Researchers working on artificial intelligence have taught a computer to create magic tricks. The researchers gave a computer program the outline of how a magic jigsaw puzzle and a mind reading card trick work, as well the results of experiments into how humans understand magic tricks, and the system created completely new variants on those tricks which can be delivered by a magician.
Math

Most Topular Stories

Magic tricks created using artificial intelligence for the first time
Mathematics News  ScienceDaily16 Nov 2014  6:10 pm 
Origin of Mysterious Portuguese Mathematical and Geographical Tiles Revealed
Scientific American  Math5 Nov 2014  9:15 amA few months ago I wrote about some mystifying mathematical and geographic tiles I encountered at the National Tile Museum in Lisbon, Portugal.  Read more on ScientificAmerican.com 
When vaccines are imperfect: What math can tell us about their effects on disease propagation
Mathematics News  ScienceDaily20 Nov 2014  3:36 pmThe control of certain childhood diseases is difficult, despite high vaccination coverage in many countries. One of the possible reasons for this is 'imperfect vaccines,' that is, vaccines that fail either due to 'leakiness,' lack of effectiveness on certain individuals in a population, or shorter duration of potency. In a new article, authors use a mathematical model to determine the consequences of vaccine failure and resulting disease dynamics. 
How Scientific Are Your Instruments?
Scientific American  Math18 Nov 2014  6:36 amWhat do coins, a Wii remote, or card games have to do with science? More than you might think. Scientific instruments are devices specifically designed to measure the subject of your research...  Read more on ScientificAmerican.com 
MATLAB R2014b Graphics – Part 2: Using Graphics Objects
Loren on the Art of MATLAB14 Oct 2014  7:55 amToday, David Garrison, our guest blogger, will continue his series on the new graphics system in R2014b.Part 1: Features of the New Graphics SystemPart 2: Using Graphics ObjectsPart 3: Compatibility Considerations in the New Graphics SystemHere is Part 2 of the series.ContentsWhat have we learned so far?The MATLAB Graphics SystemPreR2014b Numeric HandlesR2014b Graphics ObjectsGetting and Setting Object PropertiesUsing set and getHave you starting using graphics objects in R2014b?Next up  Part 3: Compatibility Considerations in the New Graphics SystemWhat have we learned so far?In Part 1 of…

MATH  Google News

Dayton students put math skills to the test  WDTN
22 Nov 2014  7:54 pmDayton students put math skills to the testWDTN“This is important because research shows when kids are engaged in competitive mathematics, they're thinking increases and they're excited about math,” said Kiara Williams with Dayton Public Schools. “So we take this very seriously. Ultimately we want and more » 
TN chooses new test to replace TCAPs in English and math  WBIRTV
22 Nov 2014  2:08 pmTN chooses new test to replace TCAPs in English and mathWBIRTVAccording to the state's website, those options include multiple choice questions, writing assessments that require students to cite text evidence at all grade levels, questions that test math abilities without a calculator, and math problems that 
PBS launches math series for kids in 'Odd Squad'  Fresno Bee
22 Nov 2014  12:06 pmFresno BeePBS launches math series for kids in 'Odd Squad'Fresno BeeConsider this math problem: PBS leaves the train station headed west under a full head of steam to find a new series to teach math to youngsters. Tim McKeon and Adam Peltzman leave a train station at top speed headed east with an idea for a show that ...PBS goes into action with mathbased 'Odd Squad'Pittsburgh Post Gazetteall 3 news articles » 
'Survivor Math' gets kids jazzed about algebra  Wausau Daily Herald
22 Nov 2014  9:46 am'Survivor Math' gets kids jazzed about algebraWausau Daily HeraldThe event was inspired by the "Propellerheads" Immunity Challenge, from the 18th season of the television show "Survivor," in which contestants must memorize a series of math symbols and then solve an equation. "Students watched the episode and ... 
MORENO VALLEY: League, events promote math as fun  PressEnterprise
22 Nov 2014  12:06 amPressEnterpriseMORENO VALLEY: League, events promote math as funPressEnterpriseThe event was part of the Moreno Valley Math League, a competition program for sixth, seventh and eighthgraders now in its second year in the Moreno Valley Unified School District. Earlier this year, the California Teachers Association Institute for ...

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Changes coming to Common Core Standards
22 Nov 2014  9:34 pmThe state Board of Education has posted revisions to the Common Core Georgia Performance Standards for the public to review over a 60day period. The revisions were made following an executive order from Gov. Nathan Deal for a formal evaluation. 
Engineering careers: Webelos get handson look at STEM fields
22 Nov 2014  9:20 pmTwo dozen Webelos from Packs 78, 79 and 129 from Corning and Painted Post participated in a variety of activities involving science, technology, engineering and math while working on their engineering activity badge, one of 20 activities the Webelos must complete before moving on to become Boy Scouts. Saturday's event included handson activities involving electricity, building a catapult out of orange juice cartons, pencils and plastic spoons, designing their dream house and using engineering principles to build model bridges. 
In NEPA, boy from Afghanistan finds hope, opportunity
22 Nov 2014  9:18 pmIn the last 13 months, doctors moved the 9yearold's bladder from outside his body to its proper place. Instead of making bricks back home, he attends first grade at Clarks Summit Elementary School  and dreams of becoming a doctor and returning to Afghanistan to help children, who like him, had little hope. 
Mackey: Some postgame thoughts from Nassau
22 Nov 2014  9:17 pmAnd maybe that's what most will do after the Penguins managed one point out of a homeandhome series with a Metropolitan Division rival. Those inside the locker room, though, won't be among the group going nutty after Saturday's 41 loss to the New York Islanders at Nassau Coliseum. 
Crow'sFeet Chronicles: School is a stomach ache
22 Nov 2014  9:15 pmThe ignorance gap that the new math created between parent and child has not even begun to mend. Before the new math, I had a mysterious aura about me.

Mathematics News  ScienceDaily

Theater arts research offers insight for designers, builders of social robots
21 Nov 2014  11:12 amResearchers have provided insight into human behavior for scientists, engineers who design and build social robots. 
When vaccines are imperfect: What math can tell us about their effects on disease propagation
20 Nov 2014  3:36 pmThe control of certain childhood diseases is difficult, despite high vaccination coverage in many countries. One of the possible reasons for this is 'imperfect vaccines,' that is, vaccines that fail either due to 'leakiness,' lack of effectiveness on certain individuals in a population, or shorter duration of potency. In a new article, authors use a mathematical model to determine the consequences of vaccine failure and resulting disease dynamics. 
Gifted men and women define success differently, 40year study finds
19 Nov 2014  7:17 amResearchers spent four decades studying a group of mathematically talented adolescents, finding that by midlife they were extraordinarily accomplished and enjoyed a high level of life satisfaction. Gender, however, played a significant role in how they pursued—and defined—career, family and success. Intellectually gifted women tracked for 40 years were found to earn less money, be less present in STEM fields, and work fewer hours than their male counterparts. Despite that, they expressed a high level of personal satisfaction and sense of achievement, defining success more broadly than… 
Magic tricks created using artificial intelligence for the first time
16 Nov 2014  6:10 pmResearchers working on artificial intelligence have taught a computer to create magic tricks. The researchers gave a computer program the outline of how a magic jigsaw puzzle and a mind reading card trick work, as well the results of experiments into how humans understand magic tricks, and the system created completely new variants on those tricks which can be delivered by a magician. 
Stock market models help researchers predict animal behavior
12 Nov 2014  9:01 amModeling used to forecast fluctuations in the stock market has been discovered to predict aspects of animal behavior. The movement of zebrafish when mapped is very similar to the stochastic jump process, a mathematical model used by financial engineers. The model could improve the effectiveness of experiments, minimize the number of fish used, and allow researchers to make better use of their data following experiments.

Scientific American  Math

How Scientific Are Your Instruments?
18 Nov 2014  6:36 amWhat do coins, a Wii remote, or card games have to do with science? More than you might think. Scientific instruments are devices specifically designed to measure the subject of your research...  Read more on ScientificAmerican.com 
A Proof of the Math Fact of Rolle in Short Words
17 Nov 2014  8:40 pmThis proof of the math fact of Rolle, I wrote it down; here was my goal: Use just words with one part. (So it won’t sound too smart.) Please tell me if you find a hole.  Read more on ScientificAmerican.com 
It is Never too Early to Think – and Communicate – Like a Scientist
14 Nov 2014  8:21 amWhen you think about the job of a scientist, what images come into your mind? A chemist wearing a lab coat surrounded by beakers? A geologist out studying rocks in the desert?  Read more on ScientificAmerican.com 
Physics Week in Review: November 8, 2014
8 Nov 2014  2:09 amIt was a big week for physics in the movies, with the premiere of Interstellar, and the Stephen Hawking biopic The Theory of Everything. That translates into lots of pixels commenting on the science...  Read more on ScientificAmerican.com 
Origin of Mysterious Portuguese Mathematical and Geographical Tiles Revealed
5 Nov 2014  9:15 amA few months ago I wrote about some mystifying mathematical and geographic tiles I encountered at the National Tile Museum in Lisbon, Portugal.  Read more on ScientificAmerican.com

NYT > Mathematics

Alexander Grothendieck, Math Enigma, Dies at 86
15 Nov 2014  9:00 pmHis gift for abstraction excavated new ground in algebraic geometry and supplied a theoretical foundation for the solving of some of the most vexing conundrums of modern mathematics. 
The Voice That Sends Help
15 Nov 2014  9:00 pmA 911 dispatcher in Hartford has taken emergency calls for the last 10 years. Each call, she says, makes her stronger. 
Doubting the Economic Data? Consider the Source
6 Nov 2014  9:00 pmIf government economic statistics prove to be wrong, it may have more to do with how they are compiled than with deliberate manipulation. 
Academic Science Isn’t Sexist
1 Nov 2014  9:00 pmPhysics and engineering are no longer bastions of male bias. 
Preparing Your Child for Common Core Tests
6 Oct 2014  9:00 pmThe when and what kind of tests depend on the state, but make sure your children take the tutorial about using the computer.

Ars Mathematica

Learning about Stochastic Processes the Almost Sure Way
9 Nov 2014  1:21 pmGeorge Lowther at Almost Sure has written a terrific series of posts explaining stochastic processes and the stochastic calculus. Stochastic calculus is widely used in physics and finance, so there are many informal introductions that get across the main ideas in a form sufficient for applications. Most of the formal presentations of the subject seem very far away from the informal ones, to an unusual extent. For example, for the important technical notion of semimartingale the Wikipedia definition is the usual one, which has a very different flavor from the naive picture useful in… 
Arguesian Lattices
23 Sep 2014  12:46 pmAs is wellknown, the lattice of submodules of a module is modular. What I did not know is that the converse is not true, and that lattices of submodules must satisfy a stronger property, the arguesian law. The Arguesian law is a latticetheoretic analogue of Desargues’ theorem in projective geometry. I read the statement of the theorem several times and I have no intuition about what it means. There is a kind of converse to this result: a complemented lattice can be embedded into the lattice of submodules of a module if and only if it is arguesian. (I found the result in… 
K2, not the mountain
20 Mar 2014  2:18 pmChandan Singh Dalawat has a nice survey article about K2. It just gives the highlights of the theory, without proofs, so it’s closer to a teaser trailer than it is to fulllength movie. But sometimes you just want a teaser trailer to tell you if you want to invest the time in the movie. 
Cayley Bacharach Theorem through History
10 Feb 2014  3:04 pmI came across this terrific article that describes a sequence of results beginning with Pappas’ theorem through the CayleyBacharach theorem to modern formulations in terms of the Gorenstein (!) condition. The connection between classical topics in algebraic geometry and modern techniques is fascinating. 
Nonassociative Algebras
30 Dec 2013  2:00 pmI periodically feel like I should learn more about nonassociative algebra. (I’ve studied Lie algebras, and technically Lie algebras are nonassociative, but they’re pretty atypical of nonassociative algebras.) There’s a mysterious circle of “exceptional” examples that are all related — the octonions, the five exceptional Lie algebras, the exceptional Jordan algebra — that I would like to understand better. John Baez has an article about the direct connection that I post about before, but what I don’t understand about the general theory is how…

Loren on the Art of MATLAB

MATLAB R2014b Graphics – Part 3: Compatibility Considerations in the New Graphics System
5 Nov 2014  11:48 amToday, David Garrison, our guest blogger, will continue his series on the new graphics system in R2014b.Part 1: Features of the New Graphics SystemPart 2: Using Graphics ObjectsPart 3: Compatibility Considerations in the New Graphics SystemHere is Part 3 of the series.ContentsWhat have we learned so far?Section 1: Compatibility Considerations for R2014b graphicsWhy did we make these changes?How do the changes affect me?How do I find out more about the changes in R2014b graphics?Section 2: Visual DifferencesThe New Default ColormapLine Colors in PlotsPlot Titles and LabelsSection 3: Changes… 
Using MATLAB to Detect Cookies
23 Oct 2014  2:41 amToday, I'd like to introduce a guest blogger, Tom Lowell, who is a program manager here at MathWorks. He works in our hardware connectivity group, and plays with Arduinos and Raspberry Pis in his spare time. He's relatively new to both MathWorks and MATLAB and decided to write a cookie detector as his first MATLAB project.ContentsMotivationSetupCodeTuningThe OutputNotificationDo You Have a Project that Uses an IP camera?MotivationWhen I joined MathWorks, one of the first traditions I learned was that a large plate of home made cookies is delivered every Friday to every floor of every building… 
Taking the Pulse of MOOCs
16 Oct 2014  5:45 amCoursera is a technology platform that kickstarted the current MOOCs boom. Even though there are more MOOCs players now, it still remains one of the leading companies in this space. But how are they doing these days for delivering higher education to the masses online?Today's guest blogger, Toshi Takeuchi, would like to share an analysis using Courera's data.I am a big fan of MOOCs and I benefited a lot from free online courses on Coursera, such as Stanford's Machine Learning course. Like many websites these days, Coursera offers its data through REST APIs. Coursera offers a number of APIs,… 
MATLAB R2014b Graphics – Part 2: Using Graphics Objects
14 Oct 2014  7:55 amToday, David Garrison, our guest blogger, will continue his series on the new graphics system in R2014b.Part 1: Features of the New Graphics SystemPart 2: Using Graphics ObjectsPart 3: Compatibility Considerations in the New Graphics SystemHere is Part 2 of the series.ContentsWhat have we learned so far?The MATLAB Graphics SystemPreR2014b Numeric HandlesR2014b Graphics ObjectsGetting and Setting Object PropertiesUsing set and getHave you starting using graphics objects in R2014b?Next up  Part 3: Compatibility Considerations in the New Graphics SystemWhat have we learned so far?In Part 1 of… 
Reversal of Sorts – New in Release R2014b
9 Oct 2014  5:36 amI wanted to show you a glimpse of some of the new math functionality available in R2014b.ContentsThe QuestionMy Original AnswerSolution with R2014bWhat New Math Have You Enjoyed in R2014b?The QuestionRecently on the MATLAB newsgroup, Christoph asked this question:I have a vector A shown below, which has 6 elements. the elements are already sorted in descending order. now i want to create vector C by deleting elements from A, starting with element a1, until the sum of the vector equals or is smaller the value BA= 26 23 20 19 15 14 B=70So, the output should beC= 20 19 15 14Any idea how to do…

Homeschool Math Blog

Man who had half of his brain removed
21 Nov 2014  4:49 amI received this story in an email and thought it was very encouraging and heartwarming! True story. I asked Scott for his permission to post it online.In the beginning he is referencing this article of mine (I sent it to my list last year):http://www.mathmammoth.com/lessons/value_of_mistakes.php Enjoy... and SHARE. :)Hello Maria, I am just NOW ... today reading this email from about one year ago. I know terrible, but late than never, right. Anyway, I wanted to write you and tell you that like Cameron, I had more than half of my brain removed in 1978. I had brain surgery for an AVM, arterial… 
Will there be Math Mammoth Algebra 1?
18 Nov 2014  6:52 amI've had several people ask me if I'm planning to write algebra 1, algebra 2 and other high school math courses.The answer is no. I'm planning to stop at prealgebra. The main reason is, I've seen some fantastic high school math books other people have written  people with lots of teaching experience etc.  and I feel I could not surpass what those people have done. Especially when I don't have lots of experience teaching high school math to students.You see, with elementary math, there exist numerous homeschool math curricula. I've seen most of them and I can tell many of them are… 
Math Mammoth Thanksgiving sale
15 Nov 2014  12:31 pmMy traditional Thanksgiving sale has started: you can get 25% off of all Math Mammoth & Make It Real Learning downloads & CDs at Kagi.Use the coupon code THANKSGIVING. The sale starts TODAY and runs till Monday, December 1, 2014. You can go to www.MathMammoth.com first, then find the links to Kagi's order pages there.Or, if you know what you want to get, you can use these direct links: Light Blue series (complete curriculum)Blue seriesGolden and Green SeriesMake It Real Learning activity workbooksBundles (CDs or downloads)Review workbooksLight Blue Series, South African versionThanks! 
New prealgebra topic books for Math Mammoth Blue Series
15 Nov 2014  6:00 amThree new books in the Blue Series! These books deal with some prealgebra level topics.Check out their free samples! Math Mammoth Expressions & EquationsThis is a worktext covering the order of operations, equations, expressions, and simplifying expressions in several different ways in 6th7th grade level.The main principles are explained and practiced both with visual models and in abstract form, and the lessons contain varying practice problems that approach the concepts from various angles. We also touch on inequalities and graphing on a very introductory level. In order to make the… 
Group buy for Math Mammoth bundles  only TODAY!
3 Nov 2014  6:05 amHomeschool Buyers Coop is running a GROUP BUY for large Math Mammoth bundles at 40% discount – but just for today, November 3, 2014.So hurry! It's only for ONE day!

Let's Play Math!

Roadmap to Mathematics: 2nd Grade
21 Nov 2014  11:30 am[Feature photo (above) by Loren Kerns. (CC BY 2.0 via Flickr)] A frequentlyasked question on homeschooling forums is, “Are my children working at grade level? What do they need to know?” The Council of the Great City Schools has published a handy 6page pdf summary of second grade math concepts, with suggestions for how parents can support their children’s learning: Parent Roadmap Supporting Your Child in Grade Two Mathematics Whether you are a radical unschooler or passionately devoted to your textbook — or, like me, somewhere in between — you can help your… 
Roadmap to Mathematics: 1st Grade
18 Nov 2014  6:32 am[Feature photo (above) by woodleywonderworks. (CC BY 2.0 via Flickr)] A frequentlyasked question on homeschooling forums is, “Are my children working at grade level? What do they need to know?” The Council of the Great City Schools has published a handy 6page pdf summary of first grade math concepts, with suggestions for how parents can support their children’s learning: Parent Roadmap Supporting Your Child in Grade One Mathematics Whether you are a radical unschooler or passionately devoted to your textbook — or, like me, somewhere in between — you can help… 
Education Bloggers: Share Your Post!
17 Nov 2014  6:48 amphoto by Omar Omar via flickr If you are a homeschooler or classroom teacher, student or independent learner, or anyone else who writes about math, now is the time to send in your favorite blog post for next week’s Math Teachers at Play (MTaP) math education blog carnival. Click here to submit your blog post. Browse all the past editions of the Math Teachers at Play blog carnival Don’t procrastinate: The deadline for entries is this Friday. The carnival will be posted next week at Triumphant Learning. Click to tweet about the carnival: (No spam, I promise! You will have a chance… 
Roadmap to Mathematics: Kindergarten
13 Nov 2014  6:57 am[Feature photo (above) by MIKI Yoshihito. (CC BY 2.0 via Flickr)] A frequentlyasked question on homeschooling forums is, “Are my children working at grade level? What do they need to know?” The Council of the Great City Schools has published a handy 6page pdf summary of kindergarten math concepts, with suggestions for how parents can support their children’s learning: Parent Roadmap Supporting Your Child in Kindergarten Mathematics Whether you are a radical unschooler or passionately devoted to your textbook — or, like me, somewhere in between — you can help… 
Math Teachers at Play #79
22 Oct 2014  7:00 am[Feature photo above by Jimmie, and “79″ image (right) by Steve Bowbrick via flickr (CC BY 2.0).] Do you enjoy math? I hope so! If not, browsing this post just may change your mind. Welcome to the 79th edition of the Math Teachers At Play (MTaP) 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, game, or trivia tidbits. If you would like to jump…

Basic mathematics blog

Dice Roll Simulator
10 Nov 2014  6:25 amDice roll simulator to roll up to 4 dice online. It is like rolling dice in real life 
How to Multiply Matrices
28 Oct 2014  5:17 amLearn how to multiply matrices with crystal clear directions 
Add and Subtract Matrices
27 Oct 2014  9:34 amLearn to add and subtract matrices with this great lesson 
Compute with Scientific Notation
23 Oct 2014  5:40 pmLearn to compute with scientific notation. Add and subtract with scientific notation. Multiply and divide with scientific notation 
Online Matrix Calculator
16 Oct 2014  4:31 amThis online matrix calculator will do addition, subtraction, multiplication, determinant, and inverse of matrices

Computational Complexity

A November to Remember
20 Nov 2014  5:25 amThe Imitation Game starring Benedict Cumberbatch as Alan Turing opens in the US on November 28. If you read this blog you should see that movie. If one challenged British scientist biograph is not enough for you, The Theory of Everything with Eddie Redmayne as Stephen Hawking opened earlier this month. Also this month has the physicsladen Interstellar and the nerdhero robot adventure Big Hero 6. Science rules the box office, though likely to be clobbered by a Mockingjay. Speaking of Turing, The ACM Turing Award will now come with a $1 million dollar prize, up from $250K, now… 
A Fly on the wall for a Harvard Faculty meeting: Not interesting for Gossip but interesting for a more important reason
17 Nov 2014  1:51 pmI was recently in Boston for Mikefest (which Lance talked about here) and found time to talk to my adviser Harry Lewis at Harvard (adviser? Gee, I already finished my PhD. FormerAdvisor? that doesn't quite sound right. I'll stick with Adviser, kind of like when they refer to Romney as Governor Romney, or Palin as halfgovernor Palin). He also invited me to goto a Harvard Faculty meeting. NO, I didn't see anything worth gossiping about. NO I am not going to quote Kissinger ``Academic battles are so fierce because the stakes were so low'' NO I am not going to say that under… 
From Homework Solution to Research Paper
13 Nov 2014  8:22 amInspired by the Dantzig Story I occasionally put an open problem on a class assignment. Never worked, though I did have a student get a research paper from solving a homework question the hard way. Teaching in the early 90's, I showed Valiant's proof that computing the permanent of a 01 matrix was #Pcomplete, including showing that the 01 permanent was in #P, the class of functions representable as the number of accepting paths of a nondeterministic polynomialtime Turing machine. I gave a homework assignment to show that the permanent of a matrix with nonnegative integer… 
Non controversial thoughts on rankings
11 Nov 2014  7:49 amUS News has a ranking of CS depts and various subcategories. Recently MohammadTaghi Hajiaghay and Luca Trevisan have suggested alternative rankings here (Moh) and here (Luca). These rankings inspire me to record some thoughts about rankings. When making a ranking one must ask: What is it for? For Academic depts it may be to help guide potential ugrads or grads in their choice of where to go. Rankings of the most influential people of all time (Michael Harts book here), or in a given year (Time magazine does this) are made to (I think) organize our thoughts and start debates. Michael Hart… 
George Dantzig >= 100
8 Nov 2014  5:34 amWe celebrate the 100th anniversary of the birth of George Dantzig today. In his obituary post we talked about his work on optimization, particularly the simplex method for solving linear programs. For this centenary let's recall the urban legend of the famous mathematician (I heard it as John von Neumann) who as a student wasn't paying close attention in class. The professor wrote down four of the major open problems in the field. von Neumann wrote them down thinking they were homework problems. The next day he went back to the professor, ashamed that he could only solve two of them.

Mathematics and Computation

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… 
Seemingly impossible constructive proofs
8 May 2014  7:15 amIn the post Seemingly impossible functional programs, I wrote increasingly efficient Haskell programs to realize the mathematical statement $\forall p : X \to 2. (\exists x:X.p(x)=0) \vee (\forall x:X.p(x)=1)$ for $X=2^\mathbb{N}$, the Cantor set of infinite binary sequences, where $2$ is the set of binary digits. Then in the post A Haskell monad for infinite search in finite time I looked at ways of systematically constructing such sets $X$ with corresponding Haskell realizers of the above omniscience principle. In this post I give examples of infinite sets $X$ and corresponding constructive… 
Brazilian type checking
6 May 2014  2:59 amI just gave a talk at “Semantics of proofs and certified mathematics”. I spoke about a new proof checker Chris Stone and I are working on. The interesting feature is that it has both kinds of equality, the “paths” and the “strict” ones. It is based on a homotopy type system proposed by Vladimir Voevodsky. The slides contain talk notes and explain why it is “Brazilian”. Download slides: braziliantypechecking.pdf GitHub repository: https://github.com/andrejbauer/tt Abstract: Proof assistants verify that inputs are correct up to judgmental…

Natural Blogarithms

Get “Things” for Free (An Excellent ToDo list app)
21 Nov 2014  7:42 amBefore I moved all my action items to Trello, the “Things” app was my favorite ToDo list for getting things done (#GTD). It’s free this week if you want to try it out. I think they have separate apps for iPhone and iPad, so if you have both you might go ahead and get it now to try out later. Remember, if you get a free app, it’s yours for good, even if they raise the price again later. So you could get it this week, then delete, but reinstall it anytime in the future for free. Give thanks to Apple for offering Things as its free App of the Week on the App… 
Blackboard Grader App for iOS
7 Nov 2014  2:28 pm[Crossposted on the ELearning Pioneer – Blog of the Virtual Campus] There is finally an app for Blackboard that has been designed with the online instructors in mind. The Blackboard Grader App is now available and gives instructors an option for reviewing, providing feedback, and grading student submissions to Blackboard Learn Assignments. With the new Bb Grader app, instructors can view a detailed list of all submissions to any assignment and can sort based on category of information. Instructors can add comments directly to student previews, annotate paper submissions, and… 
Connect the Dots Like a Numerical Analyst
4 Nov 2014  3:06 pmI have to say, teaching Numerical Analysis is one of the highlights of my job. Granted, my primary responsibility at Wayland is the Virtual Campus Director, and I will never teach Numerical Analysis online. Nevertheless, I LOVE it. In fact, the course banner that I use in Blackboard reinforces that fact to my students every time they log in: Just as a for instance, I was able to get them to “solve” the ageold ConnecttheDot problem. What is that, you ask? Well, simple: We all know, from the time we are toddlers, how to complete a Connect the Dot worksheet: BUT, what is the… 
The Importance of Your Worldview
2 Sep 2014  8:06 pmThis week, I have the privilege and honor to lead the discussion in the Faith and Science course at Wayland. The topic of discussion will be the importance of your worldview. We start with a discussion on the 19th century masterpiece, “Flatland: A Romance of Many Dimensions” by Edwin A. Abbot. Then we’ll discuss a couple of readings: Are Scientists Biased by Their Worldview The Importance of Worldview Slides for guided discussion: This is an embedded Microsoft Office presentation, powered by Office Online. 
9 Essential Settings for the Teacher’s iPad
19 May 2014  8:20 pmWhen using your iPad to teach, particularly in the oneiPad classroom, you can run into a few frustrations with the technology. In spite of all the exciting new features you bring to the classroom with the iPad, there are also some headaches that come along with it. Here are some of the settings that our teachers have discovered and implemented to help to alleviate many of those frustrations. 1. Use Side Switch to Lock Rotation Tap the Settings icon on your home screen and go to the General tab. You can configure the side switch to either “Lock Rotation” or “Mute.” It…

IMA Journal of Applied Mathematics  current issue

Orbital stability of periodic waves
21 Nov 2014  6:19 amIn this paper, we deal with the existence and orbital stability of periodic waves for a large class of dispersive equations. We use the classical theory of orbital stability to propose a method of obtaining orbital stability that can be applied to classes of dispersive equations which include Korteweg–de Vries (KdV)type equations and nonlinear Schrödinger equations. An important feature of the method is that the sufficient conditions for stability can be checked numerically, so that method can be used in problems where the waves are not known explicitly. As applications we study… 
Realtime active wave control with preservation of wanted field
21 Nov 2014  6:19 amIn active wave control, a quite arbitrary bounded domain is protected from the field (noise), generated outside, via implementation of additional sources. The secondary sources can be situated at the boundary of the domain to be shielded. Apart from the noise, the existence of the required field, generated inside the protected domain, is also allowed. The solution to the problem is obtained in a rather general formulation. The input information to the secondary sources is based on the total field at the perimeter of the shielded domain only. In the previous publications, the input data for… 
Blowingup solutions to systems of fractional differential and integral equations with exponential nonlinearities
21 Nov 2014  6:19 amWe consider two separate systems of fractional differential equations with exponential nonlinearities. We also consider the corresponding systems of nonlinear Volterra integral equations. We present results on the nonexistence of global solutions for each system. Bounds on the blowup time for each system are provided along with the asymptotic growth near blowup. Each system can be regarded as a model for the interaction of two weakly diffusive media subjected to Arrheniustype reactions. Our results indicate that a thermal blowup cannot be avoided under such conditions. 
Deadtime effects on the voltage spectrum of a PWM inverter
21 Nov 2014  6:19 amAn inverter converts a directcurrent power supply to an alternatingcurrent power supply. This conversion is achieved by switching the output between the inputs at high frequency. The resulting output voltage may be described by a highfrequency train of variablewidth pulses. Pulse widths are slowly modulated so that this output waveform contains a prescribed lowfrequency component, which may then be isolated by an appropriate filtering regime. Techniques for determining the full harmonic spectrum of input and output voltages and currents are well established, at least for an idealized… 
Stability of a timeperiodic flow incorporating a simple model for noise
21 Nov 2014  6:19 amA horizontal layer of Boussinesq fluid is known to be susceptible to vortex instability when the lower surface of the fluid is subjected to a timeperiodic heating of sufficient strength. In this paper a quasisteady technique is used to trace the stability of the layer right from a standard linear theory to the problem when the vortices are so strong so as to change the thermal profile at leading order. Furthermore, this system is used to assess the possible influence of the noise that inevitably arises in many physical and laboratory situations. Even though in many problems a fluid flow is…

WordPress Tag: Mathematics

The Only Word Game You Can NEVER LOSE! Brian explores a form of...
19 Nov 2014  3:06 pmView video here. 
Basic Facts Assessments
19 Nov 2014  2:33 pmI haven’t learnt much for basic facts this term, but I have only been revising as I had forgotten some skills. My results have improved a lot this term compared to the rest of the year, especially on the year 7 test. In the year 7 test I got 50/5 and last term I got 50/3. In the year 8 test I got 98/100 and last term I got 96/100. 
Algebra and Number Assessment
19 Nov 2014  2:29 pmThis term I think I did well in my algebra and number assessment and I learnt a lot. I learnt how to solve two step equations and how to plot coordinates. I also learnt about integers, multiplying, adding, subtracting and dividing fractions as well as working out written problems. For this assessment I got an E. 
VIDEO: Mathematics, Philosophy and Giving Answers to Our Questions
19 Nov 2014  1:37 pmA reminder of the depth, beauty and philosophy that can be derived from numbers. 
You’ll Never Amount to Anything
19 Nov 2014  12:39 pmAncient wisdom has it that we must never speak ill of the dead, and so the depths of bitterness we harbour for certain people now numbered among the departed must be muted by a resented pauciloquence. As those who damned the name of Bin Laden demanded and enforced silence for Thatcher’s requiem, I will permit myself some few cathartic words on a deceased terrorist from my past. Now that he has been immortalised in a school memorial prize, and for the sake of his bereaved loved ones I shall name the assassin only as ‘McDonald’ – a mathematics teacher and a murderer. Casting our eyes…

MathNotations

Implementing The Core: B lives twice as far from A as from C. Draw that!
8 Nov 2014  8:26 amFrom twitter.com/dmarain 11814... A,B,C live on a straight road. B lives 5 times as far from A as from C. If AC=12 draw,determine all possible distances! COREFLECTIONS 1. 140 characters make the writing and interpretation of the problem challenging. But within each group of students there will usually be a few who will make more sense of it and they should be allowed to convince others in their group. When the inevitable hands go up and they ask "Do you mean...?" it's tempting to clarify but don't! Unless everyone is lost of course. The confusion will resolve itself in the… 
Implementing The Core: Draining A Tank  A RealWorld (?) Quadratic Model Problem
3 Nov 2014  10:38 amFrom twitter.com/dmarain today (of course the wording of the problem will exceed 140 characters!)...Water is flowing out of a tank. The number of gallons after t min is given by the function V(t) = k2tt^2. [Assume t≥0 and other suitable restrictions] If 153 gallons remain after 3 min, in how many additional min will the tank empty?I'll even provide an answer: 9 minCOREFLECTIONSProblems like these which *artificially* model the real world are common these days on standardized tests but let's go beyond assessment issues.Before throwing this problem out to the class I usually began with some… 
Implement The Core: No *Mean* Tricks!
31 Oct 2014  6:43 amHalloween Twitter Problem (@dmarain) Treats__Kids 1 ___4 2____5 3____4 4____4 M🎃an treats/child? M🎃dian? COREFLECTIONS (1) This question fits where in Common Core? Grade levels? (2) What questions could you ask before calculation to develop number sense/conceptual thinking? Some ideas... Why is this sometimes referred to as a frequency table? OR Which is easier to determine  mean or median? OR If frequency = 4 kids for all # of treats, mean = ? Mental Math!! OR Explain to your partner why mean >… 
A Dose of Reality  My Latest Common Core Rant
22 Oct 2014  9:55 amI'm reproducing my comment to the post, "Who Needs Algebra?"on Mr. Honner's outstanding blog... http://mrhonner.com/archives/14291#comment10579. I strongly recommend you read all of his excellent pieces. The current one is compelling for all math educators not to mention the public... MY COMMENTS... First of all requiring an indepth conceptual understanding of algebra for all students shows complete insensitivity to special needs students and their longsuffering teachers and parents. Sure just modify the curriculum for them. Go ahead. Show me exactly what that looks like… 
Just How Common is our Core?
22 Oct 2014  7:54 amBorrowing a problem from the comments in the excellent blog CorkboardConnections. Hope that's ok... http://corkboardconnections.blogspot.com/2014/08/commoncoremath.html?showComment=1413889358852#c7893872002833512194 THE PROBLEM Mdm Shanti bought 1/3 as many chocolates as sweets. She gave each of her neighbours' children 4 chocolates and 3 sweets, after which she had 6 chocolates and 180 sweets left. (a) How many children received the chocolates and sweets? (b) how many sweets did she buy? ans: 18 children; 234 sweets. FROM THE COMMENTER ON THE BLOG ABOVE This is the questions our 12…

Neoformix

Stars and Stones
5 Nov 2014  3:00 amI just launched my first mobile app. It's a game, called Stars and Stones, and you can download it now on the Apple App Store for free. I enjoy games that have a simple natural user interaction, are easy to learn, but have a rich depth of play  an elegant complexity. That's what I attempted to create and I think I came close in many respects. Stars and Stones is a series of dynamic puzzles that get progressively more challenging. There are over 100 levels and the first 50 are free. In each puzzle you drag a token around to try and capture five stars while avoiding stones. The stones move as… 
A Short Reflection on Storytelling in Data Visualization
28 Apr 2014  6:15 amThe role of storytelling in Data Visualization has become much discussed over the last year or so. One reason I find this aspect of Data Visualization so interesting is that my own natural tendencies are to focus on exploratory visualization. Much of my own past data visualization work is weak in the storytelling side of things. Coming from a scientific background and personally enjoying the act of discovering patterns in data means my default approach is to build exploratory tools. For me, personally, this whole storytelling aspect seems a rich area to mine in order to improve my work. I… 
Markham Winter of 2014
1 Apr 2014  3:30 amWinter has finally ended in Markham where I live and it has seemed a very long and cold season this year. I decided to take a look at the weather data from Environment Canada and see whether my impression is supported by the data. The result is the graphic below. Click on it to see a larger version. Yes, 2014 was the coldest winter in Markham since 1994. We had an average temperature during the winter of 8.2 C this year and in 1994 it was 9.2 C. Both last year and especially 2012 were warmer than usual so it likely felt that much worse in comparison. We also had the 4th most snow in the… 
Toronto Visible Minorities
27 Sep 2013  4:30 amToronto is the most multicultural city in the world. According to the 2011 National Household Survey, 46% of the population were foreignborn immigrants and 47% are members of a visible minority. (ref) These immigrants come from a wide variety of places across the globe and their diversity makes the city a truly remarkable place. I have created a Dot Map that shows a single point for every person in the Toronto area, coloured by visible minority status. There are 5,700,628 in all and they are positioned at their place of residence and coloured based on the information from the 2011 census and… 
Toronto 311 Visualization
6 Sep 2013  4:20 amThe calls people make into the 311 service line in Toronto give an interesting glimpse into the pulse of the city. The City of Toronto makes this data available through their Open Data initiative. I did some analysis and design work with it to produce a visualization for illuminating timebased patterns during 2012. The visualization is a set of small multiple calendar heatmaps, one for each data series. The one shown above is for reports about 'long grass and weeds'. I was inspired to use this visual form by this example: Vehicles involved in fatal crashes by Nathan Yau. I experimented with…

Math Bootcamps

How to Determine if a Vector is a Linear Combination of Other Vectors
12 Nov 2014  5:47 pmThe idea of a linear combination of vectors is very important to the study of linear algebra. We can use linear combinations to understand spanning sets, the column space of a matrix, and a large number of other topics. One of the most useful skills when working with linear combinations is determining when one vector is a linear combination of a given set of vectors. Suppose that we have a vector and we want to know the answer to the question “is a linear combination of the vectors , , and ?”. Using the definition of a linear combination of vectors, this question can be restated… 
Using the NFL to Understand Hypothesis Testing
10 Nov 2014  2:07 pmThe logic of hypothesis testing can be really confusing. Why do we “reject ” or “fail to reject “, and what does that really mean? Did we prove the null hypothesis when we didn’t reject it? These are common questions for any student studying these ideas. It turns out that we have a very nice example of the logic behind hypothesis testing right in your everyday NFL or college football game. The basic idea comes from the “challenge” that a coach can use to dispute a call on the field by a referee. For example, a referee may say that the other team has… 
The Tools Needed for Math Screencasting
9 Nov 2014  3:55 pmWhile many of you are students, I know that a few of you are math teachers. This update is just for you! Over on my personal homepage (jerimiannwalker.com), I have started a series that will cover the tools and tricks I have learned about creating high quality math screencasts – the same screencasts I produce for this website and for my online courses. Part 1 of the series specifically talks about the software and hardware tools you would need if you were just getting started. You can read that article here: Math Screencasting – Part 1: Tools The post The Tools Needed for Math… 
Understanding Exponents
9 Nov 2013  7:44 amWhen working with exponents, there are two new words that come up: exponent and base. As an example, in , 2 is the exponent while is the base and in , 12 is the exponent while is the base. As long as the exponent is a positive whole number, you can think of it as telling you how many times you should multiply the base by itself. As you can see, means “4 multiplied by itself 12 times” and that is a really big number. Many values that you calculate from exponents will be quite large. There are a couple of things to note: Anything with an exponent of zero is defined to… 
Confidence Intervals for the Mean Using the TI83 or 84 Graphing Calculator
3 Nov 2013  5:26 pmIn order to estimate the value of an unknown population mean, we can use a confidence interval based on the standard normal distribution (zinterval) or the tdistribution (tinterval). The choice is usually determined by the following rule: Use a zinterval if: the population standard deviation is known and either the population is normally distributed or the sample size is larger than 30. Use a tinterval if: the population standard deviation is unknown and either the population is normally distributed or the sample size is larger than 30. In both cases, you can either use the formula to…

MathFour

Indian Corn Craft with Fractions, Decimals and Percent Practice!
14 Nov 2014  3:13 amI found this awesome activity on fractions, decimals and percents a few months ago that was perfect for understanding, well… fractions, decimals and percents! Last night, browsing pinterest, I got the idea of putting it into a math craft for Indian Corn. #lightbulb So just for you, kind reader, here is the free downloadable handout with all the great goodies. (That’s on Teachers Pay Teachers, btw, but it’s free.) Supplies The free downloadable template Crayons or colored pencils Scissors Glue or glue stick Optional: one piece of paper or construction paper… 
Geometric Turkeys – Live AND Baked with FREE Downloads!
1 Nov 2014  10:06 pmI had this great idea to create a geometric turkey (the baked kind). Then I found a ton of live foul on Pinterest – so I made one of those too! Halloween Math is over, but Thanksgiving Math is just beginning. (And look for more Christmas Math and even Hanukkah Math soon!) You’ve got four choices of free downloadable templates: Live Turkey for young kids Live Turkey for older kids Baked (or fried) Turkey for young kids Baked Turkey for older kids Supplies One of the free downloadable templates above Construction paper in your prefered colors Scissors Glue or glue stick Crayons,… 
BeeBot Floor Robot – Teaching Basic Programming
25 Oct 2014  7:11 amA friend gave me a BeeBot floor robot on “permanent loan.” She wanted me to figure out some good ways to teach the basics of programming as well as some algebra. I was happy to take on the challenge. What is the beebot? I handed the beebot to the kids with the prompt, “What do you think?” When they asked about it, I answered: “Figure it out.” They mashed some buttons. Some students figured it out. But some needed my prompts: Press clear. Now press two arrow buttons. Put it down and press “Go.” With this they got enough of what it is, a… 
Using the Hundreds Chart to Teach Beginning Multiplication
21 Oct 2014  5:50 amWe typically think of beginning multiplication as memorizing your math facts for 2’s, 3’s, 4’s and 5’s. But in my new job, things aren’t so typical. So I’m trying something new. Sieve of Eratosthenes It started with a brilliant idea to teaching the Sieve of Eratosthenes. I began by asking the students to color in (or cross out) each of the multiples of 2, 3, 5 and 7. Alas, the plan went awry quickly. Students got confused when they needed to cross out a number that was previously crossed out (like 6). So they moved to the next number and crossed it out:… 
Really Big Numbers: The 100 Dots Project
13 Oct 2014  10:26 amNote: this post has affiliate links. If you use these, you support my work in giving you free content. The AMS sent me a copy (for free, yay me!) of their first publication ever – Really Big Numbers by Evan Schwartz. I loved reading the first few pages with K8, and it gave me an idea. What if I used this in class to introduce numbers? I started teaching at a private, special education school recently. I quickly figured out that everything I know about math education is wrong. I thought this book (and the activity that spawned from it) might work well. And for once, with these kids, I…

CSE Blog  quant, math, computer science puzzles

Pebble Placement Puzzle 2
9 Nov 2014  5:30 amSource: AUSTMS Gazette 35 Related Problem: Pebble Placement Puzzle 1 Problem: Peggy aims to place pebbles on an n × n chessboard in the following way. She must place each pebble at the center of a square and no two pebbles can be in the same square. To keep it interesting, Peggy makes sure that no four pebbles form a nondegenerate parallelogram. What is the maximum number of pebbles Peggy can place on the chessboard? 
Pebble Placement Puzzle 1
6 Nov 2014  5:27 amSource: AUSTMS Gazette 35 Problem: There are several pebbles placed on an n × n chessboard, such that each pebble is inside a square and no two pebbles share the same square. Perry decides to play the following game. At each turn, he moves one of the pebbles to an empty neighboring square. After a while, Perry notices that every pebble has passed through every square of the chessboard exactly once and has come back to its original position. Prove that there was a moment when no pebble was on its original position. 
Diminishing Differences Puzzle
18 Oct 2014  3:05 amSource: Australian Mathematical Society Gazette Puzzle Corner 34 Problem: Begin with n integers x1, . . . , xn around a circle. At each turn, simultaneously replace all of them by the absolute differences Repeat this process until every number is 0, then stop. Prove that this process always terminates if and only if n is a power of 2. Shameless plug: Follow CSE Blog on CSE Blog  Twitter and CSE Blog on Quora. :) 
Balancing Act Puzzle
19 Sep 2014  1:21 amSource: Australian Mathematical Society Gazette Puzzle Corner 35 Problem:There are some weights on the two sides of a balance scale. The mass of each weight is an integer number of grams, but no two weights on the same side of the scale share the same mass. At the moment, the scale is perfectly balanced, with each side weighing a totalof W grams. Suppose W is less than the number of weights on the left multiplied by the number of weights on the right.Is it always true that we can remove some, but not all, of the weights from each side and still keep the two sides balanced? 
"Flawless Harmony" Puzzle
26 Aug 2014  2:40 amSource: AUSTMS Puzzle Corner 35 Problem: Call a ninedigit number flawless if it has all the digits from 1 to 9 in some order. An unordered pair of flawless numbers is called harmonious if they sum to 987654321. Note that (a, b) and (b, a) are considered to be the same unordered pair. Without resorting to an exhaustive search, prove that the number of harmonious pairs is odd. Update (23 Oct 2014): Solution: Posted by me (Pratik Poddar) in comments!

Mathforallgrades Blog

Nov 16, 6thgrademath
16 Nov 2014  3:53 ammath for all grades covers in depth all math subjects :algebra, arithmetic, calculus with essential concepts and unlimited solved problems. 
Nov 16, Prime factorization
16 Nov 2014  3:53 amprime factorization is expressing a natural number as product of only of its prime factors 
Nov 16, 7thgrademath
16 Nov 2014  3:53 ammath for all grades covers in depth all math subjects :algebra, arithmetic, calculus with essential concepts and unlimited solved problems. 
Nov 16, MathLessons
16 Nov 2014  3:53 amMath Lessons 
Nov 16, Arithmetic
16 Nov 2014  3:53 amArithmetic

Marauders of the Lost Sciences

Poynting wants to know how energy is transfered
22 Nov 2014  2:10 amThe Poynting vector represents energy in the electromagnetic fields and is given by Students often read it as the “pointing vector”, but Poynting was a person, not a direction. Here are his own words. A SPACE containing electric … Continue reading → 
Merton was on to Itó’s formula before it was cool
21 Nov 2014  2:10 amJudging from his published papers Merton was already expert at continuous time finance before the 1973 option pricing papers came out. A Digression on Itó Processes To apply the dynamic programming technique in a continuoustime model, the state variable dynamics … Continue reading → 
Metropolis inadvertently creates a major tool for statistics in a physics paper.
20 Nov 2014  2:10 amWhile trying to do Statistical Mechanics simulations a group of physicists at Los Alamos faced the problem of simulating from the canonical distribution. The method they created was generalized by Hastings to the become the MetropolisHastings workhorse of statistics. Notice … Continue reading → 
Heisenberg on turbulence
19 Nov 2014  2:10 amHeisenberg writing shortly after World War II had some deep insights into turbulence. A few remarks may be added with regard to the physical picture of turbulence presented in the recent papers. In the earlier years one thought that turbulence … Continue reading → 
Pigou on the stationary state
18 Nov 2014  2:10 amIt’s left to the reader to decide how relevant the following passage is to the current state of the economy. In his Fiscal Policy and Business Cycles Professor Hanson writes: “The classicals were quite right when they argued that without … Continue reading →