# Math

• ## Most Topular Stories

• ### Math Teachers at Play #79

Let's Play Math!
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 pre-college. Let the mathematical fun begin! By tradition, we start the carnival with a puzzle, game, or trivia tidbits. If you would like to jump straight to our…
• ### Technology helps even the odds for blind students

Mathematics News -- ScienceDaily
21 Oct 2014 | 1:21 pm
Technology to help a blind student see math clearly and pursue a degree has been uncovered by researchers. Despite losing her vision three years ago due to complications from the flu, one study entered university last fall with the specific goal of pursuing a dual degree in mathematics and business. Technology is helping her make this a reality.
• ### Doing math with your body

Mathematics News -- ScienceDaily
2 Oct 2014 | 7:09 am
You do math in your head most of the time, but you can also teach your body how to do it. Researchers investigated how our brain processes and understands numbers and number size. They show that movements and sensory perception help us understand numbers.
• ### Oct 20, Area-of-circle

19 Oct 2014 | 11:47 pm
Area of circle is Π times the radius of the circle squared or Π times one-fourth the diameter of circle squared.
• ### An effective, cost-saving way to detect natural gas pipeline leaks

Mathematics News -- ScienceDaily
22 Oct 2014 | 7:35 am
Major leaks from oil and gas pipelines have led to home evacuations, explosions, millions of dollars in lawsuit payouts and valuable natural resources escaping into the air, ground and water. Scientists say they have now developed a new software-based method that finds leaks even when they're small, which could help prevent serious incidents -- and save money for customers and industry.
• ## Search for "math OR mathematics"

• ### Common Core Not State Led - Here's Proof

24 Oct 2014 | 12:57 pm
Supporters of Common Core love claiming Common Core is a state led initiative. Proponents of the scheme will instantly label anyone who says otherwise a conspiracy nut and fit them for a tin foil hat.
• ### FTDI-gatea

24 Oct 2014 | 12:56 pm
My hardware hacking friends have been all a-twitter about recent actions by FTDI . In case one of my three or so regulars haven't heard about this dust-up, here's a brief synopsis.
• ### Question of the day

24 Oct 2014 | 12:56 pm
Oberweis is personally against gay marriage. A campaign spokesman told IR that Oberweis' quote about times changing "refers to the ability of social conservatives to be able to stop the momentum toward government allowing it Democratic U.S. Sen. Dick Durbin enters the final days of his campaign for a fourth term holding a substantial advantage over Republican challenger Jim Oberweis, a new Chicago Tribune poll shows.
• ### Venezuelans brace for slump in oil prices

24 Oct 2014 | 12:54 pm
The falling oil prices that are providing relief to drivers around the world threaten to bring more misery to the life of Milagro Alvarez and millions of other Venezuelans, whose country depends almost exclusively on oil revenue. The math teacher has been getting up before dawn each day and rushing out to hunt for disposable diapers, one of scores of products that have been in short supply due to price restrictions and currency controls put in place by the socialist government long before the slide in petroleum prices.

• ## Mathematics News -- ScienceDaily

• ### An effective, cost-saving way to detect natural gas pipeline leaks

22 Oct 2014 | 7:35 am
Major leaks from oil and gas pipelines have led to home evacuations, explosions, millions of dollars in lawsuit payouts and valuable natural resources escaping into the air, ground and water. Scientists say they have now developed a new software-based method that finds leaks even when they're small, which could help prevent serious incidents -- and save money for customers and industry.
• ### Technology helps even the odds for blind students

21 Oct 2014 | 1:21 pm
Technology to help a blind student see math clearly and pursue a degree has been uncovered by researchers. Despite losing her vision three years ago due to complications from the flu, one study entered university last fall with the specific goal of pursuing a dual degree in mathematics and business. Technology is helping her make this a reality.
• ### New theorem determines age distribution of populations from fruit flies to humans

6 Oct 2014 | 8:41 am
The initial motivation of a new study was to estimate the age structure of a fruit fly population, the result a fundamental theorem that can help determine the age distribution of essentially any group. This emerging theorem on stationary populations shows that you can determine the age distribution of a population by looking at how long they still have to live.
• ### Doing math with your body

2 Oct 2014 | 7:09 am
You do math in your head most of the time, but you can also teach your body how to do it. Researchers investigated how our brain processes and understands numbers and number size. They show that movements and sensory perception help us understand numbers.
• ### Adding uncertainty to improve mathematical models

29 Sep 2014 | 3:05 pm
Mathematicians have introduced a new element of uncertainty into an equation used to describe the behavior of fluid flows. While being as certain as possible is generally the stock and trade of mathematics, the researchers hope this new formulation might ultimately lead to mathematical models that better reflect the inherent uncertainties of the natural world.
• ## Scientific American - Math

• ### The Top 10 Martin Gardner Scientific American Articles

21 Oct 2014 | 7:32 am
The “Mathematical Games” column in Scientific American that began in January 1957 is a legend in publishing, even though it’s been almost 30 years since the last one appeared. -- Read more on ScientificAmerican.com
• ### Garrett Lisi Explains His Grand Unified Theory

15 Oct 2014 | 8:00 am
Deep down, the particles and forces of the universe are a manifestation of exquisite geometry -- Read more on ScientificAmerican.com
• ### Beyond Emmy and Sophie: Resources for Learning about Women in Math

14 Oct 2014 | 12:00 pm
Today is Ada Lovelace Day, an international celebration of women in science, technology, engineering, and math. If you’d like to read about women in math for the occasion, you're in serious... -- Read more on ScientificAmerican.com
• ### Atomic Reporters Curbs “Egregious” Coverage of Nuclear Perils

13 Oct 2014 | 4:32 am
Yes, the Cold War ended long ago, but we still live in a nuclear-armed world, in which the possibility of nuclear war, terrorism and accidents is all too real. -- Read more on ScientificAmerican.com
• ### How Well Do You Know Martin Gardner? [Quiz]

10 Oct 2014 | 11:00 am
Do you think of yourself as a true fan of Martin Gardner’s? Test your knowledge of him here -- Read more on ScientificAmerican.com

• ## NYT > Mathematics

• ### Preparing Your Child for Common Core Tests

6 Oct 2014 | 9:00 pm
The when and what kind of tests depend on the state, but make sure your children take the tutorial about using the computer.
• ### The Math of Whips, Chains and Ropes

5 Oct 2014 | 9:00 pm
Some people in applied mathematics are looking at the physics behind so-called viscous threads and elastic rods.
• ### The Odds, Continually Updated

29 Sep 2014 | 9:00 pm
In Bayesian statistics, new data is used to shape assumptions, the opposite of the frequentist (classical) approach.
• ### MacArthur Awards Go to 21 Diverse Fellows

16 Sep 2014 | 9:00 pm
Stipends will be awarded to a psychologist studying racial perceptions in crimes, the maker of the film “The Act of Killing” and a law professor seeking to help American Indian women, among others.
• ### Incentives Aid A.P. Science and Math Scores

1 Sep 2014 | 9:00 pm
A Pittsburgh high school took part in an initiative to raise its performance in math and science, but did its results match the high expectations?
• ## Loren on the Art of MATLAB

• ### Using MATLAB to Detect Cookies

23 Oct 2014 | 2:41 am
Today, 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 am
Coursera 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 am
Today, 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 SystemPre-R2014b 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 am
I 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…
• ### MATLAB R2014b Graphics – Part 1: Features of the New Graphics System

3 Oct 2014 | 1:00 am
Today I’d like to introduce a guest blogger, David Garrison, who is a MATLAB Product Manager here at MathWorks. This is the first in a series of blogs over the next few weeks describing the new graphics system in R2014b and how some of the changes will affect you.Part 1: Features of the New Graphics SystemPart 2: Using Graphics ObjectsPart 3: Compatibility Considerations in the New Graphics SystemHere is Part 1 of the series.ContentsBig Changes in R2014bThe New MATLAB Graphics SystemThe New Look of MATLAB GraphicsRotatable Tick LabelsAutomated Updating of datetime Tick LabelsAnimated…

• ## Homeschool Math Blog

• ### Math teachers at play #79

22 Oct 2014 | 2:15 pm
Math teachers at play #79 blog carnival is up!Go check it out. I found for example these interesting resources:A variation of Sudoku puzzle plus a link to many more. Spider web math art - I want to do this one with my kids.
• ### Math Mammoth South African version, grades 4 and 5

15 Oct 2014 | 7:05 am
Math Mammoth South African version is now available for grades 4 and 5! Math Mammoth South African version, Grade 4Math Mammoth South African version, Grade 5You can read detailed descriptions and download free samples at the above links. The South African version has been customized to South Africa in the following manners:The names used are South African names (instead of Jack and Jill, there are Ansie and Mampho).The currency used in word problems is rand. The money chapter teaches both rand and cents, of course.The material is "all metric". In other words, the US customary measuring…
• ### Math Mammoth giveaway!

14 Oct 2014 | 7:33 am
It is time for a giveaway of my Math Mammoth products! There will be 17 prizes! The "grand prize":ONE (1) winner will get Math Mammoth All Inclusive bundle - either a download or a CDTWO (2) winners will get Math Mammoth Light Blue Series bundle - either a download or a CDFOUR (4) winners will get Math Mammoth Blue Series bundle - either a download or a CDTEN (10) winners will get one grade level of Math Mammoth Light Blue series - download - the grade level is chosen by each winner.The winners will be chosen by a random number generator. Something SPECIAL This giveaway is COUPLED with…
• ### Lesson on Fibonacci numbers

12 Oct 2014 | 7:09 pm
Have you ever heard about the Fibonacci numbers and the Golden ratio?A tiling that uses squares whose side lengths are successive Fibonacci numbers. Ask students to continue it! Image from Wikipedia. Here's a lesson I just wrote about them:Fibonacci numbers and the golden section – lesson for middle and high school studentsIf you like it, share it!You might ask, "Should our children or students even learn about Fibonacci numbers or the golden ratio?"True, they aren't any standard fare in math books. However, I feel that yes, students should know about them. I think it's important that our…
• ### Worksheets in PDF form

11 Oct 2014 | 7:56 pm
You can now make worksheets for these topics in both html and PDF formats at my site: Basic division facts (grades 3-4)Long division (grades 4-6) Division with remainders (grades 3-5)Equivalent fractionsClockMeasurement units, grade 3Measurement units, grade 4Measurement units, grade 5Measurement units, grade 6The pages also include lots of ready-made PDF worksheets. Enjoy!
• ## Let's Play Math!

• ### 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 pre-college. Let the mathematical fun begin! By tradition, we start the carnival with a puzzle, game, or trivia tidbits. If you would like to jump straight to our…
• ### Horseshoes: A Place Value Game

20 Oct 2014 | 7:00 am
[Feature photo above by Johnmack161 via Wikimedia Commons (CC BY 2.5).] I first saw place value games on the old PBS Square One TV show (video below). Many teachers have posted versions of the game online, but Snugglenumber by Anna Weltman is by far the cutest variation. Anna kindly gave me permission to use the game in my upcoming Math You Can Play book series, and I added the following variation: Horseshoes Math Concepts: place value, strategic thinking. Players: two or more. Equipment: one deck of playing cards, or a double deck for more than three players. Separate out the cards numbered…
• ### Math Teachers and Homeschool Bloggers: We Want You!

15 Oct 2014 | 2:47 pm
[Photo by Olga Berrios via flickr.] Do you have a favorite blog post about math activities, games, lessons, or hands-on fun? The Math Teachers at Play (MTaP) math education blog carnival would love to feature your article! We welcome math topics from preschool through the first year of 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. [Note: Sometimes the automated Google form refuses to load in my browser. If you have trouble, leave a link to your entry in the comments below.] Browse all the past…
• ### Math Storytelling Day: The Hospital Floor

24 Sep 2014 | 6:14 am
[Feature photo above by Christiaan Triebert via flickr (CC BY 2.0).] Have you ever heard of Math Storytelling Day? On September 25, people around the world celebrate mathematics by telling stories together. The stories can be real — like my story below — or fictional like the tale of Wizard Mathys from Fantasia and his crystal ball communication system. Check out these posts for more information: Happy Math Storytelling Day Math Storytelling Day resources Moebius Noodles: Math Storytelling Day archive My Math Story My story begins with an unexpected adventure in pain. Appendicitis…
• ### Math Teachers at Play #78 via 1001 Math Problems

23 Sep 2014 | 12:35 pm
Math Teachers at Play is a traveling collection of math tidbits — games, lesson ideas, and more — from around the Internet. It moves around from month to month, and the September edition is now posted at 1001 Math Problems blog. What a fun list of math posts to browse! Special Blog Carnival Edition of 1001 Math Problems Welcome to the 78th edition of the Math Teachers At Play math education blog carnival, which I am thrilled to be hosting this month in celebration of my soon-to-be-released book, Camp Logic. What is the blog carnival? It is a monthly snapshot of some interesting…
• ## Basic mathematics blog

• ### Compute with Scientific Notation

23 Oct 2014 | 5:40 pm
Learn 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 am
This online matrix calculator will do addition, subtraction, multiplication, determinant, and inverse of matrices
• ### Introduction to Matrices

15 Oct 2014 | 8:06 pm
Easy to follow introduction to matrices -learn how to add, subtract and multiply matrices. Learn how to find the determinant and the inverse of matrices
• ### Union of Sets Calculator

11 Oct 2014 | 4:14 pm
union of sets calculator: Easily find the union of sets
• ### How to calculate the weighted mean

10 Oct 2014 | 10:22 am
This lesson will show you how to calculate the weighted mean using a simple formula

• ## ChapterZero

• ### Mirror descent is, in a precise sense, a second order algorithm

1 Oct 2014 | 10:47 pm
For one of our projects at eBay, I’ve been attempting to do a Poisson MLE fit on a large enough dataset that Fisher scoring is not feasible. The problem is that the data also has such large variance in the scales of the observation that stochastic gradient descent does not work, period — because of the exponentiation involved, you need to take a very tiny step size to avoid overflow errors, but this step size is shared by all the parameters, so you can’t make progress in this way. An alternative is adagrad, which maintains separate stepsizes for each parameter, but that…
• ### Algebra: it matters

15 Sep 2014 | 4:42 pm
I’m looking at two different models for learning polynomial functions, and trying to determine if they are equivalent. After a couple days of thinking, I’ve reduced the question to the following: Can every symmetric polynomial of degree $$r$$ in $$d$$ variables that has no constant term be written as a sum of the $$r$$-th powers of linear polynomials in $$d$$ degrees and a homogeneous polynomial of degree $$r$$ each of whose monomials involves at most $$d-1$$ variables?
• ### Julia, once more

9 Aug 2014 | 12:43 pm
Julia + PyCall + CCall + Gadfly or PyPlot (+ Julia Studio ?) looks delicious. The only feature that absolutely needs to be added is shared memory parallelism (why wasn’t this an initial core feature of the language?), but I’m extremely excited by the current awesomeness of the Julia ecosystem. I recommend you get into it now, if you’re a scientific computation person. Update: Julia has experimental support for shared-memory arrays on Unix, which is really all that I need at this point. Great!
• ### a bit on word embeddings

25 Jul 2014 | 9:31 pm
Lately I’ve been working almost exclusively on continuous word representations, with the goal of finding vectorial representations of words which expose semantic and/or syntactic relationships between words. As is typical for any interesting machine learning problem, there are a glut of clever models based on various assumptions (sparsity, hierarchical sparsity, low-rankedness, etc.) that yield respectable embeddings. Arguably, however, the most well known of these representations are the word2vec models due to Mikolov et al., which are part of a larger class of neural network-based…
• ### Installing Hadoop on Ubuntu (works for Ubuntu 12.04 and Hadoop 2.4.1)

18 Jul 2014 | 4:11 pm
I’m trying to use LDA on a large amount of data. A quick recap: Tried vowpal wabbit … it’s fast, I’ll give it that, but it’s also useless: the output is dubious (what I think are the topics look like they haven’t changed very much from the prior) *and* I have no idea how it maps onto topics and documents (the documentation is AWFUL, and the dimensions of the output files are WONKY). Tried two implementations of SCVB0, a stochastic collapsed variational bayes LDA algorithm: one doesn’t work at all (as in, it stalls on any amount of data — so…
• ## Computational Complexity

• ### Guest Post by Dr. Hajiaghayi: A new way to rank departments

23 Oct 2014 | 8:11 am
(This is a guest post by MohammadTaghi Hajiaghayi. His name is not a typo- the first name really is MohammadTaghi.) Due to our belief in the lack of transparency and well-defined measures in methods used by U.S News to rank CS departments in theoretical computer science (and in general), my PhD. student Saeed Seddighin and I have worked for several months to provide a ranking based on a real and measurable method of the number of papers in TCS for the top 50 US Universities. To make this possible, we gathered the information about universities from various resources. You may see the ranking…
• ### MSR SVC Letters

22 Oct 2014 | 9:34 am
The Committee for the Advancement of Theoretical Computer Science put together an open letter to several research leaders at Microsoft. We feel that there should have been a better way to close down this lab, one that would have allowed them to have continuous employment until academic jobs are available again in September 2015. Given that this lab was continuing to produce exceptional — indeed revolutionary — research, we fail to understand why closing it had to be done so suddenly. I recommend reading the whole letter. Many in the theory community and beyond, including myself, signed…
• ### Martin Gardner Centennial

21 Oct 2014 | 8:09 am
Martin Gardner was born on October 21, 1914, so today is his Centennial (he died on May 22, 2010, at the age of 95). We've mentioned him in the blog before:  The Life of Martin Gardner  Contribute to the Gardner Centennial  Another Post on Martin Gardner I used the anagram Tim Andrer Gran in both my review of the Lipton-Regan book (see here) and my Applications of Ramsey Theory to History paper (see here) So what can I add on his centennial? He was not the first person to write on recreational mathematics, but he was certainly early and did it for a long time. I suspect he…
• ### The Curious Case of NP and NEXP

16 Oct 2014 | 9:34 am
NP (nondeterministic polynomial time) and NEXP (nondeterministic exponential time) are provably different classes by the nondeterministic time hierarchy. No surprise, given exponentially more time we expect to solve more problems. But the proof requires collapses at many input lengths and odd things happen when we look at the infinitely-often question. We say a language L is in i.o.-C for a complexity class C if there is an A in C such that for infinitely many n, A and L agree on strings of length n (for all x of length n, x is in A if and only if x is in L). Straightforward diagonalization…
• ### Luddite or not?

13 Oct 2014 | 9:33 am
My first ever guest post for Lance was on Are you a luddite. I certainly am to some extent a luddite, but there are some things where it not clear if they are luddite-ish or not. I prefer reading books to blogs. This came up when I reviewed both Lipton and Lipton-Regan blog-books, and I am now reading some of Terry Tao's Blog book.  l look forward to reading Scott's Blog book. At first I thought that preferring books was luddite-ish. But some high tech people and some young people who I've asked AGREE with me. Why is this?  when reading a blog (or doing anything on line) its so easy…
• ## Mathematics and Computation

• ### TEDx “Zeroes”

16 Oct 2014 | 12:01 am
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…
• ### Reductions in computability theory from a constructive point of view

19 Jul 2014 | 5:50 am
Here 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 non-constructive 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 am
In 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 am
I 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: brazilian-type-checking.pdf GitHub repository: https://github.com/andrejbauer/tt Abstract: Proof assistants verify that inputs are correct up to judgmental…
• ### Intuitionistic Mathematics and Realizability in the Physical World

4 Mar 2014 | 7:57 am
This is a draft version of my contribution to “A Computable Universe: Understanding and Exploring Nature as Computation”, edited by Hector Zenil. Consider it a teaser for the rest of the book, which contains papers by an impressive list of authors. Abstract: Intuitionistic mathematics perceives subtle variations in meaning where classical mathematics asserts equivalence, and permits geometrically and computationally motivated axioms that classical mathematics prohibits. It is therefore well-suited as a logical foundation on which questions about computability in the real world…

• ## WordPress Tag: Mathematics

• ### MOOCs and Mathematics Self-Learning

21 Oct 2014 | 4:25 pm
Over time, this blog has morphed from being about actuarial self-learning to being more about mathematics and statistics self learning, reflecting my personal career peregrinations. I kind of hope that such readers as there are not too turned off – to me it seems there is a lot of crossover. It also seems, at least from reading forums for actuarial learners (weak evidence, so feel free to provide your own counterpoint), that insufficient mathematics is at the root of a lot of difficulties that actuarial students discover along the way. I intend to soon write a blog piece about my…
• ### Enrollment in Teacher Education Courses is Declining

21 Oct 2014 | 2:56 pm
Apparently students are deciding in large numbers that teaching is not such a safe, stable career any more, and as a result, in several large states, the numbers of students enrolled in programs to prepare students for a career in education is going down dramatically. In California, the numbers have dropped by over 40 percent in just a few years (from 44,692 in 2008/9 to 26.321 in 2011/12). In New York State, they went from 79,225 im 2009/10 to 61,821 in 2011/12, a 22% drop. They don’t seem to give teacher-preparation enrollments for 2013-14 or for the present year. I wouldn’t be…
• ### Mathematical diversion: the ladder problem

21 Oct 2014 | 2:17 pm
This is a mathematical diversion to while away some time, and stim- ulate your brain. Try solving it before looking at the paper, as it states some basic equations and approaches quickly. The problem is stated be- low. There is a vertical wall, and a horizontal floor. A box, measuring 1m x 1m x 1m lies on the floor, and is flush against the wall and the floor. The problem is actually in 2D, so you can ignore depth. Suppose there is a ladder, of length c, which is propped so that the top of the ladder touches the wall, the bottom touches the floor, and somewhere along its length it touches the…
• ### MicroBlink Launches PhotoMath To Solve Math Equations With A Phone

21 Oct 2014 | 1:49 pm
Imagine you are a 14-year-old kid again. You need to do this really difficult math exercise for tomorrow, but have no idea how to do it. What if you could just open an app on your phone, point your camera at your textbook, snap a picture and get the detailed instructions to solve your equation. This is exactly what PhotoMath does. The team is launching this app today at TechCrunch Disrupt Europe in London. MicroBlink is a text recognition technology company that has been developing a powerful engine for mobile phone cameras for the past two years. The startup is in the business of selling its…
• ### Middle-school math game, Lure of the Labyrinth

21 Oct 2014 | 12:37 pm
MIT’s teacher education program already focuses on digital games, among other tools—it developed a middle-school math game, Lure of the Labyrinth, that has a cult following among teachers, and it is piloting a math and science multiplayer online role-playing game. The new courses are being offered through a department called the Education Arcade. But the new courses aim to help students both inside and outside of MIT produce sale-able products. The final project for the first course will be a Kickstarter-like pitch for a new game-based educational technology.   For more information…
• ## Mr. L's Math

• ### Programming with GeoGebra

14 Oct 2014 | 1:58 pm
GeoGebra logo Here’s a nice post by Riley Eynon-Lynch from the Point of Inflection website –  PROGRAMMING WITH GEOGEBRA Some of his main points: This post is about some of the virtues of programming computers in math class. I include a long anecdote and a quick geogebra tutorial. The punchline: teaching kids to program introduces them to an environment that gives instantaneous, continuous, 100% correct, 0% helpful feedback without judgement. The computer doesn’t say, “you’ve made a mistake here,” it just shows you a result, and it’s up to you to interpret it, decide if…
• ### GeoGebra Loved by Students-Teachers-Schools

5 Oct 2014 | 6:42 am
GeoGebra-a Powerful Tool for Students GeoGebra.org has had a facelift and is worth visiting/revisiting. The new interface suits computers and mobile devices well, and has something for everyone. Its strength is ease of use paired with great power to visualize mathematics. The following was taken directly from the newly configured site: GeoGebra is a multi-platform mathematics software that gives everyone the chance to experience the extraordinary insights that math makes possible. Students love it because… it makes math tangible – GeoGebra makes a link between Geometry and Algebra in…
• ### Visual Pattern Site by Fawn Nguyen

26 Sep 2014 | 2:06 pm
pattern no. 155 from Fawn Nguyen’s site visualpatterns.org When I taught 7th grade for six years visual patterns were used to start the school year because they did so many great things for students. They were engaging to the students, visually stimulating, allowed all students easy entry to the math involved, worked great for student projects, and addressed many math standards. Here’s a site with a lot of patterns you can use in your classroom, along with commentary for teacher use. As of the date of this post (Sept 2014) there are 145 patterns, along with the Equation…
• ### Malin Christersson-Digital Math for GeoGebra Enthusiasts

25 Sep 2014 | 5:46 pm
Malin Christersson’s site, Digital Mathematics, is a great place to spend some time for GeoGebra enthusiasts. It has some of the best tutorials on the web, organized into seven clusters. Malin provides clear and detailed explanations, some with embedded videos, that help the new as well as experienced user to get more out of GeoGebra. Malin also has provided further work in the areas of Non-Euclidean Geometry, Latex/LyX, Geometry, Functions, Trigonometry, Calculus, Statistics, Linear Algebra, and Fractals. From the site: “This is a collection of material that I have used when…
• ### Circle Dissection Puzzle-Four Equal Curved Areas

24 Sep 2014 | 4:30 pm
Dissect the circle into four parts of equal area by drawing three curved lines of equal length. – idea from Arithmetrics, by Jerome S. Meyer, pg 88 Move slider halfway to reveal a hint if you’re stuck. Questions for you or your students: 1- Why are the 3 curved lines of equal length? 2- How do you show that the 3 curved lines make equal areas? The downloadable file can be found here. My other GeoGebraTube apps can be found here. here.
• ## MathNotations

• ### A Dose of Reality -- My Latest Common Core Rant

22 Oct 2014 | 9:55 am
I'm reproducing my comment to the post, "Who Needs Algebra?"on Mr. Honner's outstanding blog... http://mrhonner.com/archives/14291#comment-10579. 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 in-depth 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 am
Borrowing a problem from the comments in the excellent blog CorkboardConnections. Hope that's ok... http://corkboardconnections.blogspot.com/2014/08/common-core-math.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…
• ### Round your answer to nearest cent: $1.29 or$1.30?

20 Oct 2014 | 10:27 am
Tweeted (@dmarain) the above a couple of days ago. Moderate reaction so far which I find fascinating since I've done my own "random" survey... SCENARIO 6th gr student calculates an *exact* answer of $1.29. Directions read "round ans to nearest cent." Student writes$1.30 in the answer box on the test. Teacher notes $1.29 was correct but the answer in box was wrong. No credit for problem... COREFLECTIONS Making too big a deal of this? After all "rounded to nearest cent" means "round to nearest hundredth". So$1.29 is already rounded to the nearest…
• ### Implement The Core -- Opposite Corners of a Square

18 Oct 2014 | 12:12 pm
Twitter Problem 10-18-14If (a,b),(-a,-b) are opposite vertices of a square, show that its area=2(a^2+b^2)EXTENSION: What if (a,b),(-a,-b) are adjacent?COREFLECTIONS(1) What do you believe will challenge your geometry students here? The abstraction? "Show that"? (2) Predict how many of your students would "complete the rectangle" by  incorrectly drawing sides || to the axes? (3) Even if not an assessment question, is it a good strategy to "plug in" values for a&b? This is worthy of more dialog IMO... (4) How many of your students would question the lack of restrictions on a&b?
• ### Implement The Core: Arithmetic Patterns & Generalizations in Middle School Math

16 Oct 2014 | 9:54 am
As tweeted on 10-16-14... Pattern #1 Explore on calculator... 352×11=3872 527×11=5797 365×11=4015 Keep going! Discuss! Explain! Generalize! Pattern #2 18=9×2,81=9×9 27=9×3,72=9×8 36=9×4,63=9×7 Keep going! Describe, extend,generalize! Is 407×9=3663 unrelated? COREFLECTIONS... (1) But these are just math curiosities, Dave. They don't really tie into the Common Core, do they? Well, doesn't multiplying by 11 connect nicely to the Distributive Property: 352×11=352×(10+1)=3520+352 etc. How about 9? (2) My goal has always been to expose our students to engaging and meaningful…

• ## mathrecreation

• ### GSP and LOGO (for MITx: 11.132x)

20 Oct 2014 | 7:51 pm
Note: This post is an assignment for the Edx MOOC MITx: 11.132x Design and Development of Educational Technology. The assignment had to be posted online, and since it relates somewhat to the themes of this blog, I put it here.Educational Technology Then and Now: Geometer's Sketchpad and LOGOGeomter's Sketchpad (GSP) is an example of current educational technology that is based on design and educational principles that can generally be described as constructionist. Widely used in contemporary classrooms, GSP is based on ideas about computer-human interaction that date back to the 1960s, and…
• ### circles, hexagons, flowers

2 Oct 2014 | 7:02 pm
Was playing around with intersecting circles, as in this post.
• ### A year of tinkering

29 Sep 2014 | 6:37 pm
You really should take advantage of the free until August 2015 license that is currently being offered with a fresh download TinkerPlots. Would that it was freely available in perpetuity without condition, but a year of tinkering is nice.If you are a middle school teacher, then this is designed for you and yours. If, like me, you are not, you may find it fun to play with anyway.  Here is something I was playing with recently:An elementary school number sense activityIn the JUMP math curriculum for grades 3 and 4, there are lessons where students investigate the patterns formed when…
• ### modular tables

17 Sep 2014 | 7:13 pm
No, not a post about IKEA furniture. A while  ago I put up a post on colouring multiplication tables by assigning ranges of numbers a colour value. You end up with something that looks like a rainbow.This image was made in Tinkerplots, so it was easy to go from a 10 x 10 table to a 50 x 50 table (removing the numbers and just keeping the colours, and shrinking each cell down a bit):Inspired by the "Zn Multiplication visualizer" found here and mentioned here, and thinking about modular arithmetic from the last post, I decided to make a few more images.If you take the values in this…
• ### squashing multiples

15 Sep 2014 | 7:21 pm
An elementary school exercise leads to writing a simple program, a little proof by contradiction, and learning about some mostly-forgotten calculation tricks: just some of the fun that can be had when playing with simple math. Sound good? It all starts with squashing numbers...No doubt you've noticed some patterns in the non-zero multiples of 9: 9, 18, 27, 36, 45,... One thing to notice is that if you (repeatedly) add up all the digits of a multiple of 9, you always get 9 as your answer.This works immediately for many multiples of 9, like 9*14 = 126 (1 + 2 + 6 = 9), for others you need to…
• ## MathFour

• ### Using the Hundreds Chart to Teach Beginning Multiplication

21 Oct 2014 | 5:50 am
We 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 am
Note: 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…

2 Oct 2014 | 2:14 am
Check out this little Halloween bat made of rectangles, squares and triangles. There’s even an opportunity to talk about trapezoids! Both of the downloads have the same bat template, they just have different discussion questions. Supplies One of the free downloadable templates: Geometric Bat for Older Kids or Geometric Bat for Younger Kids Black and orange construction paper Scissors Glue or glue stick Googly eyes Instructions Use the template shapes to cut out the geometric pieces from black construction paper. Follow the design on the download to glue the pieces onto the orange piece…
• ### How to Tell the Difference between 0.3 and 0.33 – Visually

26 Sep 2014 | 4:39 am
A student was working on this problem the other day: Find the volume of a cone with radius 2.5 units and height 5 units. Of course we all remember the formula as So she plugged in her numbers and got 29.45 cubic units. She checked the back of the book and was disappointed to see the answer listed as 32.72 cubic units. Turns out she was using 0.3 instead of 1/3! What’s wrong with the answer? I asked her to calculate with 0.33 instead. She got 32.39 – far closer to the answer from the book. Then I asked her to use 0.333. This yielded 32.69. She was amazed at how adding another 3 got…
• ### Teaching Math to Special Needs Children

16 Sep 2014 | 7:38 pm
I’m out of my depth. Like 3 bazillion leagues out of my depth. I took a math teaching position at a school for kids with neurological differences. I knew it would be hard. But I didn’t think it would be this hard. Lesson 1: Everything you know is wrong. It’s a Weird Al song, but it also applies to teaching kids with special needs. I gave this great math artwork activity that I thought would be perfect. My students are all 12-19 years old. They can communicate, be polite and follow instructions. And they are all listed as over 2nd grade in abilities. So this should have be a…
• ## CSE Blog - quant, math, computer science puzzles

• ### Diminishing Differences Puzzle

18 Oct 2014 | 3:05 am
Source: 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 am
Source: 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 am
Source: AUSTMS Puzzle Corner 35 Problem: Call a nine-digit 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!
• ### Minimum sum of numbers in an array

10 Aug 2014 | 10:21 pm
Source: Asked to me on quora ( cseblog.quora.com ) Problem: Given an array of n positive numbers (n ~ 100000), what is the algorithmic approach to find the minimum possible sum (>=0) by using all the numbers in an array? Example 1: 1 2 2 3 4 Answer : 0 (-1+2-2-3+4) Example 2: 2 3 4 7 13 Answer: 1 (+2-3-4-7+13)
• ### Caterer's Problem

5 Aug 2014 | 10:07 pm
Source: Puzzle Toad CMU Problem: You are organizing a conference, with a festive dinner on the first day. The catering service has 1024 different dinner choices they know how to make, out of which you need to choose 10 to be in the dinner menu (each participant will choose one of these during the dinner). You send an email to the 6875 participants of the conference, with the list of all 1024 choices, asking them to rank the choices in linear order from their favorite to their unfavorite. You want to find a list L of 10 choices, such that for any dinner choice d not in the list L, if we run a…

• ## Math for all Grade blog

• ### Oct 22, Interval-notation

22 Oct 2014 | 3:34 am
Interval-notation.
• ### Oct 20, Complementary-angles

20 Oct 2014 | 1:12 am
Two angles are called complementary angles, if the sum of their degree measures is 90. Each angle is called complement of the other
• ### Oct 20, Compound-interest-formula

20 Oct 2014 | 12:14 am
compound interest formula to calculate the amount for annual compounding and other investment time periods.
• ### Oct 20, Area-of-circle

19 Oct 2014 | 11:47 pm
Area of circle is Π times the radius of the circle squared or Π times one-fourth the diameter of circle squared.
• ### Oct 17, Alternate-interior-angles

17 Oct 2014 | 12:32 am
Alternate interior angles formed by parallel lines cut by a transversal are equal in measure.
• ## Marauders of the Lost Sciences

• ### The Philosopher Ramsey investigates the rate of saving

23 Oct 2014 | 11:10 pm
Ramsey was more or less a philosopher, but unlike most philosophers he was also Senior Wrangler. Today if someone died at 26 like Ramsey did, we’d never hear about them because they’d only be half way through graduate school. They’d have another decade and half to go before doing their own work. When Ramsey died though he was already a major force having proved “Ramsey’s Theorem” in combinatorics and written a number of economics papers in addition to his philosophical works. What would he have done if he’d lived to 80? Mr. Keynes, to whom I am…
• ### R. A. Fisher applies Group Theory to the Design of Experiments

22 Oct 2014 | 11:10 pm
R. A. Fisher was one of the founders of Frequentist statistics and was instrumental in introducing statistical design principles into agricultural experiments. Here he invokes Group Theory to study the theory of confounding in factorial experimental designs. THE GROUP PROPERTIES OF TREATMENTS AND COMPARISONS A group may be formed, of which the elements are all the selections that can be made of none or more out of n letters. The order of the group is . The product of any two elements is formed by combining the letters they contain, deleting any they may have in common. The group is,…
• ### Gödel gives Einstein a helping hand

21 Oct 2014 | 11:10 pm
Kurt Gödel is known for his incompleteness theorem and other major contributions to mathematical logic. After befriending Einstein at The Institute for Advanced Study, he set about finding a novel solution to the field equations of Einstein’s general relativity. THE MAIN PROPERTIES OF THE NEW SOLUTION All cosmological solutions with non-vanishing density of matter known at present have the common property that, in a certain sense, they contain an “absolute” time coordinate, owing to the fact that there exists a one-parametric system of three-spaces everywhere orthogonal on the…
• ### Feynman describes a world without fields

21 Oct 2014 | 9:57 am
In 1949 Feynman together with his advisor Wheeler considered the idea that the electromagnetic field wasn’t real, but was rather a kind of accounting device used to use keep track of action-at-a-distance particle interactions. Many of our present hopes to understand the behavior of matter and energy rely upon the notion of ﬁeld. Consequently it may be appropriate to re-examine critically the origin and use of this century old concept. This idea developed in the study of classical electromagnetism at a time when it was considered appropriate to treat electric charge as a continuous…
• ### Why learn from the giants?

20 Oct 2014 | 12:38 pm
Denizens of the exact sciences often believe reading the great works is a waste of time. Surely everything of value has been extracted and refined by more recent authors. You’ll be fine just reading textbooks, review papers, and the latest research. They are wrong. The value of studying the greats is proven. Even well known papers hundreds of years old can yield important new research with fresh eyes. Often great works aren’t well known and their potential is unfulfilled. And it doesn’t take much reading from the giants to realize they themselves learned directly from the…