Sally Reis' letter to the editor pointed to prominent English professor, Regina Barreca, and philosophy professor Michael Lynch as a reason for an unassailable record on the humanities. The author disagrees.


Most Popular Stories

Despite letter to editor, UConn still corporatized
Search for "math OR mathematics"27 Sep 2016  10:45 pm 
New model could point way to microbiome forecasting in the ocean
Mathematics News  ScienceDaily22 Sep 2016  8:28 amA new mathematical model integrates environmental and molecular sequence information to better explain how microbial networks drive nutrient and energy cycling in marine ecosystems. 
Zeno on the Mountain
Scientific American  Math26 Sep 2016  12:20 pmHiking my way to a new appreciation of a classic mathematical paradox  Read more on ScientificAmerican.com 
47 Great Moments in Education Equality
Blog – DreamBox Learning1 Sep 2016  9:20 amA timeline of events that have helped close the equality gap in education. While we’re still working toward education equity, our nation has made great strides during the past two centuries. For example, thanks to the ConnectED Initiative, the FCC ERate program, and the efforts of organizations like EducationSuperhighway, we should soon be able to take advantage of the promise of educational technology to reach every student. Check out our timeline of 47 great moments in education equality. 1785 The Land Ordinance of 1785 states that the western territories are to be divided into townships… 
Indexing with Curly Braces
Loren on the Art of MATLAB26 Sep 2016  6:57 amI have talked about indexing a bunch of times in the past, including my last post. Recently I have visited quite a few customers who still get tripped up a bit sometimes. So I thought I'd try again.ContentsCell ArraysWhere People TripHow to Extract Contents from a CellWhat If I Want the Contents from Multiple Cells?TablesExtra the Data Compatible with NumbersFollow UpCell ArraysWhat are cell arrays? In MATLAB, they are variables that hold, in each "cell", other MATLAB variables. And they are "regular". By that, I mean that they have a uniform layout, equal numbers of elements in each row,…




Search for "math OR mathematics"

Despite letter to editor, UConn still corporatized
27 Sep 2016  10:45 pmSally Reis' letter to the editor pointed to prominent English professor, Regina Barreca, and philosophy professor Michael Lynch as a reason for an unassailable record on the humanities. The author disagrees. 
UNC In Focus: Professors work to bridge gap for English language learners
27 Sep 2016  10:42 pm"UNC in Focus" is an occasional series that seeks to highlight the myriad research efforts undertaken by University of Northern Colorado faculty. Send ideas to tsilvy@greeleytribune.com. 
Project has WG Beekeepers Association abuzz
27 Sep 2016  10:42 pmJennifer Leavey, director of the Georgia Tech Urban Honey Bee Project, spoke to members of the West Georgia Beekeepers Association Monday night. 
New, stronger crypto standard lacks backward compatibility
27 Sep 2016  10:37 pmThe Standards News Portal is updated on a daily basis to bring you the most important news about standards  how they are created, how they affect you  and who's doing what to whom. The Standards News Portal was launched in February 2002 and currently contains 8289 categorized, searchable articles, perhaps the largest archive of its type in existence. 
Eugenie Rae McGlaughlin
27 Sep 2016  10:33 pmEugenie Rae McGlaughlin, 71, of West Railroad Street, passed away late Monday, Sept. 26, 2016, at her home in McClure.



Mathematics News  ScienceDaily

New model could point way to microbiome forecasting in the ocean
22 Sep 2016  8:28 amA new mathematical model integrates environmental and molecular sequence information to better explain how microbial networks drive nutrient and energy cycling in marine ecosystems. 
Video games can have lasting impact on learning
20 Sep 2016  7:42 amA computerbased brain training program helps improve student performance in reading and math — in some cases even more than individualized tutoring, according to a new study. 
Math study shows our brains are far more adaptable than we know
19 Sep 2016  7:02 pmHuman babies and even animals have a basic number sense that many believe evolves from seeing the world and trying to quantify all the sights. But vision has nothing to do with it  neuroscientists have found that the brain network behind numerical reasoning is identical in blind and sighted people. 
3D printed material helps to regenerate bone
12 Sep 2016  9:27 amA biomaterial with the ability to serve as a support for regenerating bone tissue has been developed by researchers. The material is biodegradable and can be printed in 3D with controlled porosity. 
Sleeping brain's complex activity mimicked by simple model
1 Sep 2016  12:19 pmResearchers have built and tested a new mathematical model that successfully reproduces complex brain activity during deep sleep, according to a new study.



Scientific American  Math

Zeno on the Mountain
26 Sep 2016  12:20 pmHiking my way to a new appreciation of a classic mathematical paradox  Read more on ScientificAmerican.com 
New Take on an Ancient Method Improves Way to Find Prime Numbers
24 Sep 2016  4:00 amThe modified version of the sieve of Eratosthenes could accelerate computer calculations  Read more on ScientificAmerican.com 
A Mathematical Birthday Life Hack
11 Sep 2016  1:00 pmSave money and be the life of the next party with this one weird trick  Read more on ScientificAmerican.com 
The Kilogram's Makeover Is Almost Complete
4 Sep 2016  4:30 amIt’s the last standard of measurement that is still based on a physical object—but it will soon be derived from a mathematical constant  Read more on ScientificAmerican.com 
How Converting between Addition and Multiplication Makes Math Easier
3 Sep 2016  9:00 amThe power of logarithms, zero and the word or  Read more on ScientificAmerican.com



Blog – DreamBox Learning

47 Great Moments in Education Equality
1 Sep 2016  9:20 amA timeline of events that have helped close the equality gap in education. While we’re still working toward education equity, our nation has made great strides during the past two centuries. For example, thanks to the ConnectED Initiative, the FCC ERate program, and the efforts of organizations like EducationSuperhighway, we should soon be able to take advantage of the promise of educational technology to reach every student. Check out our timeline of 47 great moments in education equality. 1785: The Land Ordinance of 1785 states that the western territories are to be divided into townships made up of 640acre sections, one of which was to be set aside “for the maintenance of public schools.” From... 
What’s New
23 Aug 2016  1:49 pmThe DreamBox development team has done it again! In following through on our promise to continuously innovate and provide actionable insight into student learning, we are excited to share our latest enhancement to DreamBox. Don’t take our word for how cool it is. Login and experience it for yourself! Activity Feed Enhancements. Get specific details about what your students are working on. In addition to usage and progress data, you can see what your students have been working on in DreamBox over thelast 30 days. Activity Feedsat the classroom and the student level provide actionable information on the Dreambox Lesson Groups your students are working on and their success in completing ... 
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...



Loren on the Art of MATLAB

Indexing with Curly Braces
26 Sep 2016  6:57 amI have talked about indexing a bunch of times in the past, including my last post. Recently I have visited quite a few customers who still get tripped up a bit sometimes. So I thought I'd try again.Contents<ul><li>Cell Arrays</li><li>Where People Trip</li><li>How to Extract Contents from a Cell</li><li>What If I Want the Contents from Multiple Cells?</li><li>Tables</li><li>Extra the Data Compatible with Numbers</li><li>Follow Up</li></ul>Cell ArraysWhat are cell arrays? In MATLAB, they are variables that hold, in each "cell", other MATLAB variables. And they are "regular". By that, I mean that they have a uniform layout, equal numbers of elements in each row, each column, each page, etc. as you march along the dimensions. How do you get information into them, and out from... 
Introducing String Arrays
15 Sep 2016  6:02 amToshi is back for today's guest post. You may have seen Toshi's earlier posts about text analytics and he often deals with text in his data analysis. So he is very excited about new string arrays in R2016b. One of the new features I love in R2016b is string arrays, which give you a new way to handle text in MATLAB in addition to the familiar character arrays and cell arrays of character vectors. String arrays are most helpful when dealing with text in your data. In today's post I walk through some practical examples with text data to demonstrate how to use string arrays.Contents<ul><li>Analyzing Baby Name Trends</li><li>String Concatenation</li><li>Combine Files to Create a Single Table</li><li>String Comparison</li><li>Memory Use and Performance of...</li></ul> 
Fifteen Years of MATLAB Central Memories!
6 Sep 2016  5:55 amWow! It's been fifteen years since MATLAB Central was set up for the MATLAB community! What a crazy and wonderful time it's been.Contents<ul><li>The Art of MATLAB</li><li>Favorite Topics</li><li>MATLAB Central is More than Blogs</li><li>Celebrate</li></ul>The Art of MATLABThe first blog to appear was Pick of the Week. As you may know, I have been writing my blog for a fairly long time  I started in December 2005. I chose to call it the Art of MATLAB because that expresses my feelings about programming. There are often many ways to say the same thing. It's an art to say what you want and say it well. I hope I've accomplished that most of the time.I know I've messed up sometimes, and thankfully, with smart and generous readers as you are, I am... 
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...



Homeschool Math Blog

Make It Real math workbooks
26 Sep 2016  8:19 amMake It Real Learning products are back at MathMammoth.com! Make It Real Learning workbooks each concentrate answering the question, "When am I ever going to use this?" The workbooks contain activities or problem situations taken from reallife, with real data. Some examples of the situations are: cell phone plans, autism, population growth, cooking, borrowing money, credit cards, life spans, music downloads, etc. etc.As students work through the problems, they can use the math skills and concepts they have learned in their math curriculum (such as the concept of average or graphing), and apply those to a situation from reallife.=> Read more here Check out also the FREE samples and try the... 
Free video lessons for decimal arithmetic
22 Sep 2016  2:51 pmDecimals, decimals, decimals... math curricula spend a LOT of time with decimals in grades 46. And yes, a lot of it is necessary.But perhaps your child can grasp the concepts quicker with these videos, and then be able to progress faster and easier. Decimal division in particular can be a stumbling block.So, check out my new videos and bookmark the page for later use! 
Substitutions for the word "very" + adjective
19 Sep 2016  6:52 amI know this is offtopic but I enjoyed glancing through it and it might very well benefit and be of interest to your students... so here goes. :)It's a list of 128 adjectives you can use instead of "very" and some weak adjective, and comes from a company that does professional proofreading: 
Visual tool  find all the factors of a number
18 Sep 2016  8:07 pmHere's a nice factoring calculator that lists all the factors of a given number and also gives a neat VISUAL that pairs the factors. You could use it to show your children/students some examples, and then of course let them PLAY with it! :)See for example factors of 72, And all the factors of this large number.Personally, I think it could be improved by listing the factors in order from 1 to the number itself, so that the pairing will then show how the largest and the smallest factors are paired, then the 2nd largest with the 2nd smallest, and so on. Neat anyway! 
Probability games
16 Sep 2016  9:42 amHere's a REALLY NEAT collection of interactive activities & games for basic probability concepts. Great for middle school!For example, you get to experiment what happens to the probability distribution when a die is biased. Just roll the die 100s or 1000s of times at one push of a button and see the distribution. In another activity you need to figure out IF a die is biased or not.Then the collection includes games that are based on the probabilities of obtaining different sums or differences with two dice. Or, you get to fix a match box machine that is producing too much variation in the number of matches per box. First you take lots of samples and analyze the situation using boxplots, and then you adjust...



DeniseGaskins.com

Calling All Math Teacher Bloggers and Homeschoolers: Carnival Time!
19 Sep 2016  5:32 am[Image by Bob Jagendorf (CC BYNC 2.0) via Flickr.] The monthly Math Teachers at Play (MTaP) math education blog carnival is almost here. If you’ve written a blog post about math, we’d love to have you join us! Each of us can help others learn, so in a sense we are all teachers. Posts must be relevant to students or teachers of schoollevel mathematics (that is, anything from preschool up to firstyear calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival. <ul> <li>Click here to submit your blog post.</li> </ul> Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to... 
If You Read Fiction, Check This Out
1 Sep 2016  7:54 amI love reading fiction, especially when I find a good story by a newtome author. And that’s why I LOVE the Fiction River anthology series. I’ve been reading it for the last three years, and I just signed up for a twoyear subscription renewal. If you like pageturning, heartwrenching, uplifting (mostly) stories that cross and transcend genre, check it out: <ul> <li>Fiction River Kickstarter Campaign</li> </ul> I’m not the only one who enjoys Fiction River — the Kickstarter drive met its funding goal in only 23 hours. Wow! But there’s still plenty of time to get in on the fun… Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other... 
Making Sense of Arithmetic
29 Aug 2016  12:34 pmHomeschoolers have an advantage in teaching math: As our students grow, our own understanding of math grows with them because we see how the ideas build on each other. This is especially true for those of us with large families. We pass through the progression of concepts with each student, and every pass lays down another layer in our own minds. If you’d like to shortcut that process, check out Graham Fletcher’s Making Sense of Elementary Math video series. He’ll walk you through the topics, showing how manipulatives help build early concepts and gradually give way to abstract calculations. “Understanding the vertical progression of mathematics is really important in the conceptual development of... 
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,...



Computational Complexity

Who's Afraid
27 Sep 2016  4:36 amThe playwright Edward Albee passed away earlier this month at the age of 88. I had never actually seen any of his plays so I took the opportunity to watch the 1966 movie Who's Afraid of Virginia Woolf?based on the play. The play has four characters, George, a history professor in his forties and his wife Martha, the daughter of the University's president. Joining them for a late get together is a young biology professor and his wife. The movie had an incredible cast: Richard Burton, Elizabeth Taylor, George Segal and Sandy Dennis. All nominated for academy awards. The women won. The movie covers many themes, mostly revolving around the disintegrating relationship between George and Martha. George did... 
Boris Trakhtenbrot (19212016)
22 Sep 2016  10:02 amI woke up this morning to two pieces of news. Subhash Khot has just been named a MacArthur Fellow, the "genius" award, for his work on unique games. But I also just learnedabout Monday's passing of the great Russian theorist BorisTrakhtenbrot at the age of 95. Trakhtenbrot has a number of important results in automata theory, model theory and logic to name just a few areas. In computational complexity we know him best for the Gap Theorem which he proved independently with Allan Borodin. Roughly the gap theorem states that for any computable f there is a computable timebound t such that DTIME(t) = DTIME(f(t)), every problem solvable in time f(t) can also be solved in time t. For example there is a time... 
Academic Rankings Foster Competition
14 Sep 2016  10:26 amThis week US News and World Report released their undergraduate rankingsearlier this week. A time for schools to brag. US News and World Report used to publish an actual weekly news magazine, now they mostly just focuses on rankings. Besides various categories of undergrad institutions USN&WR ranks engineering and business programs. There are many other ranking systems of varying quality but in the US we take the USN&WR rankings the most seriously. Computer Science does not get an undergraduate ranking. Computer engineering doesnot the same. CS does get rankings as a PhD program, last time in 2014. I've posted on rankings in 2005, on the failed NRC rankings of 2010, on using metrics for rankings, and... 
Noam Nisan wins the Knuth Prize
10 Sep 2016  8:40 amNoam Nisan will receive the 2016 Donald E. Knuth Prize, the highest honor in theoretical computer science,for his work in computational complexity and algorithmic game theory. He'll receive the award at the upcoming FOCS conference. I've known Noam since we were fellow grad students in Berkeley in 1985 and we have become good friends and colleagues. Noam Nisan started his career in computational complexity and Luca posts about several of his seminal works in derandomization, interactive proofs, communication and circuit complexity. I'll focus this post on Nisan's 1992 paper with Mario Szegedy,On the degree of boolean functions as real polynomials. Let f be a Boolean function on n variables and p a... 
Why I Don't Believe in ET
7 Sep 2016  12:48 pmIs there life on other planets? The naive answer is "of course, why should Earth be special." What makes a lottery winner special? We could have just won the life lottery and the losers aren't around to complain. The more scientific approach uses variants of the Drake Equation. I'll use the variant from the recent paperA New Empirical Constraint on the Prevalence of Technological Species in the Universe by Frank and Sullivan. We define the ‘‘Aform’’ of the Drake equation, whichdescribes the total number of technological species that haveever evolved anywhere in the currently observable Universe: A = Nfpnpflfift where N is the total number of stars, fp is the fraction ofthose stars that...



Mathematics and Computation

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

Factorization diagram cards are here!
11 Sep 2016  8:50 pmIt’s been a long process, but factorization diagram cards are finally available for purchase! If you just want to purchase a set right this minute, then click the above link! If you want to learn more, keep reading. History As explained in this original blog post from 2012 and this followup post, the basic idea behind factorization diagrams is to visualize the prime factorization of a positive integer by taking dots and recursively grouping them according to the prime factors. For example, can be visualized by making two groups of three groups of five dots, as seen in one of the cards above. You can find a lot more information about factorization diagrams here, including links to related things... 
Post without words #11
8 Sep 2016  7:14 pm 
A few words about PWW #10
30 Aug 2016  8:07 amIf you still want to think more about the picture in my previous post, stop reading now! Here’s a simple way to think about how the picture is made, as noted by Fergal Daly. The th circle (starting with ) has evenly spaced radial spokes, which we think of as being numbered clockwise from through , with spoke always lying on the positive xaxis. Then spoke has a blue dot at its end if and only if is relatively prime to , that is, . So, for example, the tenth circle has dots on spokes , , , and , since every other number shares a factor with . Note in particular that , and in general (this is not a special case, it’s just a natural consequence of the definition of $). This is why no circle except... 
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>



eon

Truncatable Primes
27 Sep 2016  7:06 pmA colleague asked about sequences of primes a(n) such that a(n+1) is obtained by appending a single digit (in base 10) to the right of a(n). For example: 3, 31, 311 … Some thinking lead to the conjecture that such sequences are of finite length and that it is possible to use an exhaustive search to find all of them. A natural question would be what is the longest possible sequence but I was unable to find any conclusive answer on the web. So I decided to write a simple (and not very efficient) recursion in maple to search for all such primes. Here’s my ugly code: cat3prime:= proc(n) local d, s, i; s:=n; d:=irem(n,10); if isprime(s) then print(s); return(cat3prime(10*s+1)); else for i from d to 7 by 2 do ... 
Twin corrections
19 Sep 2016  5:41 pmToday is the 20th anniversary of the passing of Erdős and I would like to make two corrections. I had always thought the accent on Erdős’ name was ö , html code ö but it is actually Hungarian, html code ő. The second is the coffee quote which I had attributed to him. I realised my mistake a number of years ago but never got a chance to correct it online. Both errors were perpetuated in this post from 2004. Here is a quote from Erdős’ paper “Child Prodigies” In Hungary, many mathematicians drink strong coffee, in fact Rényi once said “a mathematician is a machine which turns coffee into theorems.” Correction done but sadly I am still not quite sure how to pronounce his name... 
Bollobas on solving problems
24 Aug 2016  6:24 pmWhat you should be terrified of is a blank sheet in front of you after having thought about a problem for a little while. If after a session your wastepaper basket is full of notes of failed attempts, you may still be doing very well. Avoid pedestrian approaches, but always be happy to put in work. In particular, doing the simplest cases of a problem is unlikely to be a waste of time and may well turn out to be very useful. Bela Bollobas, from Advice to Young Mathematicians 
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]



WordPress Tag: Mathematics

Homework for 28.09.16
27 Sep 2016  10:39 pmDear Learners Here is your today’s H.W hw280916 
Homework as on 28.9.16
27 Sep 2016  8:41 pmDear Learners, Here is your today’s H.W wednesday With Regards, Preeti Lashkari 
Homework as on 28.9.16
27 Sep 2016  8:35 pmDear Learners, Here is your today’s H.W wednesday With Regards, Charu Soni 
Bonus blog, being about Bob's boast
27 Sep 2016  7:48 pmAnd now for something a little different… (This is adapted from a Car Talk puzzler.) Bob and Sally are ball players. They both show up for spring training (they play in the Bluehorse pro league) and Bob, as ever, is boastful. “Hey Sally,” he says, “I hit better than you before the All Star Break.” “Yeah, I was injured in April,” says Sally. “You didn’t have to hit that well to beat me.” “Well, the point is, I had a higher average than you did before the All Star Break. And then after the All Star Break, you went on a tear, you were hitting a lot more, getting on base a lot more. And yet I still had a higher average than you, since the All Star Break. Even though, you know, I was tired from being on the All... 
Water under the bridge
27 Sep 2016  7:27 pmSt. Petersburg, 1835 The past week has been very grueling and I hardly had time to catch my breath. Analysis is occupying a major chunk of my time and I have not been able to get to other interesting problems. Today, I finally got around to checking the mail. Most of the mail is regarding acceptance of some of the papers I submitted over the past couple of years. Only minor corrections needed before final publication. With the funding situation as it is, I will take acceptance from any journal as good news. There was one letter from the Mayor of Konigsberg and I thought I will get to it later, dismissing it as something not very relevant. Katharina insisted I respond promptly as it could as well be some...



Institute for Mathematics and Computer Science

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



mathrecreation

octagonal star and monster tilings
20 Sep 2016  7:32 pmRegular octagons can be placed edge to edge so that their centers lie on the vertices of a square.These form a nice tiling of octagons and squares (a semi regular tiling):Regular octagons can also be placed edge to edge on the vertices of a larger octagon by skipping an edge  this leaves a star in the center.These rings of octagons also fit together nicely, leaving those square gaps, so we see both the 4rings (whose centers are squares) and the 8rings (whose centers are eightpointed stars).In a couple of posts a while back (here and here), there is a rule that describes how copies of the same regular polygon can fit into rings like these. I have been playing around with these, noticing that there are... 
islamic geometric patterns of Eric Broug
14 Sep 2016  8:04 pmbased on Kairouan Mosque pattern(p. 30)I first heard about Eric Broug's work from a post by Alex Bellos, mentioned here. Alex provided a set of instructions by Eric that showed how to construct a design like the one below.similar to Mosque of alNasir Muhammad,but on a square grid instead of hexagonal (p. 82)I was reminded of Eric's work after playing around with sliceformstudio, and ordered a copy of his book Islamic Geometric Patterns. It provided exactly the sort of instructions I was looking for, and has been a lot of fun to play with  the page numbers in the image captions of this post refer to that book.These are pure straightedge and compass constructions and building up the elaborate designs... 
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...



Maths Tips From Maths InsiderMaths Tips From Maths Insider

8 Things to Love About Tabtor Math
1 Sep 2016  10:50 pmBy far the most popular post on Maths insider is my post, 8 Things to Hate About Kumon! As a former Kumon instructor who now works as an instructor with Tabtor (a play on the words Tablet and Tutor!) I’m writing this post to give a unique perspective as someone who has worked for both companies. At Tabtor I look after many, many exKumon students including a family with 4 kids who switched from Kumon to Tabtor so that their children could explore the wider curriculum that Tabtor offers. So whether your kids are currently doing Kumon, another math program or you’re just starting to look into math programs to support your child’s math, let me share with you the 8 things to love about Tabtor. 1.... 
12 Brain Building Math Board Games for Curious Kids
31 May 2016  6:02 amWith summer coming up, I’m on the lookout for a new game or two to liven up quiet afternoons. It’s an added bonus if I can sneak a little math practice in without anyone noticing what I’m up to. Here are my top twelve picks for fun games with math skills at the core. Take a look at this previous post on math board games for even more inspiration. 1. SmashUp Game Aliens, Ninjas, Pirates, Dinosaurs and more battle to smash more bases than the opposing team. Eight different factions and dozens of combinations to try. ‘It’s really fast setup, it’s really fast play … It’s easy to pick up the rules.’ 24 players, recommended for age 13+. 2. Melissa & Doug ShutTheBox A deceptively... 
15 More Cool, Beautiful and Inspiring Math Quotes
20 May 2016  4:16 amMath Quote Inspiration Are you looking for some cool and beautiful math inspiration? Check out the Math Quote GIF’s below that highlight the eternal beauty of math. For more math inspiration check out my post 13 Cool, Beautiful and Inspirational Math Quotes. Enjoy! “Wherever there is number, there is beauty.” Proclus “The book of nature is written in the language of Mathematic” Galileo “Mathemathics is the queen of the science” – Carl Friedrich Gauss “The advancement and perfection of Mathematics are intimately connected with the prosperity of the State” Napoleon “A Mathematician who is not also something of a poet will never be a complete mathematician” Karl Weierstrass “The mathematician does... 
How to Help Your Child with Math – Even If You’re Not a “Math” Person
19 May 2016  7:57 pmHave you ever found yourself going round and round in circles when trying to help your child with math? Believe it or not – I’ve been there! Yes – I’m a math teacher – a lover of math Hello, this is Caroline from www.mathsinsider.com and I’m going to talk today about a question that a Maths insider reader asked which was,” How can I help my child with their maths if I’m not a math person?” I understand where you’re coming from So to start off, I’d just like to say that I obviously…I really like maths, I love sciences, I like geography, history I like most of the subjects, but one of the subjects that I don’t feel completely confident in supporting my kids in is English or Language Arts. I kind... 
The Complete Guide to Faster Times Tables in Just 31 days.
3 May 2016  1:13 am“I’ll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is–oh dear!” Alice’s Adventures in Wonderland If, like Alice, your child is struggling with remembering their times tables, you’re not alone! Ask a random selection of kids some of the trickier times tables and you’re going to get quite a few “Ums” or “It’s….well…it’s…….” The thing is – it’s not necessarily your kids fault that they’re not comfortable with the times tables facts. Perhaps: <ol> <li>They weren’t given time to thoroughly learn them</li> <li>They haven’t had time to practise them</li> <li>They don’t see the point of being fast at...</li></ol>



Motion Math

New game content…update your apps!
22 Sep 2016  10:38 amWe’re encouraging all Motion Math subscribers to update your apps, or politely ask your local IT guru to do so. (Even better, turn on “Automatic app updates” on your iPads.) Why?... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
The Loan Shark
22 Sep 2016  10:00 amWe’ve just added a new feature to the latest version of our economics simulation game Cupcake: the loan shark. Loans and debt are a significant economic and lifeskill issue worth discussing with... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
More ways to Match – new levels!
20 Sep 2016  5:26 pmHello Motion Math Educators! We hope your school year is off to a great start. We’ve been working hard to improve the Motion Math experience for administrators, teachers, and of course,... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
Top 7 Criteria of a Great Learning Game
17 May 2016  9:52 pmAccording to a 2015 study by Project Tomorrow, 62% of elementary school teachers use games in the classroom. At Motion Math, we’re positively thrilled that more and more teachers recognize gaming’s... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
Control which games appear in Motion Math
20 Mar 2016  9:55 amWe’ve added a new level of customization to Motion Math. If there are games with content too advanced or too basic for your students, or if you want students to focus on a particular math... [[ This is a content summary only. Visit my website for full links, other content, and more! ]]



MIND Research Institute Blog

4 Changes This Middle School Math Teacher Made to Boost Student Motivation
27 Sep 2016  11:00 amKris Baker likes to have fun in class. When you walk into her 7th and 8th grade math intervention classes at Milford Junior High School in Ohio, you see students jotting math problems on their desks with dryerase markers, solving equations to earn the chance to make a shot in “Trashketball,” or playing classic board games as a reward for working hard. Last year, Baker started using ST Math in her classroom and, like many teachers who incorporate education technology in the classroom, she used a rotation model. She would put a group of students on ST Math, which freed her up to teach another small group. Unfortunately, when her students got stuck on one of the learning games in the program, she was... 
How My Daughter Finally Learned Math
23 Sep 2016  9:00 amBy: Suzie Murphy “Look, honey, 4 + 6 = 10, and 6 + 4 = 10, always, always, always! It will never change today, tomorrow, or the next day! Now, what is 6 + 4?” My 11yearold daughter looked at me perplexed. “Ummmm … let me see …” she said, as she tried to puzzle it out in her head. “Honey,” I said, “here, look at these blocks. See the 4 block? See the 6 block? Now watch how I put these together to equal the 10 block.” My daughter shook her head and said, “Mom, you don’t seem to understand that I just don’t get it. How can I ever learn it if I don’t get it?” As a homeschool mom, I was afraid that my worst fears were going to be realized: my daughter would never, ever... 
5 Reasons You Should Definitely Volunteer at the Math Fair
20 Sep 2016  9:00 amAutumn, the best season of all, is upon us! Some people look forward to finally busting out their sweaters and others are waiting for that first sip of pumpkin spiced latte. For me though, fall has come to mean one thing: Math Fair. I look forward to it all year, but the excitement really ramps up around this time. Exhibits are being finalized, registration has opened and there’s a certain electricity around the MIND offices as November 5th draws near. Math Fair is a massive event, to be sure. Just take a look at this video and you can see all of the time and talent that goes into changing kids’ perceptions of mathematics through this single event. It cannot be done alone. No one knows that better than... 
Bulletin Boards: A Visual Way to Build School Culture
16 Sep 2016  12:00 pmI have always loved the beginning of the school year. It is a time filled with excitement, and new beginnings. It is also a great opportunity to establish a strong school culture that engages and excites students about mathematics. While on the surface, school culture seems like a purely nonacademic factor, it can strongly influence students’ academic achievement. Through the Every Student Succeeds Act (ESSA), nonacademic factors are now being included in statewide accountability plans. While assessments tend to be the focus when student’s academic performance is discussed; the inclusion of the nonacademic factors, specifically school culture, highlights the importance of an engaging learning... 
ResearchBased Solutions to Address Math Anxiety
13 Sep 2016  9:00 amHeadlines about math anxiety never seem to stop making the rounds on my newsfeed: <ul> <li>Stop telling kids you’re bad at math. You are spreading math anxiety ‘like a virus.’ –Washington Post</li> <li>Square root of kids’ math anxiety: Their parents’ help –The New York Times</li> <li>High anxiety: How worrying about math hurts your brain –TIME Magazine</li> </ul> As an educational design researcher, it was concerning to encounter so many media reports about the detrimental effects of math anxiety but not nearly as much about how to address it. We know that many students experience math anxiety firsthand: that feeling of fear, apprehension, and helplessness when tackling a math problem. And research shows that these...



StudyPug

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