The Islamic State seized Mosul in June 2014 and has fought doggedly to retain the group's largest stronghold in Iraq. The United Nation believes that up to half a million people remain in the area still controlled by the militants in Mosul, 400,000 of which are in the Old City with little food and water supply and no access to hospitals.


Most Popular Stories

US service member killed near Mosul, Iraq
Search for "math OR mathematics"30 Apr 2017  4:59 am 
Math under My Feet
Scientific American  Math29 Apr 2017  7:00 amI took a walk and tripped—almost literally—over a beautiful octagonal tiling  Read more on ScientificAmerican.com 
Fending Off Math Anxiety
Mathematics24 Apr 2017  4:00 amParents can help by starting to talk to children at an early age about numbers in everyday life. 
ESSA Unlocks Exciting New Opportunities for Creativity and Innovation
Blog â DreamBox Learning4 Apr 2017  7:00 amThe Every Student Succeeds Act (ESSA) is a true game changer. It gives states the right to define educational standards for their schools and the flexibility to determine how students meet those standards. The bill also authorizes new funding streams that can potentially help states and districts invest in technology to support everything from personalized learning and enhanced digital content to advanced assessment and data analyticsâas well as the staff development needed to put these tools to use. Here are some things to consider as you prepare to make these critical investments for your… 
Working with Text in MATLAB
Loren on the Art of MATLAB24 Apr 2017  6:43 amI'd like to introduce today's guest blogger, Dave Bergstein, a MATLAB Product Manager at MathWorks. In today's post, Dave discusses recent updates to text processing with MATLAB.ContentsExample: How Late Is My Bus?Text as DataRecommendations on Text TypeLooking to the FutureIn today's post I share a text processing example using the new string array and a collection of new text manipulation functions, both introduced in R2016b. I also give recommendations on when best to use string, char, or cell for text and share some of our thinking on the future.Also be sure to check out Toshi's post…




Search for "math OR mathematics"

US service member killed near Mosul, Iraq
30 Apr 2017  4:59 amThe Islamic State seized Mosul in June 2014 and has fought doggedly to retain the group's largest stronghold in Iraq. The United Nation believes that up to half a million people remain in the area still controlled by the militants in Mosul, 400,000 of which are in the Old City with little food and water supply and no access to hospitals. 
Even the Bulls' star agrees, the BradleyButler matchup goes Celtics' way
30 Apr 2017  4:59 amChicago G Isaiah Canaan was inactive the first three games of the series and made his career postseason debut Sunday in Game 4, finishing with 13 points and three assists in 34 minutes. Simple math tells us three points is more than two, but there's nothing wrong with a simple jumper from 15 feet. 
Peg + Cat
30 Apr 2017  4:58 amIn each episode, Peg and Cat find themselves thrust into the middle of a wacky word problem. This problem isn't just an academic exercise for them, it's a real life problem...a messy funny crisis they have to solve to get them out of trouble. 
Testgrading business helps Lynbrook firm double revenue in 5 years
30 Apr 2017  4:45 amIf you used an Optimum login , click the Connect Account button to use your Optimum login info to manage your Newsday subscription account. If you used a Newsday login , it looks like it's not connected to an active subscriber account. 
3 Reasons It's Dumb to Take Social Security Benefits at 62
30 Apr 2017  4:40 amAre you thinking about claiming benefits as soon as you possibly can? Here are three reasons you might want to reconsider. The year in which you can claim your "full" retirement benefits is 67, according to the Social Security Administration.



Scientific American  Math

Math under My Feet
29 Apr 2017  7:00 amI took a walk and tripped—almost literally—over a beautiful octagonal tiling  Read more on ScientificAmerican.com 
Shoelace Study Untangles a Knotty Problem
12 Apr 2017  5:48 pmResearchers have trotted out data that show a combination of whipping and stomping forces is what causes laces to unravel without warning. Karen Hopkin reports.  Read more on ScientificAmerican.com 
The Simple Math behind Crunching the Sizes of Crowds
12 Apr 2017  6:30 amHow large was the crowd at the recent U.S. presidential inauguration? Or the inauguration eight years ago? Keep on reading to find out how crowd sizes are estimated  Read more on ScientificAmerican.com 
Probing the Great Unknown
11 Apr 2017  5:45 amAre there are questions in science and mathematics that by their very nature are unanswerable?  Read more on ScientificAmerican.com 
Watch Live Today: Exploring Pure Mathematics Through Baking [Video]
5 Apr 2017  11:50 amMathematician Eugenia Cheng will describe how cooking can offer insight into abstract math  Read more on ScientificAmerican.com



Mathematics

Fending Off Math Anxiety
24 Apr 2017  4:00 amParents can help by starting to talk to children at an early age about numbers in everyday life. 
The Worldâs Most Beautiful Mathematical Equation
15 Apr 2017  12:30 pmMath can make our brains light up in the same way art and music do. 
A Lizard With Scales That Behave Like a Computer Simulation
12 Apr 2017  11:00 amTwo mathematical models converge to illuminate the process through which an ocellated lizardâs scales repeatedly change color. 
Igor Shafarevich, Russian Mathematician With a Mixed Political Legacy, Dies at 93
13 Mar 2017  4:49 pmHis work was internationally renowned, but Professor Shafarevichâs reputation as an antiSoviet dissident was later tarnished by accusations of antiSemitism. 
Beyond âHidden Figuresâ: Nurturing New Black and Latino Math Whizzes
17 Feb 2017  2:00 amA free math camp for middleschool students from New Yorkâs poorest neighborhoods was an effort to increase the number of blacks and Latinos with advanced math degrees.



Blog â DreamBox Learning

ESSA Unlocks Exciting New Opportunities for Creativity and Innovation
4 Apr 2017  7:00 amThe Every Student Succeeds Act (ESSA) is a true game changer. It gives states the right to define educational standards for their schools and the flexibility to determine how students meet those standards. The bill also authorizes new funding streams that can potentially help states and districts invest in technology to support everything from personalized learning and enhanced digital content to advanced assessment and data analyticsâas well as the staff development needed to put these tools to use. Here are some things to consider as you prepare to make these critical investments for your schools. Embracing new models of learning that leverage technology ESSA advances personalized and projectbased... 
The Importance of Adaptivity, âBenevolent Friction,â and Finding Everyoneâs Spark
31 Mar 2017  7:35 amToday marks the last day of Womenâs History Month. It has been a great month for everyone to come together to celebrate the achievements of women across all areas and industries. On the blog, weâve enjoyed profiling topics ranging from âCelebrating the reallife ladies of STEMâ to âThree ways parents can help eliminate the educational divide.â My personal hope, of course, is that we canâand shouldâcontinue to celebrate the achievements of women beyond this month. We are also particularly honored today to have our president and CEO, Jessie WoolleyWilson, profiled as a leader in the âCorner Officeâ column of The New York Times. In addition to delving into Jessieâs early years and... 
The One Part of Your Grant Proposal You Really Need to Ace
30 Mar 2017  7:00 amEvery part of your grant proposal is important, but if you donât nail the abstract your request for funding may never see the light of day. Often, the abstract is the first section a potential grantor will read. Think of it as your opportunity to make a good first impressionâperhaps your only opportunity.Â Five tips for preparing a winning abstract You know thereâs a lot of competition for grant dollars and grantors field a ton of proposals. So itâs no surprise that they use the abstract to quickly separate fundable requests from those that may not so neatly align with their priorities. If you want to improve your chances for consideration, you need to ace your abstract. Here are five ways to make... 
DreamBox Recommendations for 2017 NCSM/NCTM Conference Attendees
28 Mar 2017  5:00 amThe first week of April, San Antonio will host two of the biggest math education events of the year and DreamBox will be in town for both. Weâll kick things off on April 3rd at the 2017 NCSM Annual Conference and continue the fun at the NCTM 2017 Annual Meeting and Exposition, which runs the 5th through the 8th. If youâre planning to be in town for either or both events, be sure to look us up. 2017 NCSM Annual Conference This yearâs NCSM conference boasts nearly 300 sessions presented by some of the most influential, provocative, and knowledgeable math education experts and thought leaders. DreamBox VP Dr. Tim Hudson will be presenting on Tuesday April 4th and the DreamBox team weâll be hosting... 
Tips for Attending the 2017 Blended & Personalized Learning Conference in Providence
22 Mar 2017  7:46 amThe 2017 Blended & Personalized Learning Conference (BPLC) features some of the top classroom, school, and district implementers from across the nation. Once again, the conference will be held in Providence and is expected to attract some 900 educators and leaders eager to exchange the latest blendedlearning strategies and insights. This year DreamBox CEO Jessie WoolleyWilson has the honor of introducing the exciting lunch keynote panel. DreamBox will also be the subject of a Saturday session entitled, Increasing Student Engagement and Achievement through Personalized Learning. Presented by blended learning experts and DreamBox enthusiasts Jodi Tamayoshi and Dr. Michelle Paton, this 45minute session will...



Loren on the Art of MATLAB

Working with Text in MATLAB
24 Apr 2017  6:43 amI'd like to introduce today's guest blogger, Dave Bergstein, a MATLAB Product Manager at MathWorks. In today's post, Dave discusses recent updates to text processing with MATLAB.Contents<ul><li>Example: How Late Is My Bus?</li><li>Text as Data</li><li>Recommendations on Text Type</li><li>Looking to the Future</li></ul>In today's post I share a text processing example using the new string array and a collection of new text manipulation functions, both introduced in R2016b. I also give recommendations on when best to use string, char, or cell for text and share some of our thinking on the future.Also be sure to check out Toshi's post Introducing String Arrays and Loren's post Singing the Praises of Strings.Example: How Late Is My Bus?My friend in New... 
Optimizing a Structural Design
10 Apr 2017  1:43 amToday you'll see a new demonstration of applying optimization techniques. Today's guest is Takafumi Ohbiraki. This demonstration was part of the contents of the MATLAB EXPO which was held in Tokyo last year (2016).Contents<ul><li>Design of an umbrella hook</li><li>FEM model (Using Partial Differential Equation (PDE) Toolbox)</li><li>Process of Optimization</li><li>Design of Experiments (DOE) (Taguchi design)</li><li>Calculation with setting parameters for L18</li><li>Factor Effect Chart</li><li>S/N ratio</li><li>Output</li><li>Optimization using patternsearch solver</li><li>Optimization using ga solver</li><li>Multiobjective optimization using the gamultiobj solver</li><li>Conclusion</li></ul>Optimization is a universal topic in both engineering and data science. It is a technology with high needs. Speaking of... 
Find That Signpost! Using optimization and the Google Maps API in MATLAB to find a landmark
28 Mar 2017  2:36 pmInteresting problems are everywhere. Today's guest blogger, Matt Tearle, loves the chance to apply MATLAB to any intellectually stimulating puzzle. It's a fun way to learn and practice new features.Contents<ul><li>A Postcard Becomes a Puzzle</li><li>Let's Try It in MATLAB</li><li>Try an Optimization Approach?</li><li>What Does "Distance" Mean?</li><li>How Good is the Result?</li><li>What MATLAB Have You Discovered by "Accident"?</li></ul>A Postcard Becomes a PuzzleMy wife received this postcard in the mail: This is a real signpost, directing drivers to various real towns in Maine.Never one to pass up a teaching moment, I used this to explain to my daughter how you could (theoretically) figure out the location of the signpost if you knew where all these towns were, by... 
Introducing the Signal Analyzer App
14 Mar 2017  2:27 pmToday, my guest blogger is Rick Gentile, an engineer in our Signal Processing Product Marketing group. He will introduce a new app which enables you to gain quick insights into your data.Contents<ul><li>Introduction</li><li>Getting Started with Signal Analyzer</li><li>Exploring Your Signals</li><li>Extracting Signals of Interest</li><li>Gaining Insight into Your Data</li><li>Finding Signals in Your Data</li><li>Results</li><li>Learn More About Signal Analyzer</li></ul>IntroductionSignal Processing Toolbox has helped MATLAB users generate and work with signals for many years. In our recent releases, we have expanded the ability to analyze and compare signals in the time, frequency, and timefrequency domains. You can now use these capabilities to gain insights into your data, which can... 
Symbolic Analysis of the Port Passing Problem
28 Feb 2017  12:56 pmHopefully you recall the recent post where we used a montecarlo technique to simulate an infinitelystocked port decanter passing around a table of N people (always starting at position 0), moving with probability p to the left and q to the right, only stopping when everyone at the table had... read more >>



Homeschool Math Blog

Symbolism in the passover as it happened in ancient Egypt
16 Apr 2017  6:59 amI invite you to travel back to the ancient Egypt and the first passover, and to learn of its rich symbolism, tying it in with Jesus' teaching of how we need to feed upon his flesh and his blood: EXAMINING SYMBOLISM IN VARIOUS PARTS OF THE PASSOVER TYPE FROM EXODUS 12 
Considering an online college?
21 Mar 2017  9:04 amHere's a very comprehensive resource, listing the best online colleges there are  a good starting point for researching this topic!The best 50 online colleges for 2017 It features pictures, ranking scores, cost comparisons, graduation rates, and more. 
Doodling in math class?
21 Mar 2017  7:36 amThis is mostly useful for classroom teachers, but I thought it's a really NEAT idea  and could be adapted to other situations. The students "doodle" and color in the notes however they like, which makes them REMEMBER better!Math Doodle NotesYou'll find some freebies and some commercial products here, and of course the idea of doodle notes itself. You can make these yourself also! 
Penny Pinchers Sale!
20 Mar 2017  8:32 amThis sale happens at Currclick, and every item in it is less than $3!You will find a bunch of Math Mammoth products also... check them out here.The sale runs through March 31, 2017. 
Video for your Pi day
13 Mar 2017  2:57 pmIt's just proper to feature this video again... Pi day is tomorrow (3/14)! Calculating pi with REAL pies! It is a neat video, showing how to calculate the value of Pi using real pies (yum!). It might help your youngsters remember the definition of Pi better as they remember the visual pic of pies around the big circle and pies going across. :) And not to mention the taste buds!



Denise Gaskins' Let's Play Math

Playful Math Carnival #107 via Give Me a Sine
29 Apr 2017  8:37 amCheck out the new carnival of playful math for all ages at Give Me a Sine blog. Each month’s carnival brings you a great new collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun. <ul> <li>Math Teachers at Play #107</li> </ul> This month’s post features symmetry, origami, and an ant hotel. Percents, fractions, decimals, and the bathroom sink. Algebra, geometry, and trig. And much more! Click Here to Read the Carnival Blog Hey, Blogger, Can You Spare a Time? Do you write an education or family blog? Classroom teacher, math coach, homeschooler, parent, college professor, unschooler — anyone interested in helping kids play around with math? Please consider volunteering to host the MTaP... 
Rabbit Trails and Fibonacci Poetry
26 Apr 2017  4:11 amHomeschooling Memories… Well, I hadn’t planned on spending my day that way. But one of the great things about homeschooling is the freedom to follow rabbit trails. While browsing the Carnival of Homeschooling, I found a link to Farm School blog’s article Fib Foolery, which sent me to Gotta Book for his articles The Fib and More Fibbery (read the comments on both threads, but be warned that some are crude) and several other posts, all of which set me off on a morning of poetic fun. A “Fib” is a Fibonacci poem. It’s based on syllable count, like a haiku, but the lines follow the Fibonacci counting series: 1, 1, 2, 3, 5, 8… Each number is the sum of the previous two numbers. I knew what I was going to share... 
Calling All Math Teacher Bloggers and Homeschoolers: Carnival Time!
17 Apr 2017  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 havenât been published in past editions of this carnival. Click here to submit your blog post Have you noticed a new math blogger on your block that youâd like to introduce to the rest of us? Feel free to submit another bloggerâs post in addition to... 
There Ainât No Free Candy
11 Apr 2017  5:21 amAh, the infinite chocolate bar. If only it could work in real life! But can your children find the mistake? Where does the extra chocolate come from? Here’s a hint: It’s related to this classic brainteaser. And here’s a video from Christopher Danielson (talkingmathwithkids.com), showing how the chocolate bar dissection really works. Happy munchings! CREDITS: Feature photo (top) by Yoori Koo via Unsplash. “Hershey Bar Math” video by Christopher Danielson via YouTube. The infinite chocolate gif went viral long ago, and I have no idea who was the original artist. Want to help your kids learn math? Claim your free 24page problemsolving booklet, and you’ll be among the first to hear about new books,... 
Playful Math Carnival #106
28 Mar 2017  5:13 amDo you enjoy math? I hope so! If not, browsing this post just may change your mind. Welcome to the 106th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to precollege. Let the mathematical fun begin! By tradition, we start the carnival with a puzzle in honor of our 106th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents. Try This Puzzle If you slice a pizza with a lightsaber, you’ll make straight cuts all the way across. Slice it once, and you get two pieces. If you slice it...



Basic mathematics blog

Divide using Partial Quotients
3 Apr 2017  6:12 amLearn to divide using partial quotients. Understand the concept fast! 
Estimate Quotients Using Multiples
27 Mar 2017  6:34 amLearn how to estimate quotients using multiples with this easy to follow lesson. 
Printable first grade math test
24 Mar 2017  6:43 amA printable first grade math test that can readily be printed and taken to find out how well you or your kids know very basic concepts of math. 
Printable kindergarten math test
24 Mar 2017  6:41 amA printable kindergarden math test that can readily be printed and taken to find out how well you or your kids know very basic concepts of math. 
Celsius to Fahrenheit Converter
24 Mar 2017  5:54 amUse this Celsius to Fahrenheit converter to convert temperature from Celsius to Fahrenheit and from Fahrenheit to Celsius.



Computational Complexity

So Was I
27 Apr 2017  6:57 amWhile Bill marched at the main March for Science in DC, I marched at the satellite march in Atlanta, my daughter Molly in Chicago, Scott Aaronson in Austin, Hal Gabow in New York, and Donald Knuth (pictured) presumably in San Francisco. I thank the many of you who participated in your local march. Science appreciates the support. Most of the marchers I saw did not come from the ranks of academia or professional scientists. Rather people from all walks of life who believe in the important role science and scientists have in shaping our future. Parents dragged their kids. Kids dragged their parents. There have been some worry about politicizing science and whether the march would be a bad idea. The march... 
I was at the March for Science on Saturday
24 Apr 2017  2:09 pm(Will blog on Harry Lewis's 70th Bday next week Today's post is more time sensitive.) I was on the March for Science on April 22. Here are some Kolmogorov random comments 1) Why should I go to it? One less person there would not have matters. AH but if they all think that then nobody goes. The Classic Voting Paradox why vote if the chance that your vote matters is so small (even less so in my state Maryland is one of the Bluest States). In the case of the March For Science there is another factor since I live in Maryland I really CAN go at minimal effort. Most of the readers of this blog cannot (Though there were some other marches in other cities. Scott was at a March in Austin Texas.) 2) One of... 
Will talk about Harry Lewis 70th bday conference later but for now that was then/this is now
20 Apr 2017  3:28 pmOn Wed April 19 I was at the Harry Lewis 70th birthday celebration! I will blog on that later. Harry Lewis was my thesis adviser. Odd to use the past tense I DID finish my thesis with him and so he IS my adviser? Anyway, I will do a blog about the celebration next week. This week I ponder what was different then and now (I got my PhD in 1985). False predictions that I made in 1985: 1) CS depts all have different views of what a CS major should know. By the year 2017 they will have figured out EVERY CS MAJOR SHOULD KNOW XXX and I will still write questions for the CS GRE. DID NOT HAPPEN. And a MINOR source of income for me has been cut off. 2) CS will be about 45% or more female. After all, the old... 
Understanding Machine Learning
17 Apr 2017  2:02 pmToday Georgia Tech had the launch event for our new Machine Learning Center. A panel discussion talked about different challenges in machine learning across the whole university but one common theme emerged: Many machine learning algorithms seem to work very well but we don't know why. If you look at a neural net (basically a weighted circuit of threshold gates) trained for say voice recognition, it's very hard to understand why it makes the choices it makes. Obfuscation at its finest. Why should we care? A few reasons: <ul> <li>Trust: How do we know that the neural net is acting correctly? Beyond checking input/output pairs we can't do any other analysis. Different applications have a different level of trust....</li></ul> 
Alice and Bob and Pat and Vanna
13 Apr 2017  5:07 am"The only useful thing computer science has given us is Alice and Bob"  A physicist at a 1999 quantum computing workshop Alice and Bob, great holders of secrets, seemed to pop into every cryptography talk and now you see them referenced anytime you have two parties who have something to share. Someone at Dagstuhl a few weeks back asked who first used Alice and Bob. What a great idea for a blog post, and I decided to do some binary searching through research papers to find that elusive first Alice and Bob paper. Turns out Wikipedia beat me to it, giving credit to Rivest, Shamir and Adleman in their paper A method for obtaining digital signatures and publickey cryptosystems, the paper that won them the...



The Math Less Traveled

Another greedy coins game update
29 Apr 2017  2:54 pmAnother update on the analysis of the greedy coins game (previous posts here, here, and here). I will make another post very soon explaining how to compute optimal play. In my previous post I reported that Thibault Vroonhove had conjectured the following strategy to be optimal for Alice: <ul> <li> If the two end coins have unequal values, and the larger of the two is also larger than its neighbor, take it. </li> <li> Otherwise, look at the alternating totals (i.e. the total of the âredâ coins and the total of the âblueâ coins). Take the end coin corresponding to whichever group has the higher total. </li> <li> If neither of these rules apply then it doesnât matter which coin Alice takes. </li> </ul> Note that if the first rule... 
Greedy coins game update
22 Apr 2017  10:55 amI plan to write a longer post soon, but for the moment I just wanted to provide a quick update about the greedy coins game (previous posts here and here). It turns out that the game is a lot more interestingâand has generated a lot more discussionâthan I thought when I first posted it! <ul> <li> In my previous post I conjectured that the only tied games are the ones that can be built up by surrounding a tied game with a coin () or concatenating two tied games (). That conjecture was quickly shot down, with commenters tinyboss and Thibault Vroonhove independently pointing out counterexamples: or are both tied, even though they canât be built up in the conjectured way. As you can check, with best play in...</li></ul> 
Ties in the greedy coins game
20 Apr 2017  2:35 pmIn my previous post I described the âgreedy coins gameâ and conjectured that the first player always has a strategy to win or at least tie. I had been unable to prove it, but suspected there must be some nice proof. Well, commenter Thibault Vroonhove rose to the challenge and came up with a beautiful, simple proof! Color the coins alternately red and blue, like this: Note that if she wants, Alice can play so as to take all the red coins and force Bob to take all the blue coins, or vice versa. For example, if she wants all the red coins, she starts by taking the red coin on the end, leaving Bob with no choice but to take a blue coin. Bobâs choice then exposes another red coin for Alice to take,... 
The greedy coins game
17 Apr 2017  8:13 pmHereâs an interesting game Iâve been thinking about.1 There is a row of coins on the table; each coin can have any positive integer value. Two players alternate turns. On a playerâs turn she must take one of the two coins on either end of the row of remaining coins, so with each turn the row gets shorter by one. After all the coins have been taken, the player with the higher total value is the winner. Letâs look at an example. Suppose the coins start out like this: The first player (letâs call her Alice) can choose either the 3 or the 2. Letâs say she takes the 3. (3 is bigger than 2, right?) Now the table looks like this: The second player (letâs call him Bob) is now allowed to take... 
Post without words #15
9 Apr 2017  1:05 pm



eon

Queen of Mathematics
9 Apr 2017  5:26 pmNumber theory has been called the Queen of Mathematics. Until some fifty years ago, it did not occur to anyone that number theory, especially the study of prime numbers, would have any immediate applications to business. More recently, the Queen has been relegated to be the object of a courtship, inspired by material gains, rather than awe. As a result, progress has been made in unexpected directions, which have required deeper investigations. — Papa Paulo A.K.A. Paulo Ribenboim from his pseudonovelnumber theory text “Prime Numbers, Friedns Who Give Problems: A Trialogue with Papa Paulo” (p. 50). 
Triangular numbers modulo powers of 2 and its generalizations
14 Mar 2017  5:54 pmSomeone discussed with me an interesting problem that he was working on with his students. They found that the congruence [tex] \frac{1}{2}X(X+1) \equiv a \pmod{n} [/tex] has a solution for every [tex] 0 \le a n [/tex] if and only if [tex] n =2^k[/tex]. My first instinct of course was to complete the squares for triangular numbers and reduce the problem to [tex] X^2 \equiv a \pmod{n} [/tex]. This turn out to work well for odd modulus and the solutions for triangular numbers and squares correspond. But when the modulus was a power of 2, completing the square would not work. A simple search found a few websites where the phenomenon was recorded and it seems a (perhaps original?) source is Knuth’s the Art of... 
If there is some good inflammable stuff it will catch fire
21 Oct 2016  8:06 pmDo not try to satisfy your vanity by teaching them great many things. Awake their curiosity. It is enough to open the minds, do not overload them. Put there just a spark. If there is some good inflammable stuff it will catch fire. The quote appears at the end of chapter 14 of Polya’s Mathematical Discovery. Polya attributes the quote to Anatole France from Le jardin d’Epicure. Perhaps he translated the French into English. He further adds: There is a great temptation to paraphrase this passage: “Do not try to satisfy your vanity by teaching high school kids a lot of … just because you wish to make people believer that you understand it yourself …” Yet les us resist temptation.... 
Catalan numbers
20 Oct 2016  5:22 pmI really enjoyed reading Federico Ardila’s article in the Mathematical Intelligencer. Apparently there was a vote of 3030 members at an assembly of CUP (Not Cambridge University Press but the Candidatura d’Unitat Popular). The vote had to do with forming an alliance with another party and ultimately related to the independence of Catalonia. The amazing thing that happened was that the vote came out 1515 Yes and 1515 No. The probability that a YESNO vote of 2m persons ends up in a tie is [tex] \binom{2m}{m}/2^{2m} [/tex], closely related to the Catalan number [tex] \binom{2m}{m}/(m+1) [/tex]. I love the dual connections and of course Ardila did not fail to mention Stanley’s Enumerative Combinatorics. What... 
Truncatable Primes
27 Sep 2016  7:06 pmA colleague asked about sequences of primes a(n) such that a(n+1) is obtained by appending a single digit (in base 10) to the right of a(n). For example: 3, 31, 311 … Some thinking lead to the conjecture that such sequences are of finite length and that it is possible to use an exhaustive search to find all of them. A natural question would be what is the longest possible sequence but I was unable to find any conclusive answer on the web. So I decided to write a simple (and not very efficient) recursion in maple to search for all such primes. Here’s my ugly code: cat3prime:= proc(n) local d, s, i; s:=n; d:=irem(n,10); if isprime(s) then print(s); return(cat3prime(10*s+1)); else for i from d to 7 by 2 do ...



WordPress Tag: Mathematics

Differentiable Manifolds Revisited
30 Apr 2017  3:19 amIn many posts on this blog, such asÂ Geometry on Curved SpacesÂ andÂ Connection and Curvature in Riemannian Geometry,Â we have discussed the subject of differential geometry, usually in the context of physics. We have discussed what is probably its most famous application to date, as the mathematical framework of general relativity, which in turn is the foundation of modern day astrophysics. We have also seen its other applications to gauge theory in particle physics, and in describing the phase space, whose points corresponds to the “states” (described by the position and momentum of particles) of a physical system in the Hamiltonian formulation of classical mechanics. In this post, similar to what we have... 
What is projectbased learning in math?
29 Apr 2017  8:19 pmWritten Sep 10, 2016 Recommend review of the work of Jo Boaler (Inspiring Students to Math Success and a Growth Mindset) and, to a lesser extent, Keith Devlin (profkeithdevlin). Projectbased math encourages students to discuss ideas about math and numbers. (The discussion part is very important, as it encourages students to think about different approaches to problems, and to explore how ideas can work or not). By focusing on projects, it allows students to get away from the idea that math is a set of rules and formulas to be learned. The key takeaway is that math is something to be discussed and explored, rather than a fixed set of ideas to be transmitted from teacher to student. Here is an article from... 
Steps
29 Apr 2017  3:06 pmCredit to: Tom Blackwell The Antlers — Stairs to the Attic Relevant lyrics: And each step was far apart And far away from steps before it And the air was getting thinner Until I couldn’t breathe at all And if I happened to look behind me There were miles and miles of stairs Enough so I couldn’t see the doorway But I knew that it was there And on the last step I was dizzy Because there were stairs in all directions But I found another door And through the door there was the attic Without old clothes Without a ceiling Everything had opened wide Into the jaws of something bigger And suddenly I saw that I was Upstairs and outside and freezing on the roof Finally it had found me The answer, the feeling, and the... 
Workshop on "Topology of Manifolds and Group Actions (2017)"
29 Apr 2017  10:04 amThe Department of Mathematics, University of Delhi, Delhi is organizing a twoweek workshop on “Topology of Manifolds and Group Actions” during November 922, 2017 sponsored by National Centre of Mathematics. The proposed workshop is intended for the benefit of Young Researchers/Lecturers of Mathematics from various Universities and Colleges in India. For more details about program Click here and for speakers and Syllabus Click Here. The application form for ATMW on “Topology of Manifolds and Group Actions” is now available at the following link: http://www.atmschools.org/2017/atmw/tmga/applicationform Please note: The application form is only accessible to registered user on the ATM Schools... 
the universal language.
29 Apr 2017  8:36 amFor as long as I can recall, if you were to have given me colored pencils or square sheets of paper, in one automatic swoop – as if a sacred construction of the soul – I would create. Always, geometric patterns guided my instincts. There is a little saying thatÂ math is the universal language. I would agree in some regard, however outside of our planet & solar system, the physical variables we have seemingly defined, change, and dramatically so. Instead, I wonder about underlying geometric relationships. Below is geometryÂ in plant cells, succulents, romanesco, and a chameleon tail. [https://www.pinterest.com/pin/108860515968750380/] Geometric patterns – despite the numbers,...



mathrecreation

truchet en plus
29 Apr 2017  1:10 pmSince the previous post, I have been playing around with more variations on Truchet tiles (using this page). The variety of appealing patterns that you can create from these simple tiles is impressive.the humble Truchet tileFor example, using this simple base tile you can create a pathlike effect, even to the extent that paths can seem to weave under and over each other. The patterns below use this effect to create patterns that are suggestive of links and knots.Truchet patters for two links (left) and a trefoil knot (right)Slight variations in the base tile can produce interesting effects. Here's an example that uses the traditional Truchet base tile.Bulging the dark right triangle into a quarter circle... 
truchet tiles
26 Mar 2017  2:13 pmA short while back, I posted about the images found in books about Froebelian kindergarten exercises, like The Paradise of Childhood (on Google Books here). These old books provide great examples of patterns and designs that can be easily drawn by hand with graph paper, in many cases only using arrangements of congruent 4590 triangles.Nineteenth Century Froebelian DoodlesA surprising variety of patterns can be formed by restricting things even further, considering the case where each square is cut in half along a diagonal with half of the square coloured black, the other coloured white.Some arrangements of four Truchet TilesArrangements of these tiles were studied extensively by Sebastien Truchet, whose... 
probability simulations using R
24 Mar 2017  12:01 pmAn ongoing side project of mine is learning how to use the statistics scripting language R, and have been putting putting together R markdown files that set up simulations for a variety of probability problems. You can find some of them here: https://dmackinnon1.github.io/r_examples/.These are simulations that generate data based on problems like the Birthday problem, the Monty Hall problem, and the Burnt Pancake problem. Learning scripting languages aside, it is always good to keep digging into probability problems: they confuse practically everyone. 
Ulam's two step cellular automata
7 Mar 2017  6:40 pmAbove are some of the nice images generated by a cellular automata described in one of Martin Gardner's essays about Conway's Game of Life (you can find the essays here). Cells have four neighbours (north, south, east, west), and follow only two rules that are applied at each step: if a cell has one live neighbour it turns on, and if a cell is on it turns off after two steps. The images above start happening around step 100 after turning on a single cell at the centre of a 61 by 61 grid.You can play with these here. Eventually, these will start to repeat or disappear completely (I suspect they will oscillate, but have not found out when yet). On a 5 by 5 board, a single central cell will lead to a pattern... 
the ants go marching...
6 Mar 2017  2:02 pmIt's not exactly pride or satisfaction, but some related feeling, when you see your little ant marching off on the highway that emerges from the initial chaos it seemed lost in. Keep marching little buddy.You can create a small ant farm here, if you'd like.



Math â Blog

Whatâs Hiding Within Long Division?
29 Apr 2017  11:52 pmLook familiar? For most people, if they ever learned to do long division properly, they had to “master” something similar to the above procedure/algorithm. What was not required was having the vaguest notion of what’s going on, why anyone should care about knowing how to do it, or why, if you did have some idea about what the answer was supposed to mean, this mumbojumbo got you to that answer correctly. Another way of describing the situation is “a black box.” You take two numbers, throw them into the “long division box,” turn the handle as many times as necessary, and – voila! – out pops the magic quotient, with a remainder,Â if any, in some form or other. Fabulous! Who needs conceptual understanding... 
Review: SOLVE THIS! A Book for ProblemSolvers (and Those Learning To Join Them)
25 Apr 2017  9:19 pmAfter first hearing of James Tanton (the subject of our April 2017 interview), I was excited to discover that he had books in print. The first one I got was SOLVE THIS! Even though I was already a mathematics teacher and teachereducator, I found many of the problems it offered challenging, some of them more than slightly so. Very few of them were familiar to me and many required thinking in areas of mathematics I knew little about, though that didn’t make them inaccessible or overly forbidding. What grabbed my attention instantly, however, was the way in which Tanton structured the book. There were three main divisions. The first, “Activities and Problem Statements,” had 30 sections, each of... 
James Tanton: An Australian Mathematician in Uncle Samâs Court
23 Apr 2017  5:54 pmMy guest this month is James S. Tanton, a mathematician, math educator, and author. He was awarded the Kidder Faculty Prize for his teaching at the The St. Markâs Math InstituteÂ and is currently visiting scholar at the Mathematical Association of America. He is the author of over many books on mathematics, curriculum, and education, and creator of videos about mathematics available free on YouTubeÂ and his own websites. Michael Paul Goldenberg: Thanks for joining me, James, and a pleasure to ask you about mathematics and mathematics education. You have a doctorate in pure mathematics from Princeton, but you spent many years teaching high school mathematics near Boston. What made you decide to do that... 
Which States Are The Best (& Worst) At Math
4 Apr 2017  6:32 amWe gave adults across the country a numeracy test and here is what we found out… We thought it would be fun/interesting to take a few questions from a UK numeracy test created by National Numeracy and ask adults across the US to see what the results were. The questions were rated by National Numeracy as being of different difficulty levels so we selected one question from their entry level, one question from their bronze level, one question from their silver level and two from their advanced level. Giving us a total of 5 questions. We had 1,580 individuals complete the test with at least 30 adults from each state. It is important to note that we did NOT ask our readers because broadly speaking the level of... 
Raymond M. Smullyanâs Books Needed No Titles
3 Apr 2017  3:31 pmRaymond Smullyan on THE TONIGHT SHOW Â WHAT IS THE NAME OF THIS BOOK? Honoring the recent passing of its author, Raymond M. Smullyan, at age 97 If youâve never heard of Raymond Smullyan or encountered any of his books on logic and mathematics (or reverse chess problems, religion, and philosophy), you are in the fortunate position of learning about him and encountering his inescapably engaging puzzleposing for the first time. To do so is to enter into a fantastic world occupied by islands of Knights (who always tell the truth) and Knaves (who always lie); forests of Lions who lie on Mondays through Wednesdays and tell the truth the rest of the week, and Unicorns who are truthful save for Thursdays,...



MathFour

Playing the Game in Job Interviews and Math Class
19 Apr 2017  4:36 amI’ve been in education for over 20 years. I’ve learned to play the “get the job” game and gotten pretty good at it. If you’re a teacher or professor, you know the game I’m talking about: there’s the “demo teach” element of the interview process. You have a handful of other math teachers “learning” how to solve a system of equations (or some other math topic replete with pitfalls for the inexperienced) based on your minilecture for them. At some point, you stop getting annoyed at the demo teach and start thinking how it can show other math teachers a different way of teaching. Changing the Game As I mentioned previously, I’m making a transition from math teaching to math using. I’m going to be a software... 
Coding Instead of Math? Yes!
19 Mar 2017  5:34 amI’ve told so many homeschool parents to stop teaching math and instead teach coding (or programming as we used to call it). If children learn coding, then math will come as needed. The logic is the same and coding is far more exciting in today’s social setting than is math. (Yes, that’s unfortunate, but it’s true. To deny it is foolish.) So I’m taking my own advice! I’ve enrolled in The Houston Coding Bootcamp Powered by UT Austin and am tickled pink at my decision. I have a bazillion projects in my mind dying to get out (including a fully robust version of the That’s Math text messaging service). I’ve been itching to share the news on MathFour.com, but have been hesitant to do so. “I’m all math all the... 
What Kind of Math Book are You?
14 Feb 2017  8:42 amYou’ve seen the quizzes for just about every “what kindÂ of…” Now there’s a quiz tailoredÂ toÂ the math educators. Enjoy! A big thanks to TryInteract.com for sharing a complementary super version of their quiz maker. The post What Kind of Math Book are You? appeared first on MathFour. 
Think Funâs Rush Hour Is Enjoyable for the Very Young
2 Feb 2017  2:30 amThis is part of Wordless WednesdayÂ and Throwback Thursday … Rush Hour is a game of logic and skill. The colorful cars are fun for other things too. The object of the game is to move the cars and let the target car “escape.” But at 4 years old, K8 was happy to figure out how to fit all the cars in the game board. Get a copy of Think Fun’s Rush Hour – it’s a noscreen, single player logic game that appeals to girls and boys alike! You might also like: <ul> <li>Rush Hour Traffic Jam Game â Low & High Tech</li> <li>The Tower of Hanoi Math Game</li> <li>Hanukkah Math â Playing the Dreidel Game</li> <li>Chutes and Ladders â It’s a Math Game!</li> </ul> The post Think Fun’s Rush Hour Is Enjoyable for the Very Young appeared first on... 
Marathon Math â The Math Behind the Houston Marathon
14 Jan 2017  6:15 pmTomorrow I attempt to finish my first marathon. There’s a 6 hour limit to finish, which makes me think about the math behind the marathon! Assuming I run a steady 13:45 minute/mile pace for the whole 26.2 miles, I’ll finish exactly in the 6 hour time limit. But of course my pace will vary. I’ll be faster at first. And I’ll likely want to crawl across the finish line. So how fast do I need to go at the beginning so I can go as slow as possible at the end? I’ll start the marathon fast. Without a backpack (which I wear running to work), I can do about a 10:30 minute/mile pace. So here’s the math problem:Â If my first mile is at 10:30 and my last mile averages with the first to beÂ 13:45, what will my last mile...



MIND Research Institute Blog

Volunteers Put the M in S.T.E.A.M at Imaginology
27 Apr 2017  1:13 pmâA family that volunteers together, stays together,â tweeted Mike Limon after snapping a photo with his two sisters. Outfitted in signature blue âJiJi Volunteerâ shirts, the three were prepared for a full day of facilitating handson activities at Imaginology, OC Fair & Event Centerâs S.T.E.A.M. themed celebration. This is MIND Research Instituteâs third, and most ambitious, year participating in Imaginology. In the past, our organization has presented a sample of mathematical games and 3D manipulatives to entice participants. This year however, we took up more than a third of an entire hall with our mathematical activities. Five different exhibits allowed students to explore math concepts... 
Fostering the Whole Child for LifeLong Impact
25 Apr 2017  6:29 amWhat is the whole child approach to education? Rather than focusing solely on studentsâ academic achievement, the whole child approach to education focuses on studentsâ wellbeing beyond the classroom. It's centered on the idea that preparing students for the future goes beyond preparation in academia. Whole child education proposes that we must educate students to be wellrounded, productive members of society so that they possess the emotional and moral ability to tackle everyday challenges in a healthy way. Keep reading for a roundup of research articles on the importance and benefits of developing the whole child and realworld stories on how schools are implementing this approach with... 
Celebrate JiJi Day With Math Puzzles! [Giveaway]
20 Apr 2017  9:00 amCelebrate JiJi Day on Friday, April 28! JiJi is the beloved penguin in the gamebased learning program ST Math. Every time a student demonstrates understanding of a math concept, JiJi crosses the screen, signaling success and leading the way to a more challenging puzzle. JiJi Day is an opportunity to celebrate math and the growth mindset JiJi encourages in students: perseverance through challenges, a love of learning, and the thrill of success. Looking for JiJi Day activities? Have your students test their logic and reasoning skills by matching each colored JiJi to the right square. Download one of the following sudoku puzzles below: Use clues from the given colors to fill in the blank squares,... 
The Difference a Game Makes in Student Engagement [Video]
19 Apr 2017  11:30 amItâs no secret that successfully engaging students requires educators to perform a tricky balancing act. Oversimplify a lesson and students may tune out, but plan a lesson thatâs too challenging and students may become frustrated and give up. A special report from Indiana University reveals that 2 out of 3 students are bored in class every day, while 17 percent say they are bored in every class. Additionally, 75 percent of the students surveyed said they were bored because the material "wasn't interestingâ and nearly 40 percent were bored because they felt the material being taught âwasn't relevant." How can teachers work to eliminate boredom from their classrooms, and what strategies can they... 
Quality Instruction to the Core [video]
13 Apr 2017  9:00 amKnowing where to start in aligning math curriculum to your math standards can be a huge challenge for educators. According to a recent survey from the Thomas B. Fordham Institute, 42 percent of educators report that the math materials available to them are not well aligned with the common core math standards. In addition, if educators are implementing different models and materials at different grade levels, it may be difficult for students to build understanding from one year to the next. How can educators find and implement models that not only align with the standards for their grade level, but provide consistency that builds math understanding year over year? Jill Diniz, Director of Mathematics at...



Math Vault

(Contributor Post) A Primer on Statistical Significance â Grade Comparison, Fertilizer Selection, Dice Rolling and Tire Lifespan Evaluation and More!
29 Apr 2017  10:56 pmtatistical significanceÂ — in a nutshell — is a way of determining if an outcome occurred by random chance, or if there was something else that caused that outcome. For example, letâs say that a school had two teachers, each with approximately $30$ students in their class. Both classes take a standardized test, and it turns […] 
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 basicallyÂ pictures and animationsÂ created in DesmosÂ primarily through the clever use of equations and inequalities â among other features such as tables, animating sliders and regressionÂ models.Â 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 theÂ Texas Instrument TI83Â from the old days. Sure, while programmable calculators in general are still pretty muchÂ popular these days, the graphing calculators from theÂ 21stcentury are also coming in waves as we speakÂ âÂ potentiallyÂ disrupting the market of scientific computing and educational […] 
Infinite Limits and the Behaviors of Polynomials at the Infinities â A Theoretical Musing
17 Jun 2016  1:55 pmegardless of yourÂ early surroundingÂ orÂ schoolingÂ background, we know for one that there are two kinds of mathematical objects that are kind of hard to miss in life. The names? PolynomialÂ and Infinity! While the formerÂ 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 â Venturing Into The Dark Side Beneath Applied CalculusâŚ
5 Jun 2016  7:38 pmo the surprise of many math enthusiasts and the like, it seems that weÂ have been pulling out on an incredible amount ofÂ calculus modules these days. Of course, if you have had any terrible experience in learning just the mechanics of calculus, this seeminglyrelentless outpouring ofÂ materials could make you want to puke. However, if that header […]
