make about these problems. I would urge you to read the writeup pointed to before reading the post. 1) N people 1,...,N, two colors R,B, Hats put on RANDOMLY (no adversary). People are in a line and pe sees person j's hat iff i ≤ j . There is a well known strategy where nobody passes which guarantees n1 get it right (seehere), but that strategy has EVERYONE get it right 1/2 of the time. We want MORE... 
Two hat problems you may or may not have seen but I have a point to make about one of them
9 Jul 2017  2:32 pmHat problems are fun and often require clever solutions. I have posted about one type of hat problemhere. In this post I ask three. For two of them I have a point to make which I will make when I post the answer later in the week. Feel free to post your thoughts and answers, BUT be warned that if you don't want to know the answer then don't look at the comments. 1) N people stand in a line and are numbered 1,2,3,..,n. If i < j then person i can see person j's hat color. Hats are going to be put on the heads RANDOMLY prob of RED or BLUE is 1/2. (so no adversary) The people, in order 1,2,3,..., n either say RED or BLUE or PASS. We want to maximize the probability that (1) someone does not say PASS, and... 
The Complexity of Rubik's Cube
5 Jul 2017  5:09 amIn my book I use Rubik's Cube as an example of a puzzle we can computationally solve efficiently (as opposed to Sudoku or Rush Hour). How does this square with the new result ofErik Demaine, Sarah Eisenstat and Mikhail Rudoy that finding the shortest solution is NPcomplete? New Scientist now proclaimsIt’s not you – solving a Rubik’s cube quickly is officially hard. No, it's still you. To study the complexity of Rubik's cube we can't just fixate on the 3x3x3 cube with its finite state space but on the general NxNxN cube. (One could also generalize to 3sided hypercubes in N dimensions but good luck constructing a 3x3x3x3x3 Rubik's cube.) For a given mixedup NxNxN cube we can find in polynomial...



IMA Journal of Applied Mathematics Current Issue

Limit cycles bifurcating from discontinuous centres
2 Jul 2017  5:00 pmAbstractIn this article, we study limit cycles in discontinuous piecewise linear vector fields in $\mathbb R^2$ and $\mathbb R^3$. More precisely, we address the problem of understanding the dynamics around a degenerated twofold singularity in $\mathbb R^2$ and $\mathbb R^3$, where it is also called Tsingularity, which behave as discontinuous centres after suitable perturbations of the separation boundaries. We prove that, in both systems, it is possible to obtain $k$ hyperbolic limit cycles bifurcating from these discontinuous centres, for any positive integer $k$. The same holds if $k$ is infinity. 
Finite difference methods of the spatial fractional Black–Schloes equation for a European call option
28 Jun 2017  5:00 pmAbstractWe study finite difference methods for solving a spatial fractional Black–Scholes equation on a finite domain which extends the classical Black–Scholes model by replacing the secondorder spatial derivative with a fractional derivative. We design first order and second order implicit numerical schemes for the spatial fractional Black–Scholes equation, and then analyse their stability and convergence. Some numerical examples are given to confirm our theoretic results and discuss the influence of the order of the fractional derivative on the option price. 
Spatiotemporal patterns in a diffusive model with nonlocal delay effect
15 Jun 2017  5:00 pmAbstractSteady states and periodic oscillations are two important solution forms in reaction–diffusion equations. In this article, we deal with a diffusive Lotka–Volterra system with nonlocal delay effect and Dirichlet boundary condition. Firstly, the existence and multiplicity of spatially nonhomogeneous synchronous/mirrorreflecting steadystate solutions are investigated by means of Lyapunov–Schmidt reduction. Then using centre manifold reduction, normal form analysis and equivariant bifurcation theory, we show that each of the standard Hopf bifurcations gives rise to only one branch of spatially nonhomogeneous timeperiodic synchronous waves, whereas each of the equivariant Hopf bifurcations... 
Solitary gravity waves and free surface flows past a point vortex
29 May 2017  5:00 pmAbstractNonlinear free surface flows past a disturbance in a channel of finite depth are considered. The fluid is assumed to be incompressible and inviscid and the flow to be twodimensional, irrotational and supercritical. The disturbance is chosen to be a point vortex. Highly accurate numerical solutions are computed. The basic idea of the numerical approach is first to develop codes to compute solitary waves and then to introduce appropriate modifications to model the point vortex. Previous results are recovered and new solutions are presented. 
Radiating solitary waves in coupled Boussinesq equations
24 May 2017  5:00 pmAbstractIn this article, we are concerned with the analytical description of radiating solitary wave solutions of coupled regularized Boussinesq equations. This type of solution consists of a leading solitary wave with a smallamplitude copropagating oscillatory tail and emerges from a pure solitary wave solution of a symmetric reduction of the full system. We construct an asymptotic solution, where the leading order approximation in both components is obtained as a particular solution of the regularized Boussinesq equations in the symmetric case. At the next order, the system uncouples into two linear nonhomogeneous ordinary differential equations with variable coefficients, one correcting the localized...



The Math Less Traveled

A few words about PWW #20
22 Jul 2017  2:08 pmA couple commenters quickly figured out what my previous post without words was about. The dots making up the image are at integer grid points , with the center at . There is a dot at if and only if and are relatively prime, that is, . Here is a slightly smaller version so it’s easier to see what is going on: I learned from Lucas A. Brown that this is sometimes known as “Euclid’s Orchard”. Imagine that there is a tall, straight tree growing from each grid point other than the origin. If you stand at the origin, then the trees you can see are exactly those at grid points with . This is because if a tree is at for some , then it is blocked from your sight by the tree at : both lie exactly... 
Post without words #20
8 Jul 2017  7:37 pm 
The curious powers of 1 + sqrt 2: recurrences
6 Jul 2017  10:51 amIn my previous post, we found an answer to the question: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? However, the solution depended on having the clever idea to add . But there are other ways to come to similar conclusions, and in fact this is not the way I originally solved it. The first thing I did when attacking the problem was to work out some small powers of by hand: and so on. It quickly becomes clear (if you have not already seen this kind of thing before) that will always be of the form . Let’s define and to be the coefficients of the th power of , that is, . Now the natural question is to wonder what, if anything, can we say about the... 
The curious powers of 1 + sqrt 2: a clever solution
21 Jun 2017  12:28 pmRecall that we are trying to answer the question: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? In my previous post, we computed for some small and conjectured that the answer is , since these powers seem to be alternately just under and just over an integer. Today, I’ll explain a clever solution, which I learned from Colin Wright (several commenters also posted similar approaches). First, let’s think about expanding using the Binomial Theorem: We get a sum of powers of with various coefficients. Notice that when is raised to an even power, we get an integer: , , and so on. The odd powers give us irrational things. So if we could find some way to... 
The curious powers of 1 + sqrt 2: conjecture
17 Jun 2017  3:03 pmIn my previous post I related the following puzzle from Colin Wright: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? Let’s play around with this a bit and see if we notice any patterns. First, itself is approximately so its powers are going to get large. Let’s use a computer to find the first ten or so: Sure enough, these are getting big (the tenth power is already bigger than ), but look what’s happening to the part after the decimal: curiously it seems that the powers of are getting rather close to being integers! For example, is just under , only about away. At this point, I had seen enough to notice and conjecture the following patterns (and I hope...



WordPress Tag: Mathematics

যেকোনো সংখ্যা কে 11,12 দিয়ে তাড়াতাড়ি গুন করবার সহজ উপায়
22 Jul 2017  10:22 pmকোন সংখ্যা কে 11 বা 12 দিয়ে গুন করতে বললে সবাই পারবেন। নামতা জানা থাকলে একটু তাড়াতাড়ি গুন করা যাবে। কিন্তু নিম্নলিখিত উপায় ব্যবহার করলে খুব তাড়াতাড়ি এবং সহজে যেকোনো সংখ্যাকে 11 এবং 12 দিয়ে গুন করতে পারবেন। দেখে নেওয়া যাক কি এই নিয়ম। 11 দিয়ে গুনের নিয়ম : উদাহরণ দিয়ে ব্যখ্যা করলে... 
A Minimal Turing Machine
22 Jul 2017  1:45 pmEpistemic status: likely. Tagged in: programming, turing machines, mathematics Now that this blog has lain dormant for many months, there can’t possibly anyone left to object to a complete change of pace. This was my plan all along — honest. One of the many things that has distracted my attention from blogging is that I have, at long last, gotten into a rather entrenched habit of programming. I do enough now that I take it completely for granted — it’s downright uncanny to look back at some of my posts and see me wanting to start programming again. But that’s enough useless preambling (worse, useless, navelgazing preambling), let us move onto the actual subject of this post: Turing Machines. I. I... 
Sets and Logic Foundations of Mathematics
22 Jul 2017  3:02 amConcepts, Definitions, Formulae of High School Mathematics: Some Symbolic Logic: ±– plus or minus, ≤– less than or equal to ≥ –greater or equal to – for all(universal quantifier), ∃– there exists(existential quantifier), ∄– there doesn’t exist, ∈ – belongs to, ∉ – doesn’t belong to, ∍ – such that, ! – unique, ∨ – or(disjunction), ∧ – and(conjunction), ¬ – not(negation), ⊨ – tautology (always true) p0, p1, …pn1 ⊨ q – logically imply, ⊨p↔q – logically equivalent, → – implies, if…, then(implication), ↔ – if and only if (iff, biconditional), ⇒ – inference eg p→q, p⇒q is deduction where, p→q, p are premises, q is... 
Fraction.
22 Jul 2017  1:06 amShe became a part of someone who had always been incomplete. theislandgirlinthecity 
"Chaos is merely order waiting to be deciphered"*...
22 Jul 2017  1:01 amLet us say we were interested in describing all phenomena in our universe. What type of mathematics would we need? How many axioms would be needed for mathematical structure to describe all the phenomena? Of course, it is hard to predict, but it is even harder not to speculate. One possible conclusion would be that if we look at the universe in totality and not bracket any subset of phenomena, the mathematics we would need would have no axioms at all. That is, the universe in totality is devoid of structure and needs no axioms to describe it. Total lawlessness! The mathematics are just plain sets without structure. This would finally eliminate all metaphysics when dealing with the laws of nature and...



Institute for Mathematics and Computer Science

Gifted Math and Computer Science Program to Award $25,000 in Scholarships
10 Jul 2017  10:00 pmAn IMACS class, back in the days of chalkboards, enjoys some friendly competition while playing the String Game. The Institute for Mathematics and Computer Science (IMACS) celebrates 25 years of serving talented children by awarding $25,000 in a mix of scholarships to enroll in its online courses or to attend its South Florida afterschool program. From humble beginnings of just 37 students in Plantation, Florida, IMACS has grown to include four South Florida learning centers and serves more than 4,500 students throughout the United States and in more than 15 countries. IMACS President, Terry Kaufman, attributes the institute's longevity and growth to parents' concerns about education. "Many of our... 
PreAlgebra Plus: An Online Math Course Designed for Gifted Thinkers
21 May 2017  10:00 pmPrealgebra, typically taught during the middle school years, serves as a bridge from the fundamentals of number sense and arithmetic to the rigors of algebra. Problemsolving and abstract thinking skills are further developed in order to be applied to more complex situations. A typical prealgebra curriculum is designed to promote computational or procedural fluency. Unfortunately, that is rarely enough to engage gifted minds. PreAlgebra Plus, an online course within the Elements of Mathematics: Foundations program, offers gifted students a better option. Five Reasons Gifted Students Prefer PreAlgebra Plus <ol> <li>PreAlgebra Plus was created specifically for the way gifted minds work. Course material invites...</li></ol> 
Educational Summer Camp Matters:Three Reasons Why Exercising the Mind is Important
22 Mar 2017  10:00 pmThe Institute for Mathematics and Computer Science (IMACS) believes in making sure kids exercise their minds this summer, in addition to their bodies, with fun yet educational summer camp experiences. Spending summers having fun and being outside is definitely important, but a small dose of educational summer camp is essential for all students too. Here are three reasons why: 1. Retain Knowledge: Summer vacation can often lead to forgetfulness and overall loss of learning. According to a study by the RAND Corporation, students lose, on average, one month of learning during the summer, all students lose some learning in math, and summer learning loss is cumulative over time. When kids aren't working certain... 
2016 Holiday Logic Puzzle from IMACS
14 Dec 2016  10:00 pmAs most people know, Santa Clause generates an annual list of children who have been sufficiently nice to warrant a Christmas present (and, of course, a complementary list of children who have been too naughty to deserve a present). Last December, while checking his list twice, Santa discovered that the status of four children — Amy, Bobby, Charlie, and Donna — remained in doubt. He decided to talk to the four of them in order to rank them from nicest to naughtiest. In his conversations, the children made the following claims: Amy said, "I am nicer than Charlie." Bobby said, "I am naughtier than Donna." Charlie said, "I am neither the nicest nor the naughtiest of the four of us." Donna said something as... 
Gifted Math: A Better Alternative to Acceleration
16 Nov 2016  10:00 pmFor mathematically talented children, acceleration is a commonly used approach to address their need to be challenged. Acceleration is often the most affordable option for schools, and it does help gifted children avoid unnecessary repetition. As such, acceleration works to a certain degree for all parties: Students are less bored; little or no extra work is required of teachers; districts incur little or no extra cost; and parents know that something is being done for their gifted child. Acceleration has become a "good enough" solution. While acceleration can save gifted math students from unnecessary repetition, by definition acceleration cannot go deeper than the standard curriculum, and deeper is what...



mathrecreation

interactive chladni figure page
17 Jul 2017  7:45 pmA while back there were some posts about generating Chladni Figures using R scripts. These scripts generated some pretty nice images, I thought. But, to experiment a bit more it would be nice to have something interactive, so I put together this page, which you can use to make images like the one below.Adding more vibrations to the surface, you can get some pretty intricate looking patterns:If you would like to try it out, please visit: https://dmackinnon1.github.io/chladni/ (source here). 
truchet en plus
29 Apr 2017  1:10 pmSince the previous post, I have been playing around with more variations on Truchet tiles (using this page). The variety of appealing patterns that you can create from these simple tiles is impressive.the humble Truchet tileFor example, using this simple base tile you can create a pathlike effect, even to the extent that paths can seem to weave under and over each other. The patterns below use this effect to suggest links and knots.Truchet patters for two links (left) and a trefoil knot (right)Slight variations in the base tile can produce interesting effects. Here's an example that uses the traditional Truchet base tile.Bulging the dark right triangle into a quarter circle allows us create something that... 
truchet tiles
26 Mar 2017  2:13 pmA short while back, I posted about the images found in books about Froebelian kindergarten exercises, likeThe Paradise of Childhood (on Google Books here). These old books provide great examples of patterns and designs that can be easily drawn by hand with graph paper, in many cases only using arrangements of congruent 4590 triangles.Nineteenth Century Froebelian DoodlesA surprising variety of patterns can be formed by restricting things even further, considering the case where each square is cut in half along a diagonal with half of the square coloured black, the other coloured white (i.e. no blank or completely filled squares, as are found in the images above).Some arrangements of four Truchet... 
probability simulations using R
24 Mar 2017  12:01 pmAn ongoing side project of mine is learning how to use the statistics scripting language R, and have been putting putting together R markdown files that set up simulations for a variety of probability problems. You can find some of them here:https://dmackinnon1.github.io/r_examples/.These are simulations that generate data based on problems like the Birthday problem, the Monty Hall problem, and the Burnt Pancake problem. Learning scripting languages aside, it is always good to keep digging into probability problems: they confuse practically everyone. 
Ulam's two step cellular automata
7 Mar 2017  6:40 pmAbove are some of the nice images generated by a cellular automata described in one of Martin Gardner's essays about Conway's Game of Life (you can find the essays here). Cells have four neighbours (north, south, east, west), and follow only two rules that are applied at each step: if a cell has one live neighbour it turns on, and if a cell is on it turns off after two steps. The images above start happening around step 100 after turning on a single cell at the centre of a 61 by 61 grid.You can play with these here. Eventually, these will start to repeat or disappear completely (I suspect they will oscillate, but have not found out when yet). On a 5 by 5 board, a single central cell will lead to a pattern...



Math ∞ Blog

Alan Schoenfeld: At the Boundaries of Effective Mathematics Thinking, Teaching, and Learning
22 Jul 2017  10:06 pmAn Interview with Alan Schoenfeld: At the Boundaries of Effective Mathematics Thinking, Teaching, and Learning Alan Schoenfeld is the Elizabeth and Edward Conner Professor of Education and Affiliated Professor of Mathematics at the University of California at Berkeley. He has served as President of AERA and vice President of the National Academy of Education. He holds the International Commission on Mathematics Instruction’s Klein Medal, the highest international distinction in mathematics education; AERA’s Distinguished Contributions to Research in Education award, AERA’s highest honor; and the Mathematical Association of America’s Mary P. Dolciani award, given to a pure or applied mathematician... 
Dr. Devlin Finds Fibonacci
31 May 2017  8:47 pmWhat would make you write a book about writing a book you recently published on a 13thcentury mathematician? When you’re Stanford University’s Keith Devlin (aka, NPR’s “The Math Guy”) and the mathematician is Leonardo of Pisa (aka, “Fibonacci”), the story of researching the first book, The Man of Numbers, becomes an incredible story in itself: Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World. What makes Devlin’s story so compelling is that it involves many other people, multiple countries, 900+ years, and enough setbacks, twists and turns, courage, and fortitude to rival fictional adventure. Throw in the idea that Leonardo’s work helped revolutionize... 
Models and Delving Deeper Into Division
30 May 2017  8:39 pmModels and Delving Deeper Into Division Last month, we unpacked the longdivision procedure taught in American K6 classrooms, tied it into the standard “long multiplication” algorithm, discussed issues with the loss of information traded for an increase in speed and efficiency, and also explore some alternative methods for doing long division. What was taken for granted was that we knew what division “is” (I use scare quotation marks here advisedly: it’s dangerous to try to be too restrictive about the underlying meaning of “simple, elementary” mathematical operations, and I do so here without wishing to suggest that what I am offering is or could possibly be definitive). My sense is... 
Keith Devlin: An Ambassador of Mathematics for Many Eras
30 May 2017  9:32 amAn Interview with Keith Devlin: An Ambassador of Mathematics for Many Eras Keith Devlin Dr. Keith Devlin is a cofounder and Executive Director of the university’s HSTAR institute, a cofounder of the Stanford mediaX research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow, a Fellow of the American Association for the Advancement of Science, and a Fellow of the American Mathematical Society. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. In this connection, he is a cofounder and President of an educational technology company, BrainQuake, that creates mathematics learning video games. He also works... 
What’s Hiding Within Long Division?
29 Apr 2017  11:52 pmLook familiar? For most people, if they ever learned to do long division properly, they had to “master” something similar to the above procedure/algorithm. What was not required was having the vaguest notion of what’s going on, why anyone should care about knowing how to do it, or why, if you did have some idea about what the answer was supposed to mean, this mumbojumbo got you to that answer correctly. Another way of describing the situation is “a black box.” You take two numbers, throw them into the “long division box,” turn the handle as many times as necessary, and – voila! – out pops the magic quotient, with a remainder, if any, in some form or other. Fabulous! Who needs conceptual understanding...



Motion Math

Introducing Bounce for web!
6 Jul 2017  10:25 amWe’ve brought our game Fractions to the web with a new character, a new name, and seven times (!) more levels. Fractions was Motion Math’s first game, and in addition to winning awards such as... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
Playing with Prototypes
11 May 2017  12:27 pmPrototyping is one of the most important stages in the development of Motion Math’s games – the process to get our ideas from paper to something interactive and playable that we can test... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
Motion Math is now live on the web!
23 Feb 2017  11:53 am“Can my students play Motion Math on Chromebooks?” That’s the most common question we’ve been asked over the years by teachers. Well, that and “How do you make... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
Promoting a Growth Mindset Through Personalized Mindset Coaching
30 Nov 2016  6:20 amMotion Math’s company mission is to help children find delight in intellectual challenge. When children learn to love the experience of struggling through frustration and confusion,... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
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! ]]



Math for all Grade blog

Jun 29, mathforallgrades
28 Jun 2017  10:55 pmmath for all grades covers in depth all math subjects :algebra, arithmetic, calculus with essential concepts and unlimited solved problems. 
Jun 1,
1 Jun 2017  2:34 am 
May 10, Percent
10 May 2017  3:20 amPercent is a fraction with denominator hundred. How to convert percent into decimals, fractions and ratios are problems in percentages. Percent more, percent less are other problems. 
May 10, Triangle Inequality Property of sides
10 May 2017  2:52 amTriangle Inequality Property of sides 
May 10, Percentages1
10 May 2017  2:06 amPercentages1



MIND Research Institute Blog

Tapping Toward a Better Understanding of Slope
18 Jul 2017  9:00 amThoughts of a traditional math classroom may bring to mind images of students sitting silently at desks while a teacher works through a math problem on the board. There could be more to this scene though. Perhaps one student is using her fingers to keep track of numbers while another quietly taps his pencil along to key points of the equation. These are both small examples of embodied cognition, the idea that features of thought are shaped by aspects of the body other than the brain. Counting with fingers and tapping along to certain points on a number line can help with basic mathematical concepts, but what happens when it comes to understanding something a bit more complex? For instance, it can be... 
Making Math Second Nature
11 Jul 2017  9:00 amSome of our knowledge of the world is so well ingrained in us, that we don’t even have to think about it. Consider a chair, for example. When we see a chair, we know immediately what it is and how to sit on it. We even know different ways to sit depending on if it’s a stool or an easy chair or a beanbag. And this is all automatic, without thinking about it. Our brain has rich networks of information, called schemas, about chairs (and many other things). These schemas are created in the brain when we learn through theperceptionaction cycle. That’s what neuroscientists call the process in the brain where humans observe something in the world around them, decide to take action on their environment,... 
Three Ways a Touch Screen Can Help Students Succeed in Math
5 Jul 2017  9:00 amFingers, blocks, pebbles and a myriad of other physical manipulatives are all tools helping students problem solve. But does that usefulness carry over when physical manipulatives give way to digital ones?The answer is a resounding yes! In her dissertation paper“Do Gestural Interfaces Promote Thinking?”published in 2011, Ayelet Segal,confirms that interactions with touch screens are effective in helping students learn. The dissertation discusses three main types of interactions that go hand in hand with digital manipulatives: tapping, sliding, and rotating. 1. Tapping Because the action of tapping mimics discrete counting, it can be just as effective as counting pebbles or using... 
7 Best Practices For Using Digital Manipulatives in the Classroom
27 Jun 2017  9:00 amTry to think way back to when you first stopped using your fingers to count. (No, seriously. Take a second and try. Can you get back there?) Was it hard to stop your fingers from twitching? Did you find yourself imagining your fingers or another object in your head instead? Research on embodied cognition explores how physical gestures and manipulatives can benefit learning by strengthening encoding, reducing cognitive load, and inspiring the use of other strategies. Manipulatives literally allow students to play with and explore math concepts, building the neural connections that become foundational to symbolic math. With manipulatives, students have the chance to figure things out on their own. But,... 
Digital Manipulatives Help Facilitate Math Comprehension
20 Jun 2017  9:00 amManipulatives are any objects that students interact with in order to learn. Math educators have always relied on physical manipulatives to teach concepts to students such as pie wedges to showcase fractions, fake currency to explore the value of money, or blocks to build number sense. With education technology becoming more common in classrooms, a new set of digital manipulatives is being used to facilitate mathematical understanding. Digital representations that can be slid, flipped, turned, and dropped as if it were a real 3dimensional object are being leveraged to deepen the conceptual understanding of math. Concrete vs. Digital Manipulatives Research suggests that physical manipulatives are...



Ash Tutors

How to build selfconfidence in children
27 Jun 2017  2:13 amReading time: 3.2 minutes.Selfesteem is one of the greatest gifts you can give to your child. This is a gift that will last from childhood throughout their adult life. Positivity and selfconfidence help children try new challenges as well as deal with mistakes and try, try again! 
10 tips to prepare your child for secondary school
8 Jun 2017  4:22 amReading time: 3.9 minutes Moving up to Year 7 is a milestone in every child's life. I certainly remember my last day at primary school and the first at secondary! The summer holidays inbetween were a long run up to the great unknown.These days the 'transition' is much carefully thought out, and it's highly likely your child will have made many trips to their chosen school already, engaged with staff and pupils, and even participated in several lesson.However, any change can still be traumatic, so with that in mind, here are 10 tips on how to help prepare your child for the transition from primary to secondary school:1Talk to your child and listen to any concerns they might have.... 
What are Special Educational Needs (SEN)?
8 Jun 2017  4:10 amReading time: 5.2 minutes Section 20 of the Children and Families Act 2014 defines a child as having Special Educational Needs (SEN) if he or she... ''(has)... a learning difficulty or disability which calls for special educational provision to be made for them.''Or ''Their special educational needs may require extra or different provision in relation to thinking and understanding, as a result of physical or sensory difficulties, emotional or behavioural difficulties, difficulties with speech and language or how they relate to and behave with other people. Disabled children and young people may require extra or different provision, for example, if they are less mobile than... 
10 reasons to hire a private tutor for your child
5 May 2017  2:59 amReading time: 3.2 minutes Why hire a private tutor for your child? Here are 10 good reasons:The demand for private tuition is increasing, due mainly to the popularity of private tuition with parents who want to give their child extra support or prepare them for oncoming examinations.In no particular order, here are 10 reasons to hire a private tutor for your child. 1. Confidence building Some children lack confidence in school and as a result, they can fall behind and find themselves struggling academically. Private tuition can build a child's confidence in next to no time and guide them to academic success they might otherwise miss out on in school.'Getting things wrong' in... 
When is it safe to leave your child home alone?
5 May 2017  2:58 amReading time: 4 minutes Deciding when your child is ready to be left home alone is a decision not to be taken lightly.There are a lot of factors to take into consideration and it's made all that harder because there are no rules or laws to follow.The law doesn't say an age when you can leave a child on their own, but it's an offense to leave a child alone if it places them at risk. (Suitably vague!)It all boils down to how comfortable you and your child are with the idea as well as how adaptable and mature they are.While there is no determined legal age to leave a child at home alone, it should be sufficient to say that babies, toddlers and young children should never be left...
