We take a look at seven interesting and wellknown expats who did well in the Netherlands because it's always interesting to know the company you keep. Artist Marina Abramovic, famous for her performance artworks featuring tests of endurance, called Amsterdam home during the 1970s and 80s.


Most Popular Stories

Famous expats in the Netherlands, past and present
Search for "math OR mathematics"27 Aug 2016  3:37 pm 
Reproducing spots and stripes of a furry animal: Understanding nature's patterns with plasmas
Mathematics News  ScienceDaily23 Aug 2016  9:48 amPatterns abound in nature, from zebra stripes and leopard spots to honeycombs and bands of clouds. Somehow, these patterns form and organize all by themselves. To better understand how, researchers have now created a new device that may allow scientists to study patterns in 3D like never before. 
A Few of My Favorite Spaces: The Connected Sum of Four Hopf Links
Scientific American  Math20 Aug 2016  8:00 amThe mathematics of the Olympic rings  Read more on ScientificAmerican.com 
The Problem with SET®
Mathematics22 Aug 2016  10:30 amFor the popular card game SET®, how many cards is it possible to have on the table without there being a legal play? 
9 Back to School math activities for teachers, students, and parents
Blog – DreamBox Learning17 Aug 2016  11:00 pmIt’s nearly time to start setting the alarm clock earlier and revamp last year’s lesson plans! The truth is, teachers, parents, and students may all need a jumpstart to get psyched for the new school year after a summer of sun and fun. Here are nine activities to get your creativity motor running, and get parents and students onboard for a productive and fun year of math learning:Rekindle Your Passion for Math1. Get inspired. Want to see a great example of someone who has fallen head over heels for math? Check out comedian and selfproclaimed math geek Adam Spencer’s Ted Talk, Why I…




Search for "math OR mathematics"

Famous expats in the Netherlands, past and present
27 Aug 2016  3:37 pmWe take a look at seven interesting and wellknown expats who did well in the Netherlands because it's always interesting to know the company you keep. Artist Marina Abramovic, famous for her performance artworks featuring tests of endurance, called Amsterdam home during the 1970s and 80s. 
The NAACP's illconceived opposition to charter schools
27 Aug 2016  3:37 pmFirst graders at Two Rivers Public Charter School in the District attend a weekly school community meeting in 2012. "WHEN SCHOOLS get it right, whether they're traditional public schools or public charter schools, let's figure out what's working and share it with schools across America." 
Utah students hold steady in ACT scores
27 Aug 2016  3:00 pmUtah students held steady in their ACT scores this year, even as the national average slipped, the Utah State Board of Education announced Wednesday. More than 39,800 graduating seniors in Utah took the test this year, earning an average composite score of 20.2  virtually unchanged from last year. 
Graphic shows ACT scores for 2016; 2c x 4 inches; 96.3 mm x 101 mm;
27 Aug 2016  2:51 pmNearly twothirds of this year's high school graduates took the ACT college entrance exam, and their scores suggest that many remain unprepared for the rigors of collegelevel coursework. The testing company said Wednesday that only 38 percent of graduating seniors who took the exam hit the collegeprepared benchmark in at least three of the four core subjects tested  reading, English, math and science  down from 40 percent last year. 
Free coding course boosts interest in Halifax tech scene
27 Aug 2016  2:47 pmAround 115 people attended the introduction to web programming course put on by Lighthouse Labs at the Halifax Central Library. Another 80 were on a waiting list.



Mathematics News  ScienceDaily

Reproducing spots and stripes of a furry animal: Understanding nature's patterns with plasmas
23 Aug 2016  9:48 amPatterns abound in nature, from zebra stripes and leopard spots to honeycombs and bands of clouds. Somehow, these patterns form and organize all by themselves. To better understand how, researchers have now created a new device that may allow scientists to study patterns in 3D like never before. 
The math of earthquakes
18 Aug 2016  6:06 amA computational science doctoral student has successfully tied a new mathematical modeling process to the study of earthquakes. 
Extension theory of operators in Krein, Pontryagin spaces, applications
18 Aug 2016  6:00 amA new study investigates and generalizes several wellknown results from Extension theory of operators. In a new doctoral dissertation, a researcher has been able to improve a couple of classical theorems known in the area, namely Shmul'yan theorem on completion of nonnegative block operators and Krein famous theorem on description of selfadjoint contractive extensions of a Hermitian contraction. 
Babies' spatial reasoning predicts later math skills
17 Aug 2016  10:19 amSpatial reasoning measured in infancy predicts how children do at math at four years of age, finds a new study. It provides the earliest documented evidence for a relationship between spatial reasoning and math ability. 
Lack of American engineers and scientists
11 Aug 2016  2:16 pmA new study identifies factors that could lead more young students to successful careers in the science, technology, engineering and math fields.



Scientific American  Math

A Few of My Favorite Spaces: The Connected Sum of Four Hopf Links
20 Aug 2016  8:00 amThe mathematics of the Olympic rings  Read more on ScientificAmerican.com 
What Does HalfLife Mean?
17 Aug 2016  7:00 amWhat are halflives? And what do they have to do with measuring the age of the solar system and predicting the effects of a morning cup of coffee? Keep on reading to find out!  Read more on ScientificAmerican.com 
Mathematicians Are Overselling the Idea That "Math Is Everywhere"
16 Aug 2016  4:15 amThe mathematics that is most importantto society is the province of the exceptional few—and that's always been true  Read more on ScientificAmerican.com 
The Mathematical Hamilton Parody You Never Knew You Needed
15 Aug 2016  4:55 amThe discoverer of the quaternions gets Lin Manuelized  Read more on ScientificAmerican.com 
Why You Should Care about HighDimensional Sphere Packing
3 Aug 2016  8:30 amSphere packing—it's not just for oranges anymore  Read more on ScientificAmerican.com



Mathematics

The Problem with SET®
22 Aug 2016  10:30 amFor the popular card game SET®, how many cards is it possible to have on the table without there being a legal play? 
Numberplay: Olympic Strategies, Part 2
15 Aug 2016  10:00 amReflections on worldclass performance by two Olympic gold medalists, along with a numeric challenge by the math educator Sunil Singh. 
Seymour Papert, 88, Dies; Saw Education’s Future in Computers
1 Aug 2016  3:02 pmDr. Papert was a codirector of an artificial intelligence lab at M.I.T.; some considered him the foremost expert on technology and learning. 
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.



Blog – DreamBox Learning

9 Back to School math activities for teachers, students, and parents
17 Aug 2016  11:00 pmIt’s nearly time to start setting the alarm clock earlier and revamp last year’s lesson plans! The truth is, teachers, parents, and students may all need a jumpstart to get psyched for the new school year after a summer of sun and fun. Here are nine activities to get your creativity motor running, and get parents and students onboard for a productive and fun year of math learning:Rekindle Your Passion for Math1. Get inspired. Want to see a great example of someone who has fallen head over heels for math? Check out comedian and selfproclaimed math geek Adam Spencer’s Ted Talk, Why I Fell In Love with Monster Prime Numbers. His passion for these odd numbers provides a new take on the “mysterious... 
The Power of High Expectations in Equitable Education
17 Aug 2016  12:00 amI believe that all children can learn, regardless of who they are or where they live. UNESCO stated, “Education is a fundamental human right and essential for the exercise of all other human rights. It promotes individual freedom and empowerment and yields important development benefits. Yet millions of children and adults remain deprived of educational opportunities, many as a result of poverty.” UNESCO is not limiting this statement to countries other than our own. Today, according to the Southern Education Foundation, half or more of the public schoolchildren in 21 states are eligible to receive free or reducedprice lunches, a benefit available only to families living in poverty or nearpoverty.How... 
Dive into 6 Fun Ways to Close Summer Math Learning Gaps
16 Aug 2016  3:26 pmResearch for over a hundred years—since 1906!—confirms the “summer slide” phenomenon. More recently, studies like those from Rand Corporation tell us that students can lose a month or more of learning, and that summer learning loss disproportionately affects lowincome students. According to the National Summer Learning Association, by fifth grade, summer learning loss can leave lowincome students twoandahalf to three years behind their peers. But it isn’t inevitable. Even if students aren’t enrolled in summer learning programs, sneaking learning into play makes math a natural part of summer activities and keeps up learning engagement—and fosters engagement with grownups, too. Change the... 
Summer Fun, Summer School
18 Jul 2016  10:00 pmWhen it comes to getting ready for summer school, motivation is key for both you and your students. Although the school year has recently ended, creating a learning environment that makes the kids laying by the pool jealous and want to come to school is a key to success. In talking with my teacher friends who teach summer school, the following are three common denominators for success.Blended LearningMany teachers mentioned blended learning as one of the top three things that lead to summer school success. Whether you have an online learning tool you used during the school year or whether you are in search of one, having students interact with engaging technology benefits everyone involved. It is an... 
Five Hot Trends in EdTech
12 Jul 2016  4:12 pmMiss out on the ISTE (International Society for Technology in Education) conference last month? Check out these hot trends in EdTech. Be in the know, whether you attended the conference or not! The Global Classroom Connecting classrooms around the world with technology is becoming commonplace—and integral to building the 21st century skills necessary for today’s students to compete in tomorrow’s increasingly complex and connected world. “Advances in technology in the classroom allow students to engage in learning and connect with classrooms of the world in new and powerful ways,” says Jennifer Williams, cofounder and lead program developer for Calliope Global, which works with schools and...



Loren on the Art of MATLAB

Indexing with Parentheses
22 Aug 2016  6:53 amI have talked about indexing a bunch of times in the past. 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>Arrays</li><li>Where People Trip</li><li>Function Calls</li><li>Numeric Arrays</li><li>Cell Arrays</li><li>Tables</li><li>Structures</li><li>Follow Up</li></ul>ArraysWhat are arrays? In MATLAB, they are containers that hold information. 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 them?Where People TripOne of the common places I see people trip is accessing information from cell arrays (and sometimes similarly for... 
Text Mining Machine Learning Research Papers with MATLAB
8 Aug 2016  8:22 amPublish or perish, they say in academia, and you can learn trends in academic research through analysis of published papers. Today's guest blogger, Toshi, came across a dataset of machine learning papers presented in a conference. Let's see what he found! Contents<ul><li>NIPS 2015 Papers</li><li>Paper Author Affiliation</li><li>Paper Coauthorship</li><li>Paper Topics</li><li>Topic Grouping by Principal Componet Analysis</li><li>Deep Learning</li><li>Core Algorithms</li><li>Commercial Research</li><li>Top 10 Authors in NIPS 2015</li><li>Summary</li></ul>NIPS 2015 PapersNIPS (which stands for "Neural Information Processing Systems") is an annual conference on machine learning and computational neuroscience, and papers presented there reveal what experts in the field are working on. Conveniently, you can... 
MATLAB is Satisfying
20 Jul 2016  6:32 amToday's guest post comes from Sean de Wolski, one of Loren's fellow Application Engineers. You might recognize him from MATLAB answers and the pick of the week blog!Contents<ul><li>Set Up</li><li>Bounds and Integer Constraints</li><li>Equality Constraints</li><li>Row and Column</li><li>Diagonal and Antidiagonal</li><li>Solve!</li><li>View the Result</li></ul>I manned the MathWorks booth one of the days last week at the annual SIAM conference in Boston MA. The keynote speaker that day was Donald Knuth who was there to discuss satisfiability and the latest chapter of his book, "The Art of Computer Programming".At the beginning of the session, he provided a satisfiability puzzle, similar to a Sudoku puzzle, for those in the audience to do. I figured, why not solve it with... 
Clearing the Air in Your MATLAB Session
11 Jul 2016  8:18 amI have, over time, changed when, where, and how I "clean up" my MATLAB session. You may want to update your strategy as well.Contents<ul><li>What I Used to Do</li><li>What I Do Now</li><li>How Do I Run the Code?</li><li>What Do You Do?</li></ul>What I Used to DoIn the recent past, if I wanted to "start from scratch" without restarting MATLAB, I would clear my workspace, command window, and close open figures. I would issue the following commands clc clear all close all forceWhat I Do NowI still do something very similar, but with an important though smalllooking change. I remove the all from my clear statement. Here's what I do now. clc clear close all forceI no longer ask for everything to be... 
Survey Reveals Diversity in the “Learn to Code” Movement
27 Jun 2016  6:13 amDo you use any free "learn to code" website to teach yourself programming? You may already know how to program in MATLAB, but you may very well be learning other skills on MOOCs.Today's guest blogger, Toshi, analyzed a publicly available survey data to understand the demographic of selftaught coders. Contents<ul><li>Load Data</li><li>Higher Female Representation Than Expected</li><li>Mostly Studying in Countries of Citizenship</li><li>Ethnically Diverse English Speakers in US</li><li>Many Are Highly Educated and Already Employed in the US</li><li>Many Already Work In Software Development and IT in US</li><li>Academic Background in Software Development and IT</li><li>Wide Income Gap in Software Development and IT</li><li>What Affects Income in Software Development and IT?</li><li>Age Factor</li><li>Big...</li></ul>



Homeschool Math Blog

"Brainie" game for some mental math  2nd through 6th grade
27 Aug 2016  11:33 amCheck how your 2nd6th grader might like this game titled "Brainie" for a bit of mental math at the start (or end) of the day:It starts out with simple addition but advances in levels. Soon, you will see tiles with "1", "2", etc. which indicate subtraction. And after a few more levels you'll see *2 and similar, indicating multiplication.I liked it! :) 
Free online practice exercises for math
18 Aug 2016  1:18 pmDid you know that Khan Academy not only has videos, but they have added (in recent years) a TON of free interactive practice exercises? These exercises are of good quality, and also include word problems, graphing, and other problems with visual models. And they span all areas of elementary, middle, and high school math. You might bookmark some of these pages, in case some day you'd like to find just a few extra practice exercises for your child or student (on just about any math topic) to do interactively... 1. The search pageThe search for a math topic will list a lot of videos and exercises intermixed. It will help if you include the word "practice" in your search. 2. Common Core "map" page, from where... 
Math Mammoth August sale!
15 Aug 2016  2:19 pmAUGUST SALE!Get 30% off of all of Math Mammoth BLUE and LIGHT BLUE series downloads & CDs at EDUCENTS.The offer is valid till August 25, 2016. 
Is it possible to understand the book of Revelation?
27 Jul 2016  6:59 amI don't actually mean to constantly post these videos, BUT this one is of special significance, so I apologize if it's not "your kind of thing" to do... but I do believe SOME of my followers will enjoy it!The book of Revelation has always been dear to me, and I've always enjoyed whatever I've been able to learn more about it over the years. This video study is just a bare introduction. My family was privileged to help with the footage for this one — for example, you will see my "middle" daughter near the beginning reading the Book in candlelight, and that clip was shot by my other daughter, as were several others. SUMMARY provided by author: In today's world, multitudes of people are writing, teaching,... 
Pay What You Want sale
19 Jul 2016  6:27 amCurrclick is running a "PAY WHAT YOU WANT" sale for a variety of Math Mammoth books from the Blue series."Pay What You Want" means exactly that; it also means you CAN even get these books for FREE... though of course, I appreciate it if you pay. But sometimes people are in a really tight financial situation, and I understand that. :)This sale runs till July 22.



DeniseGaskins.com

Math You Can Play Combo in Paperback and Ebook
20 Aug 2016  7:29 amIf you’re interested in helping children learn math, I have special offer just for you: <ul> <li>Save 20% off the individual ebooks or 35% off the paperback prices when you buy a combined 2booksin1 edition featuring the first two books in the Math You Can Play series together.</li> </ul> The 42 kidtested games are simple to learn, quick to play, and require minimal preparation. Most use common household items such as cards or dice. Free Online Preview “Although the cover says games for young learners, the beauty of this book is that most of the games can easily be scaled up for older kids, teens, and even adults. My youngest is four and my oldest is 14, and I will be pulling games for all of them out of this... 
KenKen Classroom Puzzles Start Next Week
19 Aug 2016  10:40 amKenKen arithmetic puzzles build mental math skills, logical reasoning, persistence, and mathematical confidence. Puzzle sets are sent via email every Friday during the school year — absolutely free of charge. What a great way to prepare your kids for success in math! Sign up anytime: <ul> <li>KenKen Classroom Newsletter</li> </ul> How to Play For easy printing, rightclick to open the image above in a new tab. Place the numbers from 1 to 6 into each row and column. None of the numbers may repeat in any row or column. Within the black “cages,” the numbers must add, subtract, multiply, or divide to give the answer shown. Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions,... 
New Fantasy Adventure Novel by Homeschooled Teen Author
19 Aug 2016  10:11 amIf you or your children enjoy clean fantasy tales, check out the new installment in my daughter’s serial quest adventure The Riddled Stone, now available at many online bookstores. Click here to see the whole series. How Can a Knight Fight Magic? Trained by the greatest knight in North Raec, Sir Arnold Fredrico dreamed of valiant deeds. Save the damsel. Serve the king. Dreams change. Now the land teeters at the brink of war. As a fugitive with a price on his head, Arnold struggles to protect his friends. But his enemy wields more power than the young knight can imagine. Free Online Preview 238 pages, ebook: $3.99, paperback: $14.99. Buy now at: Review Betrayed, by Teresa Gaskins, really exceeded my... 
Do You Blog About Math?
15 Aug 2016  5:25 am[Image by Mike Licht, NotionsCapital.com (CC BY 2.0) via Flickr.] It’s carnival time again. Activities, games, lessons, handson fun — if you’ve written a blog post about math, we’d love to have you join our Math Teachers at Play (MTaP) math education blog carnival. Posts must be relevant to students or teachers of schoollevel mathematics (that is, anything from preschool up through firstyear calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival. <ul> <li>Click here to submit your blog post.</li> </ul> Don’t procrastinate: The deadline for entries is Friday, August 19. The carnival will be posted next week at The Usual Mayhem. Have you noticed a new math blogger on... 
Join the Fun: Math & Magic Virtual Book Club
2 Aug 2016  6:39 amEleven weeks of mathematical playtime kicks off this week over at Learners in Bloom blog. <ul> <li>Math & Magic in Wonderland Week One</li> </ul> Each week, we’ll be playing with the math, language, and logic topics found in a single chapter. I’ll be posting ideas for extension activities, videos demonstrating the concepts for the week, and additional resources. I’m really excited for the opportunity to share all the extra ideas that have been floating around my brain which I didn’t have room to include in the book (as in Marco Polo’s famous words: “I did not tell half of what I saw.”) — Lilac Mohr Here’s a Quick Taste of Week One This Week’s Activities Lilac’s blog post includes a full schedule for the elevenweek...



Basic mathematics blog

Average age word problem
9 Aug 2016  10:40 amAverage age of Dipu and Apu is 22 years. Average age of Dipu and Tipu is 24 years. Age of Dipu is 21 years. What are the ages of Apu, and tipu ? Let 
Phone card word problem
9 Aug 2016  10:34 amElsa purchased a phone card for $25. Long distance cost .11 a minute using this card. Elsa used her card only once to make a long distance call. If the 
Age
9 Aug 2016  8:24 amThe sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? Let x be the age of the youngest 
Math problem about age
9 Aug 2016  8:04 amArvind is eight year older than his sister. in three year, he will be twice as old as his sister. how old was they are now? Solution Let x be a Arvind's 
shen percent of increase
8 Aug 2016  8:20 amA factory has 800 workers. 40% of them are females. The management decides to employ more female workers to cope with the increasing demands of the workload



Computational Complexity

1956 Was a Fine Vintage
25 Aug 2016  6:32 amBill sends me an email last week with the subject "Our field is getting old!" and talks about upcoming 60th birthday/retirement conferences he's invited to, all of which I've been invited to as well. Bill's subject line should have read "We're getting old." Here's what's upcoming: <ul> <li>Avi Wigderson's 60th celebration before FOCS in New Jersey, October 58. Avi is a giant in computational complexity and the event has an amazing lineup of speakers.</li> <li>Albert Meyer's retirement celebration at MIT, November 11.</li> <li>Rod Downey's 60th symposium in New Zealand, January 58.</li> <li>Eric Allender and Michael Saks will have a joint 60th celebration at DIMACS in New Jersey, January 2627.</li> </ul> Surely I've missed some. Feel free to add... 
Chrisitan Comment on the Jesus Wife Thing misses the important point
22 Aug 2016  1:25 pmIn 2012 a Professor of Divisinity at Harvard, Karen King, announced that she had a fragment that seemed to indicate that Jesus had a wife. It was later found to be fake. The article that really showed it was a fake was in the Atlantic monthly here. AChristian Publication called Breakpoint told the story:here. When I read a story about person X being proven wrong the question upper most in my mind is: how did X react? If they retract then they still have my respect and can keep on doing whatever work they were doing. If they dig in their heels and insist they are still right, or that a minor fix will make the proof correct (more common in our area than in history) then they lose all my respect. The... 
Predicting in Changing Environments
18 Aug 2016  7:35 amThe New York Times yesterday ran a story connecting climate change to the Louisiana flooding. The National Weather Service reports that parts of Louisiana have received as much as 31 inches of rain in the last week, a number Dr. Easterling called “pretty staggering,” and one that exceeds an amount of precipitation that his center predicts will occur once every thousand years in the area.Dr. Easterling said that those sorts of estimates were predicated on the idea that the climate was stable, a principle that has become outdated.The third National Climate Assessment, released in 2014 by the United States Global Change Research Program, showed that “the amount of rain falling in very heavy... 
Is the examiner being pedantic? Whats really going on here?
15 Aug 2016  2:22 pmThe following are two real conversations. For each one: (1) Is the examiner correct?, and (2) Where and when do you think this conversation took place? I give the answers below so you may want to read, stop and think, and then read on. CONVERSATION ONE: EXAMINER: What is the definition of a circle? STUDENT: The set of points equidistant from a given point. EXAMINER: Wrong! It is the set of ALL points equidistant from to a given point. CONVERSATION TWO: EXAMINER: What is the definition of a circle? STUDENT: It is the set of all points equidistant from a given point. EXAMINER: WRONG! You did not specify that the distance is nonzero. AN ANSWER I HAVE HEARD FROM SOME NONMATHEMATICIANS:... 
Robin Hanson's Ems
11 Aug 2016  6:20 amRobin Hanson an economist at George Mason and author of the Overcoming Bias blog, has a new book The Age of Em: Work, Love and Life when Robots Rule the Earth. Em stands for brain emulation, a computerized version of a human brain processes including consciousness, all the wants, desires and faults of a human brain. An em can be created by copying from a human brain or another em, it can be stored and restored, slightly tweaked and can run faster or slower depending on the power consumption. Reminds me a bit of the cookies in theWhite Christmasepisode of Black Mirror. Hanson also talks about clans, the collection of all the ems that descend from a particular human. The book has two distinct parts. The...



Mathematics and Computation

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... 
The Andromeda proof assistant (Leeds workshop slides)
28 Jul 2016  6:28 amI am about to give an invited talk at the Workshop on Categorical Logic and Univalent Foundations 2016 in Leeds, UK. It’s a charming workshop that I am enjoing a great deal. Here are the slides of my talk, with speaker notes, as well as the Andromeda examples that I am planning to cover. <ul> <li>Slides: AndromedaProofAssistant.pdf </li> <li>Andromeda files: nat.m31, universe.m31</li> </ul> 
The real numbers in homotopy type theory (CCA 2016 slides)
15 Jun 2016  3:03 amI am about to give an invited talk at the Computability and Complexity in Analysis 2016 conference (yes, I am in the south of Portugal, surrounded by loud English tourists, but we are working here, in a basement no less). Here are the slides, with extensive speaker notes, comment and questions are welcome. Slides: hottrealscca2016.pdf 
A BrownPalsberg selfinterpreter for Gödel’s System T
4 Jan 2016  12:40 amIn a paper accepted at POPL 2016 Matt Brown and Jens Palsberg constructed a selfinterpreter for System $F_\omega$, a strongly normalizing typed $\lambda$calculus. This came as a bit of a surprise as it is “common knowledge” that total programming languages do not have selfinterpreters. Thinking about what they did I realized that their conditions allow a selfinterpreter for practically any total language expressive enough to encode numbers and pairs. In the PDF note accompanying this post I give such a selfinterpreter for Gödel’s System T, the weakest such calculus. It is clear from the construction that I abused the definition given by Brown and Palsberg. Their selfinterpreter has good...



IMA Journal of Applied Mathematics  current issue

Bifurcation from stable fixed point to 2D attractor in the border collision normal form
18 Aug 2016  2:30 amThe border collision normal form is a family of continuous 2D piecewise smooth maps describing dynamics close to a critical parameter at which a fixed point intersects the switching surface. It is well known that if the fixed point is stable on one side of the bifurcation point, then after the bifurcation the system may have stable periodic orbits and/or chaotic attractors with a quasi1D structure (robust chaos). We show that it is also possible to have a robust transition from a stable fixed point to an attractor with topological dimension two, i.e. the highest dimension possible in the phase space. 
A model for thermoelastic contact oscillations
18 Aug 2016  2:30 amThis paper concerns the derivation and preliminary analysis of a model for judder in devices such as brakes and clutches. The model is based on the competition between wear and thermal expansion which, in the multiplepin configuration proposed by Barber (1969, Thermoelastic instabilities in the sliding of conforming solids. Proc. Roy. Soc. (London), A312, 381–394), leads to a novel, nonlocal dynamic contact problem. 
Adapting Havelock's wavemaker theorem to acousticgravity waves
18 Aug 2016  2:30 amWe investigate the different wavemodes generated by a wavemaker in compressible flow. In addition to the propagating and evanescent waves found in the incompressible case, new radially propagating acousticgravity modes appear. We discuss the asymptotic behaviour of these waves, and give an example for a simple line wavemaker configuration. 
'Advances in applied nonlinear mathematics: a special issue in honour of John Hogan's 60th birthday
18 Aug 2016  2:30 am 
Perturbed hedgehogs: continuous deformation of point defects in biaxial nematic liquid crystals
18 Aug 2016  2:30 amA spherically symmetric isolated point defect in a 3D uniaxial nematic liquid crystal sample is often called a radial hedgehog. We use topological methods to describe local configurations of uniaxial and biaxial states into which a hedgehog naturally deforms under small perturbations: these include the biaxial torus and split core configurations studied in the literature using analytical and numerical methods. The topological results here take no account of the governing physical laws but provide a library of options from which the physics must make a choice.



The Math Less Traveled

Post without words #10
26 Aug 2016  11:33 am 
Factorization diagram card redesign: feedback welcome!
24 Aug 2016  1:56 pmAfter getting a printed set of factorization diagram cards, I decided there were a few design tweaks I wanted to make. I’ve gone through a few iterations and I think they are definitely better now. Here are some representative samples (namely, 6, 13, 21, 29, and 30): The changes I made include: <ul> <li>Better color scheme (at least I think so!)</li> <li>Primes now have a visual representation that does not depend on color (though the color is still meaningful). For example, 29 is represented by an outer shell with two halfcircles (representing the 2) and a trio of triangles (representing 9, that is, three threes).</li> <li>The triangle representing 3 is flipped upside down so it never intersects with...</li></ul> 
Post without words #9
14 Aug 2016  2:39 pm 
Post without words #8
12 Aug 2016  4:53 am 
Post without words #7
18 Jul 2016  6:28 pm



eon

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 
Logical order
22 Aug 2016  6:55 pmThe most efficient logical order for a subject is usually different from the best psychological order in which to learn it William Thurston from his book Three dimensional geometry and topology. 
Oneseventh ellipse
22 Aug 2016  1:20 amFun fact. It is well known that [tex] \frac{1}{7} = 0.\overline{142857} [/tex]. It turns out that if the repeating digits are taken in sequence as (x,y) pairs in the following manner to form six points: (1,4), (4,2), (2,8), (8,5), (5,7), (7,1), then these six points actually lie on an ellipse defined by the following equation. [tex] 19x^2+36xy+41y^2333x531y+1638=0 [/tex] 
Lakatos on Discovery
31 Jul 2016  11:47 pmDiscovery does not go up or down, but follows a zigzag path: prodded by counterexamples, it moves from the naïve conjecture to the premises and the turns back again to delete the naïve conjecture and replace it by the theorem. Naïve conjecture and counterexamples do not appear in the fully fledged deductive structure: the zigzag of discovery cannot be discerned in the endproduct. From his Proofs and Refutations. 
Notes from ICME13
29 Jul 2016  10:58 pmGila Hanna mentioned the carpet proof of the irrationality of [tex]\sqrt{2}[/tex]. A little digging reveals that it was due to Tennenbaum (1950s) and popularized by Conway (1990s). The original proof appeared in a book but the simple idea is described in this paper “Picturing Irrationality” by Steven Miller and David Montague in the Mathematics Magazine (2012). What is more interesting is the expanded version of their paper on arXiv called “Irrationality from the Book”. One can only infer the amount of editing and changes that took place from submission to publication. This is a quote from Guershon Harel that I am trying to piece together from memory. Some of us are constructing open neighbourhoods* but...



WordPress Tag: Mathematics

The scientific method
27 Aug 2016  3:28 pm 
Selfinfanticide
27 Aug 2016  2:59 pmby Roger D. Jones I am writing a new book with my colleague John Casti entitled Eddies in the Stream. It is an arrogant project about what life is. No, I mean really what life is. How did life come about? Is it constrained to be chemistrybased? Can computer programs be alive? Can cities be alive? Is a society of universes possible? That sort of thing. This series of blogs contains bits and pieces from the book as it is being written. I am writing the blog as a way to decompress. I am also creating paintings on the topics in the book as a way to decompress. To be, or not to be? Hamlet Act 3, Scene 1 Kurt Gödel and Albert Einstein were close friends. They took long walks together at the Institute for... 
How to find the nth root of a value without using scientific calculator (In an ordinary calculator)
27 Aug 2016  12:33 pm<ol> <li>Type the value in your calculator .</li> <li>Press the square root button 12 times .</li> <li>Subtract ‘1’ from the arrived figure.</li> <li>Divide the value arrived in step 3 by the value of ‘n’.</li> <li>Add ‘1’ to the value arrived in step 4.</li> <li>Now press the ‘multiply’ and ‘is equal to’ buttons 12 times each one after another.</li> <li>Now you have arrived the nth root of the value.(Calculators with maximum number of decimal places gives more accurate results).</li> </ol> 
Ontological Wallop
27 Aug 2016  11:50 amThe structure of the world is shot through with a sublimity so sublime that it simply had to exist. … The sublimity that had to burst into existence is not one that particularly concerns itself with us. Such a humancentered goodness would not pack the ontological wallop required to bring forth existence. (Plato at the Googleplex, pages 385389.) I like that phrase “the ontological wallop required to bring forth existence.” I’ll return to it in a moment. First, let’s look at a pretty picture. The area colored black is the Mandelbrot set, a set of numbers whose graph is infinitely intricate, meaning that you can zoom in to any depth and it never smooths out. (As a bonus, the “bug” shape keeps... 
What Is Long Memory In Time Series Analysis
27 Aug 2016  11:00 amWe encounter time series data very frequently in the real world. Some common examples include real time sensors, surveillance video, stock market, astrophysics, speech recognition, and so on. In order to study time series data, we try to extract various characteristics that tend to define it. One of the most important things to think about is the dependence between various points in the time series data. Is there any dependence between the values in the time series data? If so, how far apart in time do they have to be in order to affect each other? Understanding these aspects will open up new doors in terms of how we analyze the data. This is where the concept of long memory comes into picture. Let’s dig a...



Institute for Mathematics and Computer Science

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... 
Tools to Help You Think At Any Age!
13 Jul 2016  10:00 pmToolboxes are handy things to have around, especially when they are filled with useful tools. A maker might include a hack saw, hammer and soldering iron in her toolbox. A musician might include a metronome, pitch pipe and recording device in his toolbox. What would you find in the toolbox of a problem solver? Many things, to be sure, but among them is likely to be an array of logical reasoning skills. Logic promotes clarity of thought in understanding ideas. As the complexity of our world increases, each of us will face a growing number of unfamiliar and challenging situations. The shift to a knowledgebased economy keeps progressing. The significant decisions we must make keep multiplying. People are... 
Smart is Not What You Think. It’s How You Think.
4 May 2016  10:00 pmThere was a time when the ability to faithfully recall information was a strong determinant of success. Now we have highlysophisticated search engines and revolutionary chatbots that speak answers to your spoken questions. What you know and think is no longer the definitive measure of being smart. What matters now and in the future is how you make use of the vast knowledge that is readily available. The modern measure of being smart is in how you think. Leverage and Extend Existing Knowledge When it comes to knowledge, success today is more about whether you can combine and extend what is already known in order to address novel situations. For example, competitive business environments shift more... 
Teach Kids How to Think and They’ll Think for Themselves
27 Mar 2016  10:00 pmIMACS IS NOW OPEN IN SILICON VALLEY! We offer afterschool and homeschool Math Enrichment and Computer Programming classes for bright elementary and middle school students. Sign up for a FREE class and see what we’re about! As parents we instinctively want to help our children when they struggle. Our impulse is often to just fix the problem ourselves. While this approach makes sense when children are very young, as they grow it becomes counterproductive. In rescuing our kids, we provide a quick fix but deny them opportunities to practice important skills that they will need to become independent adults. This is true in general and certainly with respect to education. As children grow, we should...



mathrecreation

Monty R and Monty n
12 Aug 2016  1:17 pmAs part of my ongoing attempt to learn the R language, I decided to try to generate a data set to analyze in R using R itself. I wrote a little R script which generates simulated data for a thousand trials of the "Monty Hall" problem. The script is here, along with other R examples.If you source the script, a data frame MontyHall will be populated. The data is regenerated each time you source the script, so if you want to capture a single run, you should export the data and work from that (a saved example run is here, and contains the data I used in this post).In the classical Monty Hall problem, a game show host, named Monty Hall, presents a contestant with three (3) doors. Behind one of the doors is a... 
Chladni on Google Books
4 Aug 2016  9:11 pmWhile doing some light research a short while back (for this post), I hit a minor impasse: the Google Books scans of some figures in an early edition of Ernst Chladni's book on sound were sadly obscured by folding.Although I was able to find other digital images of similar scans, I sent in a support request to Google Books, and was surprised when within less than two weeks they had rescanned the images, properly folding out the pages.These and other nicely restored images can be found towards the end ofthe book. 
a first slice
17 Jul 2016  11:05 amHere is my first simple attempt at a geometric design using sliceformstudio I'm looking forward to trying out many more.I have played around a bit with sliceforms before, using instructions from John Sharp, who has written quite a bit about using them for creating models of conic sections and surfaces, and has a nice short blog post here about their history. I learned about sliceformstudio a short while ago from mathmunch.This design was based on a simple pattern of pentagons around a decagon, to which the wondrous sliceformstudio applied some interweaving that I tweaked only slightly using the very simple interface.After printing off the generated strip file onto cardstock, 10 long strips and 10 short... 
more Chladni figures in R
24 Jun 2016  5:02 pmFollowing on from an earlier post, the Chladni images here are made using a slightly modified version of the same R script (source here), which uses cosines instead of sines. If you imagine the square of the vibrating surface to be fixed at the center (as depicted below), using cosines seems the natural choice. When modeling standing waves, cosines are used to model openended pipes, while sines are used to model fixedend strings.Playing around with cosinebased formulas led to some images that seemed very close to Chadni's own diagrams, which can be found in an appendix to his book on Google books.For a few of these I've uploaded the scripts that produced them.Chladni image 40 bSourcehere.Chladni image... 
Rascal Triangle
24 Jun 2016  8:09 amA few early iterations of something produced by a short script in R. What is it? You may see it more clearly in some of its later stages of development.Yes, it is Pascal's Triangle modulo 2  I knew you would recognize it :). The R source for generating these images is here. Like other recent posts, this is another example of using R in some simple programming exercises, pretty much completely unrelated to its intended purpose as a language for statistical computing. A wile back, there was a post about using TinkerPlots, a data management software tool for young folk, to do something similar (more detailed instructions on drawing a general Pascal Triangle in TinkerPlots can be found in this article),



Math ∞ Blog

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:... 
Playing with Mersenne Numbers
6 Aug 2016  12:30 pmThe largest prime number we’re currently aware of has 22,338,618 digits. It was discovered in January 2016 thanks to the coordinated effort of thousands of machines across the globe. It is: As many readers will know, this is a Mersenne prime number. The overwhelming majority of the largest prime numbers we’ve discovered over the past century have been Mersenne numbers. A brief introduction to Mersenne Numbers Mersenne numbers are defined as: for n in . Not all Mersenne numbers are prime (e.g., ), and not all prime numbers are Mersenne numbers (e.g., ). Nevertheless, Mersenne numbers are currently our best bet when it comes to finding increasingly larger prime numbers. A key reason for this is that we... 
Using Programming to Teach Mathematics
29 Jul 2016  5:00 amIt is often argued that programmers need a solid mathematical background in order to be competent in their chosen profession. Discrete mathematics offers a great foundation for programming, don’t get me wrong, but the truth is that most programmers can get away with knowing very little in the way of mathematics. In fact, if you are afraid to give programming a go because you’re scared or intimidated by the mathematics that it may require, I have both good and bad news for you. The good news is that you don’t need to know a lot of math, so go ahead and grab that, say, Python tutorial. The bad news is that you’re on the wrong website. Jokes aside, there is a distinction between Computer Science (which is...



MathFour

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,... 
Empathize with an Expert
6 Apr 2016  12:03 pmThis is the second in the unofficial #HappinessHabit Series. Often we place our experts on pedestals. Rarely do we think about an expert as a “real person.” But today’s Happiness Habit is to do just that – pick an expert in an area you want to improve, and real personize them. I’m currently working on decluttering. My bedroom likes to “grow” piles of clothes. And piles of papers. And piles of… well, piles! Find your expert. I looked to my sister as my expert. She always picks up after herself. Like immediately. She never has pile growth. Ever. I asked her, “How did you create the practice of picking up after yourself?” “I hate clutter,” she replied. Well, I hate clutter too. But my...



MIND Research Institute Blog

Hitting the Jackpot in Our Friends
25 Aug 2016  9:00 amIf we are lucky (and I am) we have friends who understand us, and respect and support our personal and professional goals. In our personal life, this support might manifest in celebrating milestones and successes together, sending handwritten cards of congratulations, supporting a friend’s business by buying a bajillion “amazing” products, purchasing tickets to attend a fundraising event for a cause your friend supports, donating to your friend’s marathon campaign, buying wrapping paper from the neighbor kid … the list goes on and on. Some friends go above and beyond and provide direct help. I’ve experienced this with my friends’ support of the nonprofit organization I work for, MIND... 
The Making of ST Math's New Line Plot Games
16 Aug 2016  9:00 amTeaching statistics is hard. For one thing, stats activities often take a long time to do. Also, for any grade level, the relevant stats activities are often a combination of different math activities. Even something simple, like building alineplot of a simple bell curve, can consist of making dozens of measurements and plotting them all as points over a number line. Just one stats activity can be the same amount of work as an entire math worksheet! How can we best utilize the amount of time teachers and students have in the classroom for interactive stats activities? As a game designer at MIND Research Institute, I was excited to answer this question. I have spent the past year applying game mechanics... 
STEM Camp Shows Girls Can “Get Math”
11 Aug 2016  10:45 amLike many other parents I have spent countless hours worrying about my children’s education and whether I was setting them up for success in life. My daughters, now 22 and 19 and both attending Art Center College of Design in Pasadena, have been given as many opportunities for a strong educational foundation as any American middleclass parent can hope to provide. They attended public schools in wellfunded districts where teachers and administrators are often surrounded by supportive parents. They had the chance to join soccer, dance and swim teams, learn to play the piano and be a part of theater productions. So with this virtually picture perfect scenario, why did I lose sleep over their education? ... 
Why We Should Worry Less About The "Achievement Gap"
9 Aug 2016  9:30 amUpdate: About a year ago I wrote this article for the Huffington Post about the achievement gap and how it steers us in the wrong direction. It was additionally picked up by Getting Smart and viewed by many others. Since then, I've submitted a proposal to share even more on this topic at SXSW. Feel free to share your support by voting for the proposal. It's very common to talk about raising student achievement. After all, this is where we see gaps. Doing poorly on an assignment or failing a test denotes "poor achievement" and stands out to teachers, parents and society. We naturally want to fix student achievement. But here's the twist: The achievement gap is not the root problem, and we hurt our students... 
Students Gain New Perspectives on Math Through Nature, Movement and Games
4 Aug 2016  9:00 am“The greek mathematician Archimedes was inspired by nature in many of his mathematical discoveries. What kind of patterns do we see in the shell of a snail?” A crowd of students, enrolled in the Boys and Girls Club of Santa Ana summer program, lean in around my colleague to examine the creature in question. Thanks to our partner Chevron, MIND Research Institute brought interactive mathematical experiences like "Math and Nature" to the Boys and Girls Club students. Other sessions during the fourday program featured "Math and Movement," "Fun and Games," and "Ropes Course." As you can already judge by the titles, this is not like your ordinary math class! One of the big differences lay in the great...



Math Vault

Desmos Art: A Definitive Guide to Computational Sketching (How to Recreate Our Redditlady and Redditdog Using an Online Graphing Calculator)
3 Aug 2016  6:49 pmf you’re of the type who enjoys playing around with graphing calculator, then you might be interested in the socalled Desmos Art. These are basically pictures and animations created in Desmos primarily through the clever use of equations and inequalities — among other features such as tables, animating sliders and regression models. Indeed, if you go to this official staff […] 
Desmos: A Definitive Guide (How to Perform Cool Computations and Creating Great Graphs Using Online Graphing Calculator)
12 Jul 2016  12:37 pmhink you’re fond of of graphing and computing stuffs? Great! Because you might remember this thing called the Texas Instrument TI83 from the old days. Sure, while programmable calculators in general are still pretty much popular these days, the graphing calculators from the 21stcentury are also coming in waves as we speak — potentially disrupting the market of scientific computing and educational […] 
Infinite Limits and the Behaviors of Polynomials at the Infinities — A Theoretical Musing
17 Jun 2016  1:55 pmegardless of your early surrounding or schooling background, we know for one that there are two kinds of mathematical objects that are kind of hard to miss in life. The names? Polynomial and Infinity! While the former might have sounded a bit like the name of a snake, polynomials is a oneofitskind mathematical entity whose perfection defies our mathematical imagination. For […] 
Chain Rule for Derivative — Venturing Into The Dark Side Beneath Applied Calculus…
5 Jun 2016  7:38 pmo the surprise of many math enthusiasts and the like, it seems that we have been pulling out on an incredible amount of calculus modules these days. Of course, if you have had any terrible experience in learning just the mechanics of calculus, this seeminglyrelentless outpouring of materials could make you want to puke. However, if that header […] 
The Exponent Rule for Derivatives — Your OneStop Shop to StaircaseLooking Functions
21 May 2016  2:51 pmike the featured image above? Good for you! As students (fanatics?) of mathematics and other technical sciences, we have an intuitive appreciation of the role this topic — calculus — plays out in our daily life. While obviously not a subject to be mastered overnight, what’s true is that our first exposure to it tends to be […]



StudyPug

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> 
Why Teachers Aren’t Utilizing Tech in the Classroom
12 Aug 2016  11:44 amTake a look at any child, from age two or three onward and you’ll undoubtedly see him or her with a computer game, tablet or Smartphone in hand. This is the age of communication technology, and it’s not going away. In fact, the world will only increase its connectivity as time marches on. Schools, too, are getting in on the technological revolution, albeit more slowly and clumsily than some would like. Students have no problem adapting to new technology – in fact, there are concerns about how such intense use of tech devices will affect them long term. What the Research Tells Us About Tech and Teaching There is some evidence that technology may actually be affecting the student brain, reports... 
The Teacher Shortage
5 Aug 2016  2:19 pmThere’s an old bromide that declares, “Those who can’t do, teach.” Its assumption – that teachers are people with no practical skills, so they turn to the classroom to earn their livings – is emblematic of the lack of respect accorded to teachers in the United States today. Disdain for teaching among the general population is reflected in policy and resource allocation and is one of the reasons teachers in America are leaving the profession in droves and enrolment in teacher training programs is plummeting. Between 2010 and 2014, the number of people entering teacher training programs dropped by 30 per cent nationwide, although California, for example, experienced a 55 per cent drop from 2008... 
Homeschooling in America
22 Jul 2016  2:00 pmIf you’re one of the growing number of parents contemplating using homeschooling as an option for educating your children, there’s a lot of positive news about this learning model to help you make an informed decision. Three decades ago home schooling was illegal in 30 states, but now, it’s become recognized as an achievement springboard that continues to offer value added learning advantages that traditional education has been unable to deliver consistently. Furthermore, online learning tools are leveling the playing field and even providing advantages that were once only within the domain of the wealthy. For a quick overview of homeschooling in the US, check out the infographic below. Want To Embed... 
Military Base School Students OutAchieving Their Civilian Peers
15 Jul 2016  12:21 pmThe troubled American public school system need not look outside its borders to find a system that isn’t broken as a role model. The schools on military bases throughout the United States is outperforming their public brethren and narrowing the gap between the performance of black and their white counterparts, too, according to results from the 2011 National Assessment of Educational Progress, the U.S. national testing program. At Department of Defense Education Activity (DoDEA) schools, 39 percent of fourth graders score as proficient in reading compared with 32 percent of all public school students. DoDEA school black fourth graders alone scored an average of 222 (out of 500) in reading, compared to...
