I spoke at TEDx University of Ljubljana. The topic was how programming influences various aspects of life. I showed the audence how a bit of simple programming can reveal the beauty of mathematics. Taking John Baez’s The Bauty of Roots as an inspiration, I drew a very large image (20000 by 17500 pixels) of all roots of all polynomials of degree at most 26 whose coefficients are $1$ or $1$. That’s 268.435.452 polynomials and 6.979.321.752 roots. It is two degrees more than Sam Derbyshire’s image, so consider the race to be on! Who can give me 30 degrees? The code…
Math

Most Topular Stories

TEDx “Zeroes”
Mathematics and Computation16 Oct 2014  12:01 am 
The Equation for a Happy Mother's Day
Scientific American  Math6 May 2015  6:00 amWhat's the most important holiday in May? Obviously it's Mother's Day. But did you know there's an equation that can help you celebrate Mom? Keep on reading to find out what it is!  Read more on ScientificAmerican.com 
3 Ways to Build a Problemsolving School Culture
MIND Research Institute Blog12 May 2015  9:00 amQ&A with Jenny Robles, Principal at Palomino Intermediate School Almost two years ago, Palomino Intermediate School amazed us with their enthusiastic school culture around JiJi and the ST Math program. Recently, Palomino Intermediate School received the Innovative Award from the Arizona State Department of Education. There is something special going on at Palomino, and we asked Principal Jenny Robles to share her insights! What changes has the school made to create a problemsolving school culture that goes beyond embracing the ST Math program? 1. Raise Expectations. Robles emphasizes the… 
RSM MetroWest Hosting Math Madness Tuesday  Patch.com
MATH  Google News26 May 2015  12:45 amPatch.comRSM MetroWest Hosting Math Madness TuesdayPatch.comMath Madness will offer unique, ageappropriate and mathematicallyinspired games and puzzles such as Pin the Mustache on Albert Einstein, Bean Bag Addition, the Famous Tower of Hanoi, Secret Code Breaking, Counterfeit Coin Detective, Make Your ... 
Nat's latest honour is CBE
Search for "math OR mathematics"26 May 2015  2:23 amMr Puri , who was born in the Punjab and retains Indian citizenship, has been made an honorary Commander of the Order of the British Empire on the recommendation of the Foreign and Commonwealth Office. A letter from the FCO to Mr Puri said the honour, just below a knighthood, was being made for his services to business and charities in the UK and abroad.

MATH  Google News

RSM MetroWest Hosting Math Madness Tuesday  Patch.com
26 May 2015  12:45 amPatch.comRSM MetroWest Hosting Math Madness TuesdayPatch.comMath Madness will offer unique, ageappropriate and mathematicallyinspired games and puzzles such as Pin the Mustache on Albert Einstein, Bean Bag Addition, the Famous Tower of Hanoi, Secret Code Breaking, Counterfeit Coin Detective, Make Your ... 
Deaths of Math Genius John F. Nash Jr. and Wife Show Need to Use Seatbelts ...  New York Times
25 May 2015  6:10 pmDeaths of Math Genius John F. Nash Jr. and Wife Show Need to Use Seatbelts New York TimesThe crash that killed the mathematician John F. Nash Jr. and his wife, Alicia, on Saturday on the New Jersey Turnpike remains under investigation, but preliminary findings by the police seem to make one thing clear: The Nashes, who were thrown from the ...and more » 
Hundreds of students to compete in Math Facts Challenge at EMU  Heritage Newspapers
25 May 2015  4:03 amHeritage NewspapersHundreds of students to compete in Math Facts Challenge at EMUHeritage Newspapers"The Math Fact Challenge is an exciting competition that aims to motivate students to achieve math fluency, a critical component of the Common Core State Standards, across all the competing grade levels," said Malverne Winborne, director of the EMU ...and more » 
State Superintendent: 'Funny Math' Methods Not Required in Ga.  WABE 90.1 FM
25 May 2015  3:08 amWABE 90.1 FMState Superintendent: 'Funny Math' Methods Not Required in Ga.WABE 90.1 FMIf you've been frustrated trying to help your young child with his math homework, you're not alone. Superintendent Richard Woods says he hears that from parents a lot. And, he says, some teachers are using strategies that confuse a lot of adults. “This and more » 
West High Math Club wins Midwest Math Championship  Iowa City Press Citizen
24 May 2015  9:39 pmIowa City Press CitizenWest High Math Club wins Midwest Math ChampionshipIowa City Press CitizenThe West High Math Club competed on May 15 at the Midwest Regional Math Championship. This math league championship sponsored by the Great Plains Math League was hosted in Kansas City, Missouri. The West High Math Club earned the Midwest ...

Search for "math OR mathematics"

Nat's latest honour is CBE
26 May 2015  2:23 amMr Puri , who was born in the Punjab and retains Indian citizenship, has been made an honorary Commander of the Order of the British Empire on the recommendation of the Foreign and Commonwealth Office. A letter from the FCO to Mr Puri said the honour, just below a knighthood, was being made for his services to business and charities in the UK and abroad. 
Boulder high school students petition for demoted teacher
26 May 2015  2:10 amBoulder High students are petitioning to have their teacher's advanced placement assignment reinstated after they believe he was demoted for teaching during statewide testing sessions contrary to district policy. The Daily Camera of Boulder reports that students say Jim Vacca is being punished for holding class when all of his students opted out of the PARCC language arts and math tests. 
Re: Why aren't our STEM graduates hired?
26 May 2015  2:10 amA big part of the problem is that our STEM grads aren't allowed to rise to the occasion. Yes, they might not have literally every box checked off. 
Report cites big gaps in state, U.S. test scores
26 May 2015  1:40 amA report on student testing released Thursday finds big gaps in most states between the percentage of students shown to be proficient in reading and math on state tests and the much lower number found to be proficient on a national benchmark test. Dozens of states  including Arkansas  showed significant gaps between their state tests in the 201314 school year and the results of the National Assessment of Educational Progress on tests of reading and math in fourth and eighth grades. 
Meara, half of famed comedy duo, dies at 85
26 May 2015  1:40 amIn this Nov. 12, 2008, file photo, comedian Anne Meara attends the Museum of the Moving Image Salute to Ben Stiller in New York. Meara, whose comic work with husband Jerry Stiller helped launch a 60year career in film and TV, has died.

Mathematics News  ScienceDaily

Social structure 'helps birds avoid a collision course'
21 May 2015  6:49 amThe sight of skilful aerial maneuvering by flocks of Greylag geese to avoid collisions with York's Millennium Bridge intrigued a mathematical biologist. It raised the question of how birds collectively negotiate humanmade obstacles such as wind turbines that lie in their flight paths. 
Differences in tumor cell metabolism affect growth, invasion and response, say researchers
19 May 2015  7:58 amCells within a tumor are not the same; they may have different genetic mutations and different characteristics during growth and throughout treatment. These differences make treating tumors extremely difficult and often lead to tumor recurrence dominated by more aggressive tumor cells. Researchers are now using mathematical modeling to characterize these differences within a tumor and hope that the results of their latest study will lead to better therapeutic treatments. 
Calculating the service life of bridges: Engineers refine models
15 May 2015  5:34 amIn future, the service life of bridges may be estimated more accurate than ever before. Engineers have refined mathematical models for calculating them. Unlike previous models, they take local conditions into consideration, rather than depending on average default values. 
Not good at sports strategies? Game intelligence can be learned
14 May 2015  5:57 amNew theories on game intelligence could change the world of team sports forever. Game intelligence is not necessarily something you are born with but something you can learn, according to new research. 
Training teachers for deaf children gets a robotic helping hand
12 May 2015  8:22 amDeaf education lecturers are using the Swivl robot in school classrooms in a UK first for teacher training. Swivl is a robotic turntable onto which is placed an iPad or other tablet. It is positioned in the classroom and turns to follow people talking. It then uploads video to a secure cloud for streaming or later viewing.

Scientific American  Math

John Nash, Mathematician Who Inspired "A Beautiful Mind", Killed in Car Crash
24 May 2015  10:25 amThe Nobel Prize winner was killed in a car crash along with his wife in New Jersey, state police said on Sunday  Read more on ScientificAmerican.com 
25 Terrific Science(y) Books
20 May 2015  8:21 amJohn Horgan lists 25 of his favorite science(y) books, from Freud's The Interpretation of Dreams to Joyce's Ulysses  Read more on ScientificAmerican.com 
Moore's Law Keeps Going, Defying Expectations
19 May 2015  2:00 pmIt’s a mystery why Gordon Moore’s “law,” which forecasts processor power will double every two years, still holds true a half century later  Read more on ScientificAmerican.com 
Grapefruit Math
19 May 2015  5:00 amSpherical geometry: it's part of this complete breakfast.  Read more on ScientificAmerican.com 
The Equation for a Happy Mother's Day
6 May 2015  6:00 amWhat's the most important holiday in May? Obviously it's Mother's Day. But did you know there's an equation that can help you celebrate Mom? Keep on reading to find out what it is!  Read more on ScientificAmerican.com

NYT > Mathematics

John F. Nash Jr., Math Genius Defined by a ‘Beautiful Mind,’ Dies at 86
24 May 2015  9:00 pmThe narrative of Dr. Nash’s brilliant rise, the lost years of severe mental illness, and the eventual awarding of a Nobel Prize captured the public mind. 
Our Students’ BelowAverage Math Abilities
3 May 2015  9:00 pmReaders respond to a column by Nicholas Kristof on the importance of numeracy. 
Mathematicians and Blue Crabs
2 May 2015  9:00 pmCan a formula really predict a changing population? 
How Not to Drown in Numbers
2 May 2015  9:00 pmThe key question isn’t “What did I measure?” but “What did I miss?” 
Are You Smarter Than an 8th Grader?
25 Apr 2015  9:00 pmAmerican students are falling behind in reading and, especially, math. Just look at some of the math problems kids in other countries are doing a better job of solving.

Loren on the Art of MATLAB

Including External Code in Published Document
22 May 2015  9:40 amWhen I wanted to show you a code snippet in the past, I displayed the code in the text of my blog post.ContentsHow I Did ItHow I Do It NowLet's Try It Out!Will This Inclusive Feature Help You?How I Did ItTo do so, I often used the function type, or sometimes dbtype (if I wanted to refer to line numbers). In this way, I did not require you to download code from elsewhere to see what I was discussing.How I Do It NowNow using R2015a I can take advantage of a new feature of the markup language for publish. Using the include markup allows me to include external content. How do I do this? With the… 
MATLAB Used to Map EarthQuakes from Satellite Data
6 May 2015  7:14 amA friend just pointed out to me a really cool article: Turns Out Satellites Work Great for Mapping Earthquakes. It's about mapping earthquakes using satellite data. This sounded intriguing because I know earth scientists use MATLAB after the fact to analyze seismic data, but I was less certain what exactly they might do with satellite data and earthquakes. The article, centered on work by Bill Barnett from U. of Iowa, is very interesting. Rather than wait for data to be processed well after events occur, Bill demonstrates what can be done with the data in a much shorter time period, allowing… 
The Netflix Prize and Production Machine Learning Systems: An Insider Look
22 Apr 2015  6:10 amDo you watch movies on Netflix? Bingewatch TV series? Do you use their movie recommendations? Today's guest blogger, Toshi Takeuchi, shares an interesting blog post he saw about how Netflix uses machine learning for movie recommendations.ContentsHow Recommender Systems WorkWhat Netflix did with the winning solutionsSo, Was It Worth $1M?Lessons Learned: New MetricsLessons Learned: System ArchitectureMATLAB on Hadoop and MATLAB Production ServerClosingBack in 2006 Netflix announced a famed machine learning and data mining competition "Netflix Prize" with a $1 million award, finally claimed in… 
Can You Find Love through Text Analytics?
8 Apr 2015  7:03 amJimmy Fallon Blew a Chance to Date Nicole Kidman, but do you know there is supposedly a way to fall in love with anyone? Today's guest blogger, Toshi Takeuchi, would like to talk about finding love with MATLAB.ContentsLove ExperimentLatent Semantic Analysis with MATLABText Processing PipelineTFIDF WeightingLowRank ApproximationVisualize Online Dating ProfilesComputing SimilarityGetting the Ranked MatchesWhat about Japanese Text?Call for ActionLove ExperimentI read a very intriguing New York Times article To Fall in Love With Anyone, Do This. It was about an experiment that went like… 
The Winter of Our Vectorization
1 Apr 2015  6:19 amContentsGoing the Whole 9 FeetEnter MATLABTime for Some Logical IndexingConvoluted, Yet SimplerFun with arrayfunPutting it All TogetherSpring into Action!Today I'd like to introduce guest blogger Matt Tearle who works on our MATLAB Product Training materials here at MathWorks. Matt is on a mission to teach the world MATLAB, but this winter is testing his resolve. Annoyed that 22" of snow forced him to reschedule a training, today he shows just how bad this winter had been.Going the Whole 9 FeetIt has been a brutal winter at MathWorks' headquarters in Natick, MA (a little west of Boston). I…

Homeschool Math Blog

Math Mammoth sale  May 2015
15 May 2015  5:11 amGet 25% off of all Math Mammoth & Make It Real Learning downloads & CDs sold at Kagi!Use the coupon code MAY2015 in the order process at Kagi. The offer is valid till June 1, 2015.You will find links to Kagi's order pages at MathMammoth.com on the various product pages. Or, if you are ready to order, you can use these direct links to the order pages: Order Light Blue seriesOrder the South African version of the Light Blue seriesOrder Blue seriesOrder Spanish versions of the Blue series booksOrder Golden and Green SeriesOrder Make It Real Learning activity workbooksOrder Bundles (CDs… 
Math Stars  for summer math and more
24 Apr 2015  2:00 pmI have used Math Stars problem solving sets with my girls for several years, and they have always greatly enjoyed them. Math Stars include various puzzles and challenging math problems. They come as PDF files (free and ready to download & use) in sets for grades 18. They're great to use for summer math or for some fun problem solving at any time.I tend to use the problems from one grade level below the grade the student is in. One reason I like these so much is the variety of the problems  geometrical puzzles, number puzzles, logical thinking, etc.  all of it is… 
Lessons on statistics
14 Apr 2015  9:13 amIs statistics one of your favorite or least favorite topics in math? :)Well... however you feel about it, in middle school students need to learn some beginnings of statistics, such as how to draw a boxplot, a histogram, or a stemandleaf plot, learn about statistical distributions, measures of central tendency (mean, median, and mode), measures of variability, and so on.You can now do so with these videos of mine :^) or with this Youtube playlist.I hope they are of help! 
An update on grade MM 7B
1 Apr 2015  11:30 amSome have asked about grade 7B (once again...)I'm currently writing lessons for the last chapter (statistics & probability) AND writing the answer key for the second to last chapter (on the Pythagorean Theorem). And two people are proofreading the geometry chapter (in different sections). So it's coming along just fine. ;^) I'm hoping to have it ready in late May or early June.Here's an example of what I was working on just this morning  a problem for a lesson where students compare two sets of data. I made up the data, but it is based on real data from the official government site for… 
April math calendar
1 Apr 2015  10:22 amI just printed this math calendar out for my girls and they liked it! Something a bit intriguing and fun to look at as the month progresses  and it can help them to learn a bit of math at the same time. :)

Let's Play Math!

Puzzle: Crystal Ball Connection Patterns
20 May 2015  4:59 amIn the land of Fantasia, where people communicate by crystal ball, Wizard Mathys has been placed in charge of keeping the crystal connections clean and clear. He decides to figure out how many different ways people might talk to each other, assuming there’s no such thing as a crystal conference call. Mathys sketches a diagram of four Fantasian friends and their crystal balls. At the top, you can see all the possible connections, but no one is talking to anyone else because it’s naptime. Fantasians take their siesta very seriously. That’s one possible state of the 4crystal… 
Calling All Math Teacher Bloggers and Homeschoolers: Carnival Time!
18 May 2015  5:01 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. Click here to submit your blog post. Have you noticed a new math… 
New Fantasy Novel by Homeschooled Teen Author
16 May 2015  5:51 amAfter months of editing, formatting, proofreading, sweat, and tears: Teresa Gaskins’s new ebook Hunted: The Riddled Stone ~ Book Two is available now at Amazon. The paperback should follow within the next couple days, and the other online retailers will come along whenever their automated systems get caught up. You can download the first five chapters here: Hunted: The Riddled Stone ~ Book Two (preview) To celebrate the release of Hunted, the ebook version of Banished—the first book in the Riddled Stone series—will be on sale for 99 cents for the next… 
Math Game: Fan Tan (Sevens)
13 May 2015  7:03 amFeature photo above by Morgan (meddygarnet) via Flicker (CC BY 2.0). Math Concepts: sorting by attribute (card suits), counting up, counting down, standard rank of playing cards (aces low). Players: two or more, best with four to six. Equipment: one complete deck of cards (including face cards), or a double deck for more than six players. Provide a card holder for young children. How to Play Deal out all the cards, even if some players get more than others. The player to the dealer’s left begins by playing a seven of any suit. If that player does not have a seven, then the play passes left… 
Playful Math Snacks for May 2015
12 May 2015  5:13 amThe May “Let’s Play Math” newsletter went out Monday morning to everyone who signed up for Tabletop Academy Press math updates. This month’s issue focuses on math games, from Rosie’s Princess in the Dungeon to Jim Pai’s Trig & Logarithm War. What fun! If you’re not on the mailing list, you can still join in the play: May 2015 archive page. Sign up for future newsletters. And remember: Newsletter subscribers are always the first to hear about new books, revisions, and sales or other promotions. A Preview Math Snack: Two Math Games Playful,…

Basic mathematics blog

Sharing money and equations
17 May 2015  7:35 pmA certain value of money will be distributed among 24 students. If 6 students don't come each child will receive 300 dollars more money. Find the amount 
Candies and fractions
14 May 2015  2:16 pmRicky, Carl and Jerome have a total of n candies. Ricky ate 1/4 of the candies. Carl ate 1/3 of the remaining candies. Jerome ate 1/5 of the remaining 
Word Problems anf fractions
14 May 2015  12:41 pmAn Italian sausage is 8 inches long. How many pieces of sausage can be cut from the 8inch piece of sausage if each piece is to be twothirds of an inch 
Riddle Me Numbers
14 May 2015  6:20 amDivide me by 10 and 3 remains. A square number my first digit to be. My second digit is the product of 1 and 3. All together I'm greater than 50. 
cost of cd
13 May 2015  6:47 amAndrew had $93.00. With this money, he could buy 3 CDs and 4 books. However, he bought only 2 CDs and 3 books and had $27.00 left. What was the cost

ChapterZero

A quick thought on Supernatural and some other tv shows
24 May 2015  10:51 pmJust finished season 9 of Supernatural. You’ve got to give that show credit for being one of the few that *demands* a deus ex machina ending. Anything less, after all this fighting over who’s going to take God’s place and Castiel’s moments of mysterious grace, would be a let down. I can’t wait to see what season 10 has to offer. While we’re on the topic of shows that appropriate Christian mythology for their own ends, I want to say that Messengers is crap. We’re supposed to believe that God turned some humans into angels and sent the Devil to earth to… 
Marco Polo: I approve, so far
14 May 2015  11:01 pmI finally got around to watching Marco Polo. This is perhaps surprising news, as anyone who knows me could guess this would be right up my alley: almost superhuman martial arts (at least in the promo material), an eastern setting, and a clash of nations … I’m on episode three, and I’m suprised to say that I’m not at all disappointed! I’m enjoying seeing the tensions building within his empire as Kublai Khan tries to preserve the Mongolian spirit of his empire while incorporating the disparate cultures and religions of his client states. In particular, Khan wants… 
Wilkinson on a priori error analysis
21 Apr 2015  4:47 pmI’ve been reading a lot of NLA lately (e.g., a recent paper on communicationavoiding RRQR), and necessarily brushing up on some details I paid scant attention to in my NLA courses, like the details of the different types of pivoting. Which led me to this quote by a famous numerical analyst: There is still a tendency to attach too much importance to the precise error bounds obtained by an a priori error analysis. In my opinion, the bound itself is the least important part of it. The main object of such an analysis is to expose the potential instabilities, if any, of an algorithm so that… 
Nystrom vs Random Feature Maps
26 Dec 2014  10:37 pmI haven’t seen a truly convincing study comparing Nystrom approximations to Random Feature Map approximations. On the one hand, a NIPS 2012 paper compared the two and argued that because the bases Nystrom approximations use are adaptive to the problem, whereas those used by RFMs are not, Nystrom approximations are more efficient. This is an indisputable point, but the experiments done in the paper are not convincing: they used the same number of samples in Nystrom approximations as random features in RFMS. Instead, the fair comparison is to allot both methods the same number of FLOPs;… 
My podcast masterlist
6 Dec 2014  7:05 pmHere’s an early Christmas gift to you: a list of podcasts I enjoy! For listening while you’re doing all your holiday season travelling. APM: Marketplace KCRW’s Left, Right, and Center Newshour BBC World Update: Daily Commute Common Sense with Dan Carlin PRI’s The World: Latest Edition On the Media The Young Turks Video Podcast Citizen Radio Best of the Left Podcast The David Pakman Show TWIB! Prime (This Week in Blackness) MSNBC Rachel Maddow (video) NPR: Intelligence Squared U.S. Debates Podcast The Read The Complete Guide to Everything Throwing Shade My Brother, My…

Computational Complexity

John Nash (19282015)
25 May 2015  7:56 amJohn Nash and his wife Alicia died in a taxi accident, returning from the airport after he received the Abel prize in Norway. The public knew John Nash as the "Beautiful Mind" of book and screen, but we knew him as one of the great geniuses of the 20th century. Rakesh Vohra captures Nash's life and work, including his amazing letters to the NSA. I briefly met John Nash at some MIT alumni events in New Jersey when I lived there (even though neither of us were MIT undergrads). He would come with his wife and son, the son wearing a winter coat no matter the season. Nash just seemed like any… 
An Intentional and an Unintentional teaching experiment regarding proving the number of primes is infinite.
21 May 2015  4:56 pmI taught Discrete Math Honors this semester. Two of the days were cancelled entirely because of snow (the entire school was closed) and four more I couldn't make because of health issues (I'm fine now). People DID sub for me those two and DID do what I would have done. I covered some crypto which I had not done in the past. Because of all of this I ended up not covering the proof that the primes were infinite until the last week. INTENTIONAL EXPERIMENT: Rather than phrase it as a proof by contradiction I phrased it, as I think Euclid did, as Given primes p1,p2,...,pn you can find a prime NOT… 
Theory Jobs 2015
18 May 2015  5:24 pmIn the fall we list theory jobs, in the spring we see who got them. Like last year, I created a fully editable Google Spreadsheet to crowd source who is going where. Ground rules: I set up separate sheets for faculty, industry and postdoc/visitors. People should be connected to theoretical computer science, broadly defined. Only add jobs that you are absolutely sure have been offered and accepted. This is not the place for speculation and rumors. You are welcome to add yourself, or people your department has hired. This document will continue to grow as more jobs settle. So check it… 
Fiftieth Anniversary of the Publication of the seminal paper on Computational Complexity
14 May 2015  6:34 amJuris Hartmanis and Richard Stearns in a photo dated May 1963. The main theorem from their paper is on the board later improved by Hennie and Stearns. Photo courtesy of Richard Stearns. The seminal paper of Juris Hartmanis and Richard Stearns, On the Computational Complexity of Algorithms, appeared in the Transactions of the American Mathematical Society in the May 1965 issue. This paper gave the name to the field of Computational Complexity which I took for the name of this blog. Hartmanis and Stearns received the Turing Award in 1993 for this work. I've mentioned this paper… 
The law of the excluded middle of the road republicans
11 May 2015  5:59 amIn the book Hail to the Chiefs about the presidents, when pointing to a race between two people who had no business being president (I think it was Franklin Pierce vs Winfield Scott) wrote something like That's the thing about elections, someone has to win. Looking at the republicans running for the nomination I can (with the help of reading many of Nate Silver's Columns) tell you why, for each one, they can't win the nomination. Note that this is not a partisan thing. But again, someone has to win. Is it possible to have the statements A1 can't win AND A2 can't win AND .... AND…

Mathematics and Computation

The troublesome reflection rule (TYPES 2015 slides)
19 May 2015  8:10 amHere are the slides of my TYPES 2015 talk “The troublesome reflection rule” with fairly detailed presenter notes. The meeting is taking place in Tallinn, Estonia – a very cool country in many senses (it’s not quite spring yet even though we’re in the second half of May, and it’s the country that gave us Skype). Download slides: The troublesome reflection rule (TYPES 2015) [PDF]. 
Another PhD position in Ljubljana
3 Apr 2015  4:12 amIt is my pleasure to announce a second PhD position in Ljubljana! A position is available for a PhD student at the University of Ljubljana in the general research area of modelling and reasoning about computational effects. The precise topic is somewhat flexible, and will be decided in discussion with the student. The PhD will be supervised by Alex Simpson who is Professor of Computer Science at the Faculty of Mathematics and Physics. The position will be funded by the Effmath project (see project description). Full tuition & stipend will be provided. The candidate should have a… 
A HoTT PhD position in Ljubljana
22 Nov 2014  4:16 amI am looking for a PhD student in mathematics. Full tuition & stipend will be provided for a period of three years, which is also the official length of the programme. The topic of research is somewhat flexible and varies from constructive models of homotopy type theory to development of a programming language for a proof assistant based on dependent type theory, see the short summary of the Effmath project for a more detailed description. The candidate should have as many of the following desiderata as possible, and at the very least a master’s degree (or an equivalent one): a… 
TEDx “Zeroes”
16 Oct 2014  12:01 amI spoke at TEDx University of Ljubljana. The topic was how programming influences various aspects of life. I showed the audence how a bit of simple programming can reveal the beauty of mathematics. Taking John Baez’s The Bauty of Roots as an inspiration, I drew a very large image (20000 by 17500 pixels) of all roots of all polynomials of degree at most 26 whose coefficients are $1$ or $1$. That’s 268.435.452 polynomials and 6.979.321.752 roots. It is two degrees more than Sam Derbyshire’s image, so consider the race to be on! Who can give me 30 degrees? The code… 
Reductions in computability theory from a constructive point of view
19 Jul 2014  5:50 amHere are the slides from my Logic Coloquium 2014 talk in Vienna. This is joint work with Kazuto Yoshimura from Japan Advanced Institute for Science and Technology. Abstract: In constructive mathematics we often consider implications between nonconstructive reasoning principles. For instance, it is well known that the Limited principle of omniscience implies that equality of real numbers is decidable. Most such reductions proceed by reducing an instance of the consequent to an instance of the antecedent. We may therefore define a notion of instance reducibility, which turns out to have a…

IMA Journal of Applied Mathematics  current issue

On the method of strained parameters for a KdV type of equation with exact dispersion property
25 May 2015  7:34 amThis paper provides an alternative methodology for analysis of threewave interactions under the exact dispersion relation associated with gravity waves in fluid of intermediate depth. A Kortewegde Vries type of equation with exact dispersion property is adopted as the governing equation for unidirectional wave packet evolution. Following the idea from Zakharov's seminal paper (Zakharov, V. E. (1968) Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys., 9, 190–194), the equation is transformed from the spatial–temporal domain… 
A mathematical model for a positive permafrost carbonclimate feedback
25 May 2015  7:34 amThe permafrost methane emission problem is the focus of attention on different climate models. Here, we present a mathematical model for permafrost lake methane emission and its influence on the climate system. We model this process using the theory of nonlinear phase transitions. Further, we find that a climate catastrophe possibility depends on a value of feedback connecting the methane concentration in the atmosphere and temperature, and on the tundra permafrost methane pool. We note that the permafrost lake model that we developed for the methane emission positive feedback loop problem… 
Extended isogeometric analysis for material interface problems
25 May 2015  7:34 amWe propose an approach to extend the isogeometric analysis (IGA) method to solve material interface problems. The development is carried out through incorporating the advantages of the extended finite element method into the standard IGA approach for solving problems with discontinuities. By applying both the XIGA and IGA methods to solve Poisson's equation problem containing weak discontinuities, we demonstrate that the XIGA achieves the optimal convergence rate, whereas the IGA only converges suboptimally. The proposed method is then successfully applied to solve bimaterial and curved… 
Influence of a nonuniform external magnetic field on the oblique stagnationpoint flow of a micropolar fluid
25 May 2015  7:34 amAn exact solution is obtained for the steady plane magnetohydrodynamics oblique stagnationpoint flow of a homogeneous, incompressible, electrically conducting micropolar fluid over a rigid uncharged dielectric at rest. The space is permeated by a nonuniform external magnetic field and by a suitable uniform external electric field. The total magnetic field in the fluid is parallel to the velocity at infinity. The problem is reduced to a nonlinear ordinary differential boundary value problem by using similarity transformations. The effects of the magnetic field on the velocity and on the… 
Matched asymptotics for a spherical lowReynoldsnumber treadmilling swimmer near a rigid wall
25 May 2015  7:34 amThe evolution equations for a small spherical lowReynoldsnumber swimmer actuated by means of an imposed treadmilling action on its surface are derived by means of an asymptotic analysis. The analysis rests on the assumption that the swimmer radius is small compared with its distance from the wall. It generalizes, to the more realistic 3D case, recent work on 2D treadmilling swimmers near a noslip wall. The study is motivated by a recent work on the dynamics of Volvox algae near solid surfaces.

WordPress Tag: Mathematics

How can a shape with a finite area have an infinitely large perimeter?
23 May 2015  10:39 pmShapes are interesting. They are useful in many areas of mathematics, science and engineering and there are plenty of them to go around. Two common ways of measuring shapes is with the perimeter and the area of that shape. Generally all shapes with a finite area will have a finite perimeter. Shapes that follow this are squares, circles, hexagons, pentagons, and even shapes that are not considered polygons. So is there a shape where a finite area does not imply a finite perimeter? Yes, this shape is a fractal called the Koch’s Snowflake. To create this fractal. We first need to draw an… 
Math Joke #7: Place Your Bets
23 May 2015  7:45 pmA mathematician, a physicist, an engineer went to watch a horse race and each of them chose their ow 
Combining drugs with different penetration profiles can accelerate development of multidrug resistance
23 May 2015  6:58 pmWhat scares you? As a kid, I hid behind couch cushions while watching Jurassic Park and could never finish a Goosebumps book. Nowadays, I am terrified of the growing epidemic of antimicrobial resistance. And I’m not the only one. Last year, as part of a fiveyear strategy to combat drug resistance, British Prime Minister David Cameron commissioned a review to examine the economic and health costs of antimicrobial resistance. In their first report published last December, the panel predicted that left unchecked, antimicrobial resistance will lead an extra 100 million deaths by 2050 and cost… 
500 Pick Your Pony! Who'll Win This Number of Factors Horse Race?
23 May 2015  6:16 pmToday I factor the number 500. How many factors does it have? Each number between 401 and 500 has at 
Top Ten Tips
23 May 2015  5:49 pmThere’s so much to learn about helping students learn CCSS mathematics. Here are my top ten takeaways from working with colleagues and outside experts this here. Enjoy! 10. Context is king. 9. Manipulatives activate motor layers. 8. Number hunting is a symptom of comprehension. 7. Background knowledge is key to accessing tasks. 6. Students might approach topics in surprising ways. 5. Routine empowers creativity. 4. Portfolios celebrate growth. 3. Public notes provide academic bridging. 2. Valuable formative assessment matters. Depth of knowledge brings math…

MathNotations

Patterns ending in 25...
30 Apr 2015  5:33 amMiddle schooler playing on calculator observes 25²=625=625,2•3=6 35²=1225=1225,3•4=12 45²=2025=2025,4•5=20 COREFLECTIONS... 1) What can we do to make this a teachable moment? 2) To which of the Mathematical Practices does this relate? 3) Do you think it's important for students to describe the pattern both verbally and symbolically? 3) Algebraic derivation? (10t+5)²=100t²+100t+25 =100t(t+1)+25 4) Extensions? Does the pattern continue into 3 digits e.g., 105²=11025=11025, 235²=55225=55225, 23•24=552 Does the pattern eventually break down? VISIT ME DAILY ON TWITTER AT… 
PLAYING BY THE RULES
26 Apr 2015  4:23 pmNot exactly a math story but... My 7yr old grandson was at bat today. The next pitch appeared to graze him and the umpire told him to take 1st base. He turned around and said that the ball hit his bat and not him. The shocked ump told him to get back in. Two pitches later, he walked anyway. There's a moral here somewhere... VISIT ME DAILY ON TWITTER AT twitter.com/dmarain 
OpenEnded 2nd3rd grade PARCCType Challenge Activity
11 Feb 2015  2:21 pmChild will either draw a diagram, be given grid paper (1"x1") or use a bucket of at least 30 unit tiles. DIRECTIONS TO CHILD (a) Make the largest square you can from 18 small equal squares. Use the grid paper to show this. (c) Any left over? If yes, how many? (d) Which of the following multiplication problems is your big square most like? 3x3? 4x4? 5x5? (e) How many more squares do you need to make the next larger square? Draw it or use tiles. This is just a springboard for your own ideas. Your reaction to this? How would YOU word this type of question? Share! VISIT ME DAILY ON… 
MathNotations Survey  Best Ed Reforms Over Past 25 Years
7 Feb 2015  12:25 pmMy tweet @dmarain on 2615 has generated hundreds of views but no opportunity to freely exchange ideas. I thought about setting up a twitter chat but, for now,I've opted for my blog as the vehicle. So here's the question which is trending ... What changes in education over the past 25 yrs do you think have most impacted how children learn? Since this blog focuses mostly on issues in *math* ed I'll kick this off by suggesting 1) Increased communication in the math classroom. I favor a balanced approach of direct instruction and posing openended nonroutine problems requiring team… 
When is a rectangle an equilateral triangle?
21 Jan 2015  1:52 pmAs posted on twitter.com/dmarain ... Diagonal of a rectangle has length 6 and makes a 30° angle with a side. (a) Area of rectangle=? (b) If diagonal has length d, area=? Ans:9√3;(d^2)√3/4 COREFLECTIONS (1) A moderate difficulty problem for SATs? Appropriate or too hard for a PARCC assessment with both parts? (2) Should diagram be given or is drawing part of what's being assessed? (3) Will some students recognize that the expression in terms of 'd' is the formula for the area of an equilateral triangle of side length d? If no one does then is it our responsibility to model and…

Institute for Mathematics and Computer Science

Motivation and the Gifted Child
6 May 2015  10:00 pm"My kid could finish his math homework in no time if he would just do it, but instead he drags it out for an hour, and that’s with me having to nudge him through it." Sound familiar? Parents and teachers often assume that a gifted child will automatically be a high achiever given the child’s high abilities, so it comes as a surprise when he or she underachieves. There can be a variety of reasons for underachievement, but a common cause is lack of motivation. Whereas bright students often enjoy working toward external recognition for their accomplishments, gifted learners… 
11YearOld Davidson Young Scholar Scores Perfect 800 on SAT Math Test
8 Apr 2015  10:00 pmIMACS student Shiva Oswal and his parents pose in front of the magnificent Atlantis Hotel on a family trip to Dubai. When fewer than 1% of 2014 collegebound high school seniors attain a perfect 800 on the math section of the SAT, you know that you’ve met someone special when he’s achieved that amazing feat before even cracking the teen years. That someone is Shiva Oswal, a precocious 11yearold from Northern California who recently earned that lofty score as part of a program through Johns Hopkins’ Center for Talented Youth (CTY) called the Julian C. 
Three Tips for Nurturing the Good Habit of Delayed Gratification
12 Mar 2015  6:50 amThe ability to delay gratification has been shown in various studies to be a strong predictor of academic success, even more so than IQ. Can parents help nurture this ability in children? Yes! But it takes more than a didactic approach. Many parents are probably familiar with the famous marshmallow experiment where young children were given a choice between one marshmallow now or two if they could wait 15 minutes. It’s helpful to recall that the original experiment focused not on whether the children could wait but rather on what strategies helped them to wait. Rochester University… 
Not Your Father’s Algebra: A New Online Course for Talented Students
11 Feb 2015  10:00 pmEMF teaches modern algebra, which has important applications in publickey cryptography. The Institute for Mathematics and Computer Science (IMACS) recently released its first online algebra course, Algebra: Groups, Rings and Fields. This is the tenth course in the Elements of Mathematics: Foundations (EMF) program for talented secondary school students. Our latest selfpaced offering has generated a fair amount of inquiries from parents seeking options for their mathematically advanced child. The answers to some of those questions can be found in the FAQ at elementsofmathematics.com. IMACS… 
Which Computer Programming Language Should My Child Learn?
14 Jan 2015  10:00 pmThe "learn to code" movement has emphasized teaching computer programming to children, and so many parents are asking, "Which language should my child learn?" It’s easy to be overwhelmed by the myriad choices: Java, Python, Ruby, C++, ObjectiveC, and so on. Ten years ago, the list of languages would have been different, but the question would still have been the same. So instead of focusing on learning a particular language that is popular at the moment and wondering if it’s the "right" choice, consider that your child would benefit most from…

MathBlog

Simpson’s Paradox and Sex Discrimination
25 May 2015  6:00 amThe Lawsuit Big Name University is facing a lawsuit alleging sex discrimination in admissions to its graduate programs. Last year, 1440 men and 1440 women applied for admission to graduate school at Big Name. Twohundred and forty (240) men, but only onehundred and eighty (180) women were admitted. The evidence seems clear cut; Big Name is discriminating against women. Alarmed at the billion dollar class action lawsuit, the Board of Trustees calls upon the distinguished Ronald E. Fisher Professor of Statistics S.O. Whiteman to review the admissions data. Professor Whiteman carefully examines… 
Review of Statistics Done Wrong: The Woefully Complete Guide
4 May 2015  6:00 amStatistics Done Wrong: The Woefully Complete Guide by Alex Reinhart Paperback: 176 pages Publisher: No Starch Press; 1 edition (March 16, 2015) Language: English ISBN10: 1593276206 ISBN13: 9781593276201 Product Dimensions: 8.1 x 5.9 x 0.5 inches My Rating: 3/5 Introduction Statistics Done Wrong: The Woefully Complete Guide by Alex Reinhart, a graduate student in statistics at Carnegie Mellon University, is a guide to many common errors in statistical analyses in scientific research papers with many examples drawn mostly from the biology and medical research literature. There is also a… 
Review of StatSpotting: A Field Guide to Identifying Dubious Data
13 Apr 2015  6:00 amStatSpotting: A Field Guide to Identifying Dubious Data Joel Best University of California Press Berkeley and Los Angeles, California 2008, updated 2013 158 pages (Paperback) My Rating: 4/5 Introduction StatSpotting: A Field Guide to Identifying Dubious Data by Joel Best, author of Damned Lies and Statistics and More Damned Lies and Statistics, is a detailed, practical handbook of warning signs for false or misleading numbers and statistics and in some cases methods to determine if the numbers and statistics are false or misleading. We can say that a number or statistic is misleading if the… 
Review of More Damned Lies and Statistics: How Numbers Confuse Public Issues
6 Apr 2015  6:00 amMore Damned Lies and Statistics: How Numbers Confuse Public Issues By Joel Best University of California Press Hardcover, 217 pages ISBN: 9780520238305 September 2004 $29.95, £19.95 My Rating: 3/5 Introduction In this new world of Big Data, Data Science, and the computing power of a 1980’s Cray supercomputer in every pocket, we are inundated with more and more statistics and mathematical models based on more and more “data.” This torrent of real science and pseudoscience (sometimes officially sanctioned) includes the dubious financial models that contributed to the 2008… 
Measuring Up, SAT Scores, and Coding Interviews
16 Mar 2015  6:00 amIntroduction Measuring Up: What Educational Testing Really Tells Us is a 2008 book by Professor Daniel Koretz of Harvard. Koretz, the Henry Lee Shattuck Professor of Education at Harvard, is a noted expert on educational assessment and testing policy. Professor Koretz is both an excellent writer and also public speaker as evidenced by many short videos at BigThink and YouTube. Measuring Up is an “accessible” book that tries and mostly succeeds in teaching the basic concepts, both statistical and testing specific, of educational achievement tests such as the SAT (the test formerly…

MathFour

How to Solve Nonlinear Inequalities – Introducing ThingLink
15 May 2015  2:51 amThere are multiple steps in solving a nonlinear inequality. And making an example that’s easy to follow along isn’t easy. You have to do a video, or hope your students can follow a detailed written example. So when I found ThingLink.com via the #BFC530 educational tweetchat, I was exited. Finally I can share an example, include the steps, and not have it be overwhelming! Hover on the example below to see the step number icons. Hover over each icon to read about that step. AND… ThingLink has a very attractive educators’ price. Their freemium model allows you to do a… 
Reducing Fractions is like Folding Clothes
8 May 2015  3:27 amI was cramming my running clothes into my backpack this morning and thought, “I probably should fold those.” And then I thought, “Why do I need to fold my clothes before I cram them in my backpack?” After all, folding is a grownup thing. Does it save space to fold? Does it save space to fold? Well, the physicist in me (which is very very tiny) would say no. The matter in the shirt is the same whether it’s folded or not. Sometimes you don’t want your clothes folded. Think of those last few things you forgot to pack in your luggage. It’s jam packed but you… 
Seeing Math at Church
25 Mar 2015  3:04 amThis is part of Wordless Wednesday… 
Finding Math in the Strangest Places
11 Mar 2015  3:21 amI’ve written a lot. Including 160 posts on my crazy “cutting my teeth” blog, Idearella.com, two dozen guest posts, and 530 posts on MathFour.com. But my favorites pieces all involve how math can be seen in weird and unusual ways. Which prompted me to collect some of my fav’s. Which I thought I’d share, in case you’re as curious about it as I am. pickles toilet paper zombies Christmas trees lipstick potato chips crossing the street bedsheets and folding them tattoos drug dealing laundry hurting the ones you love social media marriage hearts and more… 
Gathering and Organizing Your Math Folder
6 Mar 2015  2:39 amI attended the 4.0 Schools “Essentials” class last week in New Orleans for That’s Math. This quote struck me: “Creativity comes from constraint.” It made me itch to do another 50 word post. So I thought I’d combine a couple of my favorite Friday fun flurries – 50 Word Friday AND Five Minute Friday. This week’s prompt for #FMFParty is gather. Take a peek under the obnoxious image to see the short 50 words I have to say about it (that I wrote in under 5 minutes!)… Here goes… Did the Tasmanian Devil organize some of your students’ folders? Try these…

Mathforallgrades Blog

May 12, 10thgrademath
12 May 2015  12:11 am10th grade math consisting of algebra, arithmetic, geometry, coordinate geometry, statistics. 
Feb 9, algebra 1 help
8 Feb 2015  10:04 pmalgebra 1 help includes data analysis tools, functions, equations, inequalities, exponents, polynomials, quadratic equations 
Feb 5, Algebra lessons
4 Feb 2015  11:07 pmalgebra lessons in one variable, two variables solved using substitution method, elimination method 
Jan 22, Advanced Problems in Percentages
22 Jan 2015  1:13 amAdvanced Problems in Percentages 
Jan 22, Algebraic Expression
22 Jan 2015  1:13 amAny expression that contains letters, numbers and basic operation signs +, , × and ÷ is called an Algebraic Expression.

MIND Research Institute Blog

Why JiJi Moves from Left to Right: Artistic Conventions for Expressing Motions
21 May 2015  9:00 amBy Martin Buschkuehl and Christine Byrd In most of our ST Math games, JiJi the penguin crosses the screen after a student successfully solves a puzzle. JiJi walks  or waddles, perhaps  from left to right. We’ve been asked over the years why JiJi travels in that direction. We asked several students why they think JiJi always moves from left to right. Listen to their answers in this video: For that matter, why do other popular computer games like Super Mario or Sonic the Hedgehog have protagonists who run from left to right? A recent article in the scholarly journal… 
Game Design 101: Guiding Questions for Students
19 May 2015  9:00 amLaura and Katie (now in the seventh grade) love all kinds of games. When their mother, June, heard about the Gameathon challenge (a handson math activity) last year and recognized JiJi from their elementary school program, ST Math, she engaged the twins and their friends in the challenge. We asked June, Laura and Katie a few questions about their experience, and their advice on how other students, parents and teachers can get started creating a game for the Gameathon. Based on our interview and chatting with other participants, here are some facilitating questions the mentor (parent,… 
3 Ways to Build a Problemsolving School Culture
12 May 2015  9:00 amQ&A with Jenny Robles, Principal at Palomino Intermediate School Almost two years ago, Palomino Intermediate School amazed us with their enthusiastic school culture around JiJi and the ST Math program. Recently, Palomino Intermediate School received the Innovative Award from the Arizona State Department of Education. There is something special going on at Palomino, and we asked Principal Jenny Robles to share her insights! What changes has the school made to create a problemsolving school culture that goes beyond embracing the ST Math program? 1. Raise Expectations. Robles emphasizes the… 
Learning Math Well: Confidence, Competence and Positive Attitude
7 May 2015  9:00 amBy: Dr. Pam Moran, Superintendent at Albemarle County Public Schools Why do Americans stink at mathematics? Why do from 3040% of people who respond to attitudinal questions about math use language describing that they “hate” it? Why do many parents and educators believe that being good at math is about ability, not capability? At a recent school board work session, board members, along with parents, teachers, principals and community professionals, tackled the question of what it takes to educate all young people well in mathematics as they move from… 
Project Based Learning: Kindergarten Students Collaborate and Create
5 May 2015  9:00 amBy: Bobbi Lynn Frensley, Kindergarten Teacher George C. Payne Elementary School is a hidden gem in the Silicon Valley, known for its use of cutting edge technology and teaching philosophies. Recently we received the California Distinguished School Award and have set forth a plan to be a Project Based Learning (PBL) school. Project Based Learning engages students in developing working products while dealing with real world issues. Learning in a project based setting involves students trying to answer a question that interests them and creating a real world product that answers or addresses the…