# Math

• ## Most Topular Stories

• ### Foreward to Special Issue for winners of the 2nd IMA Lighthill-Thwaites Prize

IMA Journal of Applied Mathematics - current issue
23 Jul 2014 | 8:44 am
• ### Math Twitter Bots, Reviewed and Rated

Scientific American - Math
28 Jul 2014 | 5:00 am
In the course of being a math person on Twitter, I have run across some math-related Twitter bots and feeds. It would just be mean to grade my human tweeps, but I have no qualms about rating the bots! -- Read more on ScientificAmerican.com
• ### Prime Mystery

eon
30 Jun 2014 | 3:27 pm
A nice puzzle from Aziz Inan on plus.maths.org The number N represents the first 6 digits of a special number. N consists of three prime numbers put side by side. These three prime numbers come xth, yth and zth on the list of primes, where x, y and z are themselves three consecutive primes (for example, x, y and z could be 3, 5 and 7, in which case we’d be looking at the third, fifth and seventh prime numbers). In addition, if N is split in the middle into two separate numbers, the prime factors of the left part of N add up to its right part. What is N? And what is the special numbers…
• ### Univalent foundations subsume classical mathematics

Mathematics and Computation
13 Jan 2014 | 9:10 am
A discussion on the homotopytypetheory mailing list prompted me to write this short note. Apparently a mistaken belief has gone viral among certain mathematicians that Univalent foundations is somehow limited to constructive mathematics. This is false. Let me be perfectly clear: Univalent foundations subsume classical mathematics! The next time you hear someone having doubts about this point, please refer them to this post. A more detailed explanation follows. In standard mathematics we take classical logic and set theory as a foundation: $\text{logic} + \text{sets}$ On top of this we build…
• ### Volume of irregular shapes

Basic mathematics blog
28 Jul 2014 | 1:28 pm
Learn to calculate the volume of irregular shapes using commonly used volume formulas
• ## Search for "math OR mathematics"

• ### Wanted, A Loving Home: Young lady is talented, loving

31 Jul 2014 | 1:46 pm
Michelle is a reserved and quiet young lady. She strives to please people and is respectful and polite toward others.
• ### Jordan Garnett, Rising 22-Year-Old Boynton Beach Comedian, to Open for Jen Kirkman This Weekend

31 Jul 2014 | 1:45 pm
Six comedians took the stage this past Tuesday at Aroma's Hookah Lounge in Wellington.
• ### Just one class3:40 pm

31 Jul 2014 | 1:42 pm
Is there a demand for basket weavers in today's economy? I didn't know you could major in that subject I had planned to major in music but my mother talked me out of that.
• ### How democracy saves Seattle schools from bad superintendents

31 Jul 2014 | 1:40 pm
With the departure of Jose Banda from the post of superintendent of Seattle Public Schools, we've seen the usual hand-wringing and recriminations over the future of the district.
• ### Hernando back-to-school briefs

31 Jul 2014 | 1:36 pm
The Friends of the Children Inc. will host the annual Operation Backpack at 10 a.m. Aug. 9 at the Jerome Brown Community Center, 99 Jerome Brown Place, Brooksville.

• ## Mathematics News -- ScienceDaily

• ### Numerical learning disability: Dyscalculia linked to difficulties in reading and spelling

30 Jul 2014 | 6:38 am
Between three and six percent of schoolchildren suffer from an arithmetic-related learning disability. Researchers now show that these children are also more likely to exhibit deficits in reading and spelling than had been previously suspected.
• ### Creating sustainable STEM teacher programs

24 Jul 2014 | 11:42 am
Faculty members who choose to champion physics teacher education, in combination with institutional motivation and commitment, ensure that STEM teacher education programs remain viable after initial funding ends.
• ### Atmosphere of Titan, Saturn's largest moon

23 Jul 2014 | 8:10 am
An astronomer has published the results of the comparison of his model of Titan's atmosphere with the latest data.
• ### Philosopher uses game theory to understand how words, actions acquire meaning

21 Jul 2014 | 9:37 am
Why does the word "dog" have meaning? If you say "dog" to a friend, why does your friend understand you? A philosopher aims to address these types of questions in his latest research, which focuses on long-standing philosophical questions about semantic meaning. Philosophers and a mathematician are collaborating to use game theory to analyze communication and how it acquires meaning.
• ### Size and age of plants impact their productivity more than climate

20 Jul 2014 | 5:43 pm
The size and age of plants has more of an impact on their productivity than temperature and precipitation, according to a landmark study. They show that variation in terrestrial ecosystems is characterized by a common mathematical relationship but that climate plays a relatively minor direct role. The results have important implications for models used to predict climate change effects on ecosystem function and worldwide food production.
• ## Scientific American - Math

• ### Math Twitter Bots, Reviewed and Rated

28 Jul 2014 | 5:00 am
In the course of being a math person on Twitter, I have run across some math-related Twitter bots and feeds. It would just be mean to grade my human tweeps, but I have no qualms about rating the bots! -- Read more on ScientificAmerican.com
• ### Mysterious Tiles from a Time When Art and Science Were Friends

25 Jul 2014 | 9:44 am
Forces in society of late have lots of us longing for the days of the Enlightenment, smallpox, powdered wigs, ridiculously uncomfortable clothing and all. -- Read more on ScientificAmerican.com
• ### The Shocking Failure of British Rail Travel to Respect the Triangle Inequality

23 Jul 2014 | 5:00 am
I spent about a month in the UK earlier this summer, and that meant I took a lot of train trips. I love riding trains: the feeling of endless possibility I get when I look at the departure boards,... -- Read more on ScientificAmerican.com
• ### When was the last time you used a print dictionary?

22 Jul 2014 | 5:39 am
I used to keep a small dictionary in my bedside table, another in the end table near the couch, one on my home office desk and another on my desk at work. -- Read more on ScientificAmerican.com
• ### Tapping Your Inner Rain Man

21 Jul 2014 | 4:30 am

• ## NYT > Mathematics

• ### Why Do Americans Stink at Math?

26 Jul 2014 | 9:00 pm
The Common Core should finally improve math education. The problem is that no one has taught the teachers how to teach it.
• ### Youngsters Who Excel at Robotics and Drollery

25 Jul 2014 | 9:00 pm
Amazon has posted seven episodes of its new show, “Annedroids,” which targets a preteen audience with its science-based story line.
• ### Don’t Teach Math, Coach It

24 Jul 2014 | 9:00 pm
What I learned from baseball about making learning fun.
• ### Beyond Energy, Matter, Time and Space

21 Jul 2014 | 9:00 pm
Humans might think we can figure out the ultimate mysteries, but there is no reason to believe that we have all the pieces necessary for a theory of everything.
• ### Seeker, Doer, Giver, Ponderer

7 Jul 2014 | 9:00 pm
The billionaire mathematician James H. Simons has led a life of ferocious curiosity.

• ### Richard Rusczyk – Inspired by Math #39

3 Jul 2014 | 6:13 pm
I never did much math competition in middle school or high school although I did score well on the MAA competition and on the Math SAT and I went to public junior and high schools that you had to test into. Nonetheless, I have always been fascinated by the world of math geniuses. Richard Rusczyk started a school, Art of Problem Solving, to serve kids who love math, love solving math problems, and maybe want to compete. Richard and I spent an hour diving into the world of elite math competitions and what it takes to succeed in them. I got to scratch the itch that is my fascination with these…
• ### Sue VanHattum – Inspired by Math #38

23 Jun 2014 | 6:44 pm
Sue VanHattum is a math professor, blogger, mother, author/editor, and fundraiser. She's a real powerhouse of motivation for making math fun and accessible to more of our young folks. Sue has teamed up with a number of writers to compile a book, "Playing With Math," which she is producing in partnership with Maria Droujkova in a community sponsored publication model. Sue and I shared a delightful chat about what math is, what the book is about, and how we can all get more inspired to engage in math with our kids. And, Sue sprinkles the conversation with some interesting open-ended math…
• ### Lou DiGioia – Inspired by Math #37

21 Jun 2014 | 9:58 am
Lou DiGioia, executive director of MATHCOUNTS, and I tried to do a podcast a couple of months ago. The audio had some serious problems and we produced a transcript instead. It was a great discussion although I asked way too much about the human Pascal's triangle that made a Guiness World record. Anyway, the second time was a charm, and we produced a good audio discussing all things related to MATHCOUNTS and how the organization inspires kids to improve their relationship with Math. If you read the transcript, or even if you didn't, check out the podcast! About Lou DiGioia As executive…
• ### Al Cuoco – Inspired by Math #36

14 Jun 2014 | 9:36 am
The MAA (Mathematical Association of America) sent me a review copy of their new book "Learning Modern Algebra: From Early Attempts to Prove Fermat's Last Theorem." I don't typically review textbooks but the title and then the contents of the book convinced me that I needed to interview the authors. Joe Rotman wasn't available but I was able to chat with the other co-author, Al Cuoco. I was really struck with Al's passion about teaching the teachers as well as the students. Al shared some great insights about the ingredients that I think should go into every math textbook to help teachers and…
• ### David Reimer – Inspired by Math #35

7 Jun 2014 | 10:33 am
I love novel ways of looking at arithmetic. I'm fascinated with how computers compute in binary, with tricks for simplifying calculations and with how Vedic mathematicians handle difficult arithmetic efficiently. So, when Princeton University Press sent me a review copy of their new book "Count Like An Egyptian," I immediately fell in love with it. I was delighted to learn even more techniques and the ideas behind them to deepen my appreciation of the beauty of what most consider to be mundane arithmetic. "Count Like an Egyptian" is a delightful book, full of color illustrations, fun stories,…

• ## Loren on the Art of MATLAB

• ### Write Once, Deploy Anywhere

28 Jul 2014 | 8:03 am
Guest blogger Peter Webb returns with another in an occasional series of postings about application deployment.ContentsDeployment TargetsDeploying to MATLABDeploying to the DesktopDeploying to a Java ApplicationReuse, Don't RewriteDeployment TargetsI've written a MATLAB application that reports on the presence of contaminants in surface water, using a publically available database of water quality observations maintained by the United States Geological Survey and the Environmental Protection Agency. Many groups of people might be interested in this kind of information. MATLAB made it easy to…
• ### Analyzing Fitness Data from Wearable Devices in MATLAB

14 Jul 2014 | 5:18 am
Collecting and tracking health and fitness data with wearable devices is about to go mainstream as the smartphone giants like Apple, Google and Samsung jump into the fray. But if you collect data, what's the point if you don't analyze it?Today's guest blogger, Toshi Takeuchi, would like to share an analysis of a weight lifting dataset he found in a public repository.ContentsMotivation, dataset, and prediction accuracyData preprocessing and exploratory analysisPredictive Modeling with Random ForestPlot misclassification errors by number of treesVariable ImportanceEvaluate trade-off with ROC…

30 Jun 2014 | 10:22 am
• ### Webcam Support – New in R2014a

17 Jun 2014 | 5:30 am
Today I’d like to introduce a fairly frequent guest blogger Sarah Wait Zaranek who works for the MATLAB Marketing team here at The MathWorks. She and I will be writing about the new capabilities for the webcam in R2014a.ContentsWebcam is AvailableInstalling the Support PackageListing Webcams and PreviewingTaking a Single ImageTaking Images Within a LoopTaking Images Within a Loop and Saving to an AVI-fileSet up video writerGrab and process framesTaking Images Within a Loop and Creating an Animated GIFHere's the movie we just madeTidy upAdditional Camera SupportDo You Have a Project that…
• ### Analyzing Twitter with MATLAB

4 Jun 2014 | 1:13 pm
Whatever your opinion of social media these days, there is no denying it is now an integral part of our digital life. So much so, that social media metrics are now considered part of altmetrics, an alternative to the established metrics such as citations to measure the impact of scientific papers.Today's guest blogger, Toshi, will show you how to access the Twitter API and analyze tweets with MATLAB.ContentsWhy TwitterSentiment AnalysisTweet Content VisualizationWho Tweeted the News?Does Follower Count Really Matter? Going Viral on TwitterVisualizing the Retweet Social GraphGetting Started…
• ## Homeschool Math Blog

• ### How to help a student who is behind in math

26 Jul 2014 | 11:00 am
Updated!Image by www.flickr.com/photos/sveinhal/How to help a student who is behind in mathIn the article I discuss some general principles in helping students that are behind in math.Test and assessMake a list of topics to studyPerhaps go back to the very beginning?Restudying some topics while using a math curriculumThe order of topicsShould you go on with new concepts or not?I hope it is of help!
• ### Worksheets for inequalities

21 Jul 2014 | 6:12 am
More new worksheet generators... This one is for linear inequalities in one variable.http://www.homeschoolmath.net/worksheets/linear_inequalities.phpThe worksheets are customizable in many different ways. You can ask the student to plot simple inequalities, such as x < -6 or write an inequality from a graph. One problem type asks you to solve the given simple inequality in the given set, such as solve x + 1 > -2 in the set {-9, 3,5,8, -2, 10}. Then you can choose from six different types of linear inequalities to solve (such as one-step inequalities, two-step inequalities, or…
• ### 1-day sale

16 Jul 2014 | 4:57 am
SAVE 40% on selected Math Mammoth bundles at Homeschool Buyers Co-op:https://www.homeschoolbuyersco-op.org/math-mammoth/ONLY for today!
• ### A thought to consider...

13 Jul 2014 | 8:19 pm
Posted with permission from http://www.heartcheer.com/ where you'll find many more thoughtful poems!
• ### Math Mammoth photo contest winning entries

11 Jul 2014 | 2:49 pm
Here are the winning entries for the photo contest I ran recently. I asked each participant to provide a photo showing a child/student(s) doing math work from a Math Mammoth book or materials. Click to see a larger version. Enjoy!1. I felt this picture was just so cute and also the composition is great."Isabelle is proudly showing her mom her correctly formed 3's. She wrote them backwards at first. She is working out of her big sister's 1st grade workbook from Math Mammoth's Light Blue Series."The second place was a tie — I just couldn't decide.2. A. First, school work upside down - quite…
• ## Let's Play Math!

• ### Math Teachers at Play #76

22 Jul 2014 | 4:51 am
[Feature photo (above) by U.S. Army RDECOM. Photo (right) by Stephan Mosel. (CC BY 2.0)] On your mark… Get set… Go play some math! Welcome to the 76th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college. By tradition, we start the carnival with a puzzle in honor of our 76th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents. PUZZLE:…
• ### Playing With Math — the Book

16 Jul 2014 | 7:23 am
There are only a few days left to reserve your copy of Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers. I don’t have time to finish the review I hoped to write, so instead I’ll share some of my favorite quotes from the book: What do mathematicians do? We play with math. What are little kids doing when they’re thinking about numbers, shapes, and patterns? They’re playing with math. You may not believe it yet, but you can have fun playing with math, too. — Sue VanHattum, editor We had a discussion at the end of the club on how…
• ### Education Bloggers: Share Your Post!

15 Jul 2014 | 7:15 am
photo 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 extended through the weekend. The carnival will be posted next week at Let’s Play Math. Click to tweet about the carnival: (No spam, I…
• ### Quotable: Math Connections

11 Jul 2014 | 2:52 pm
It turns out that the people who do well in math are those who make connections and see math as a connected subject. The people who don’t do well are people who see math as a lot of isolated methods. — Jo Boaler Math Connections If you or your children struggle with math, Boaler’s non-profit YouCubed.org may help you recover your joy in learning. Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.
• ### Math(s) Teachers At Play #75 via CavMaths

28 Jun 2014 | 11:32 am
[Feature photo above "Sconic Sections" by Lenore Edman and "75" by R/DV/RS via Flickr (CC BY 2.0).] The monthly math education blog carnival Math Teachers at Play features games, lessons, puzzles, activities, and teaching tips from classroom teachers, homeschoolers, and self-educated learners around the Internet world. Check out the 20 posts of mathematical fun in the June edition: Math(s) Teachers At Play #75 via CavMaths Hello, and welcome to the 75th issue of the Math(s) Teachers at Play Blog Carvinal! For those of you who are unaware, a “blog carnival” is a periodic post that travels…

• ## Basic mathematics blog

• ### Volume of irregular shapes

28 Jul 2014 | 1:28 pm
Learn to calculate the volume of irregular shapes using commonly used volume formulas
• ### Geometry word problems

28 Jul 2014 | 5:40 am
A collection of geometry word problems to help you practice a wide variety of concepts in geometry. All problems come with the solution
• ### Sum of Arithmetic Series

23 Jul 2014 | 11:59 am
Learn how to find the sum of arithmetic series. Derive a formula for the sum. Use summation notation
• ### Oral Solution Dosage Calculation

21 Jul 2014 | 8:47 am
Learn to calculate the amount of oral solution to give to a patient when the dosage strength is known
• ### Tablet Dosage Calculation

14 Jul 2014 | 1:34 pm
Learn to calculate how many tablets to give to a patient when the dosage strength is known
• ## ChapterZero

• ### 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…
• ### Sharing numpy arrays between processes using multiprocessing and ctypes

1 May 2014 | 4:32 pm
Because of its global interpreter lock, Python doesn’t support multithreading. To me, this is a ridiculous limitation that should be gotten rid of post-haste: a programming language is not modern unless it support multithreading. Python supports multiprocessing, but the straightforward manner of using multiprocessing requires you to pass data between processes using pickling/unpickling rather than sharing memory. Needless to say, this slows down execution when large amounts of data need to be shared by processes. In my case, I’ve been using multiprocessing to speed up the training…
• ### Eigenvector two-condition number for a product of PSD matrices

7 Apr 2014 | 9:31 am
I’m pushing to submit a preprint on the Nystrom method that has been knocking around for the longest time. I find myself running into problems centering around expressions of the type $$B^{-1}A$$, where $$A, B$$ are SPSD matrices satisfying $$B \preceq A$$. This expression will be familiar to numerical linear algebraists: there $$B$$ would be a preconditioner for a linear system $$A x = b,$$ and the relevant quantity of interest is the spectral radius of $$B^{-1} A$$. It’s not hard to show that the spectral radius of this product is at most 1… but instead, I’m…
• ### Canonical Correlation Analysis (CCA)

7 Apr 2014 | 9:20 am
I am not completely satisfied with the expositions of CCA that I’ve come across, so I decided to write one that reflects my own intuition. CCA is useful in the case where you observe two random variables that are both noisy linear functions of some underlying latent random variable, and you want to use this fact to help you guess the latent variable. Formally, assume $x = T_X z + n_x, \quad \text{ and } \quad y = T_Y z + n_y,$ where, without loss of generality, we assume that the entries of $$z$$ are uncorrelated and unit variance. Here $$T_X$$ and $$T_Y$$ are matrices whose image…
• ## Computational Complexity

• ### The Change Problem and the Gap between Recreational and Serious Mathematics

27 Jul 2014 | 6:50 pm
In a prior post (here) I discussed the change problem: given a dollar, how many ways can you make change using pennies, nickels, dimes, and quarters (and generalize to n cents). Scouring the web I found either programs for it, the answer   (242), and answers like `is the coefficient of x^100 in ... . What I didn't find is a  formula for n cents. So I derived one using recurrences and wrote this up with some other things about the change problem, and I posted it on arXiv. (I have updated the paper many times after comments I got. It is still where it was, but updated, here.) I…
• ### Need some book reviewed- faster than usual

24 Jul 2014 | 4:54 pm
I have been the SIGACT NEWS book review editor since 1997. I have tried to get about 10 books reviewed per column. I have succeeded- perhaps too well! I have gotten so many reviews out that I only have six reviews left. I DO have many books that could be reviewed, and that is where YOU come in! List of books available for review: Here Advice for reviewers: Here LaTeX  Template for reviews: Here ALL of my prior columns: Here IF you want to review a book DO NOT leave a comment- just email me (ADDED LATER- EMAIL ME at gasarch@cs.umd.edu. Someone emailed Lance instead which you shouldn't…
• ### The Burden of Large Enrollments

22 Jul 2014 | 8:42 am
This week I'm at the CRA Snowbird conference, the biennial meeting of CS chairs and other leaders in the field. In 2012 many of the discussion focused on MOOCS. This year the challenge facing most CS chairs are booming enrollments in CS courses. A nice problem to have, but a problem nevertheless. Last night we had a broad discussion about the burgeoning number of students. Ed Lazowska showed his NCWIT slides giving anecdotal evidence. It's too early to get a complete survey of CS departments but hardly anyone in the audience felt that enrollments were not going up by double (or triple)…
• ### Elfdrive

17 Jul 2014 | 6:24 am
New York Times, dateline June 11, 2019 With a near record-setting investment announced last week, the self-driving car service Elfdrive is the hottest, most valuable technology start-up on the planet. It is also one of the most controversial. The company, which has been the target of protests across Europe this week, has been accused of a reckless attitude toward safety, of price-gouging its customers, of putting existing cabbies out of work and of evading regulation. And it has been called trivial. In The New Yorker last year, George Packer huffed that Elfdrive typified Silicon Valley’s…
• ### What to call the top and bottom part of (n choose k)

13 Jul 2014 | 8:34 pm
In my last post I asked for candidates for names for the top and bottom part of (n choose k) . Here are the candidates and my comments on them and ... the winner! Top part: Degree, Bottom part: Index.  Top part: Bino, Bottom part: Mial Top part: Numerator, Bottom part: Denominator Top part: Outcomes, Bottom part: Possibilities Top part: Binomerator, Bottom part: I've got nothing Top part: *, Bottom part: * Top part: Biponendo, Bottom part: Bividendo Top part: Choosand, Bottom part: choosee Top part: Set size, Bottom part: Subset size. I leave out the explanations for these since one…

• ## Mathematics and Computation

• ### 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…
• ### Univalent foundations subsume classical mathematics

13 Jan 2014 | 9:10 am
A discussion on the homotopytypetheory mailing list prompted me to write this short note. Apparently a mistaken belief has gone viral among certain mathematicians that Univalent foundations is somehow limited to constructive mathematics. This is false. Let me be perfectly clear: Univalent foundations subsume classical mathematics! The next time you hear someone having doubts about this point, please refer them to this post. A more detailed explanation follows. In standard mathematics we take classical logic and set theory as a foundation: $\text{logic} + \text{sets}$ On top of this we build…
• ## IMA Journal of Applied Mathematics - current issue

• ### Dynamics of a slowly evaporating solvent-polymer mixture with a deformable upper surface

23 Jul 2014 | 8:44 am
This paper examines how surface deformations affect the stability of a slowly evaporating solvent–polymer mixture. The destabilizing effect of surface-tension variations arising from evaporation-induced concentration gradients and the counteracting influence of mean gravity and surface tension are incorporated into the mathematical model. A linear stability analysis that takes advantage of the separation between the characteristic time scales of the slowly evolving base state and the perturbations is carried out in combination with numerical solutions of the linearized system. It is…
• ### Foreward to Special Issue for winners of the 2nd IMA Lighthill-Thwaites Prize

23 Jul 2014 | 8:44 am
• ### The effect of membrane-regulated actin polymerization on a two-phase flow model for cell motility

23 Jul 2014 | 8:44 am
Two-phase flow models have been widely used to model cell motility and we have previously demonstrated that even the simplest, stripped-down, 1D model displays many observed features of cell motility [Kimpton, L.S., Whiteley, J.P., Waters, S.L., King, J.R. & Oliver, J.M. (2013) Multiple travelling-wave solutions in a minimal model for cell motility. Math. Med. Biol. 30, 241—272]. In this paper, we address a limitation of the previous model.We show that the two-phase flow framework can exhibit travelling-wave solutions with biologically plausible actin network profiles in two simple…
• ### On air cushioning in axisymmetric impacts

23 Jul 2014 | 8:44 am
This paper extends the work of Moore et al. (2013, Air-cushioning in impact problems. IMA J. Appl. Math., 78, 818–838) by using a displacement potential formulation to analyse the post-impact effect of an air-cushioning layer on the normal impact of an axisymmetric rigid body on a liquid half-space. The liquid and the air are both incompressible, inviscid and their flows are irrotational. The leading-order problem is reduced to a pair of Titchmarsh integral equations and a far-field analysis shows that the method applies for impactors whose elevation grows at least as fast as a…
• ### Three mechanical models for blebbing and multi-blebbing

23 Jul 2014 | 8:44 am
Membrane protrusions known as blebs play important roles in many cellular phenomena. Here we present three mathematical models of the bleb formation, which use biological insights to produce phenotypically accurate pressure-driven expansions. First, we introduce a recently suggested solid mechanics framework that is able to create blebs through stretching the membrane. This framework is then extended to include reference state reconfigurations, which models membrane growth. Finally, the stretching and reconfiguring mechanical models are compared with a much simpler geometrically constrained…
• ## eon

• ### Millenium Bookball

19 Jul 2014 | 9:54 pm
is a pretty cool mathematical sculpture by George Hart. Gone with the Wind, Charlie and the Chocolate Factory, The Cat in the Hat, Green Eggs and Ham. What is not to like? Speaking of which, I still cannot believe that it was only because of my son who is now four that I read Dr Seuss for the first time in my life. Growing up with parents who do not speak English, I only started reading English books in Primary School. I still remember the joy when I did well in school examinations and the prize was to go to the school hall and select one free book for keeps.
• ### On practice

19 Jul 2014 | 9:56 am
I’m sure I am interpreting this in a context different from Vygotsky who was quoting Lenin Man’s practice, repeated a billion times anchors the figure of logic in his consciousness.
• ### Math videos

9 Jul 2014 | 1:08 am
“Speaker, I’d like to talk about twin prime numbers …” goes McNerney in the US Congress. This took place on 11 Feb 2014. More details may be found here. There is still hope in politics afterall. I would love to see the day when mathematics is discussed in our parliament. I’ve longed known about the discussion on the Monty Hall problem in the movie 21. But it was preceded by a short take on Newton’s or Newton-Raphson method. See the clip here at Mathematics in Movies site.
• ### Prime Mystery

30 Jun 2014 | 3:27 pm
A nice puzzle from Aziz Inan on plus.maths.org The number N represents the first 6 digits of a special number. N consists of three prime numbers put side by side. These three prime numbers come xth, yth and zth on the list of primes, where x, y and z are themselves three consecutive primes (for example, x, y and z could be 3, 5 and 7, in which case we’d be looking at the third, fifth and seventh prime numbers). In addition, if N is split in the middle into two separate numbers, the prime factors of the left part of N add up to its right part. What is N? And what is the special numbers…
• ### 10 surprising things about our brains

29 Jun 2014 | 7:28 pm
an article from huffington. Worth the read.

• ## WordPress Tag: Mathematics

• ### Mathematical and Intuitive Minds

28 Jul 2014 | 1:49 pm
The difference between the mathematical and the intuitive mind — In the one the principles are palpable, but removed from ordinary use; so that for want of habit it is difficult to turn one’s mind in that direction: but if one turns it thither ever so little, one sees the principles fully, and one must have a quite inaccurate mind who reasons wrongly from principles so plain that it is almost impossible they should escape notice. But in the intuitive mind the principles are found in common use, and are before the eyes of everybody. One has only to look, and no effort is…
• ### Euler Circuit in a Directed Graph

28 Jul 2014 | 11:19 am
Eulerian Path is a path in graph that visits every edge exactly once. Eulerian Circuit is an Eulerian Path which starts and ends on the same vertex. http://www.geeksforgeeks.org/euler-circuit-directed-graph/

28 Jul 2014 | 11:01 am
I have two quotes for y’all today! First, a brainy one from a person who hardly anyone has heard of, Shakuntala Devi, and  a second one (not so brainy, but kind of funny) from a person everyone in at least the USA has heard of, George W. Bush. I should first let you know though, math is and has always been one of my least favorite subjects to learn about. It’s not that I’m awful at it, I just really hate the idea of learning it and thinking about it. However, ever since watching the show “Cosmos” this year and working with the finance department at my job, I have a whole…
• ### World Peace: Reason and Probability

28 Jul 2014 | 10:32 am
In his book Conjectures and Refutations, Karl Popper writes a statement that he thinks might characterize a reasonable individual: “I think I am right, but I may be wrong and you may be right, and in any case let us discuss it, for in this way we are likely to get nearer to a true understanding than if we each merely insist we are right.” Using this as a basis for what a reasonable individual might look like, I came up with a mathematical formula that illustrates the probability of world peace. GP = global population ri = reasonable individual (0-1, likelihood of an individual to…
• ### Why the Third-Pounder failed

28 Jul 2014 | 10:16 am
Because ‘Murica! One of the most vivid arithmetic failings displayed by Americans occurred in the early 1980s, when the A&W restaurant chain released a new hamburger to rival the McDonald’s Quarter Pounder. With a third-pound of beef, the A&W burger had more meat than the Quarter Pounder; in taste tests, customers preferred A&W’s burger. And it was less expensive. A lavish A&W television and radio marketing campaign cited these benefits. Yet instead of leaping at the great value, customers snubbed it. Only when the company held customer focus groups did it become…
• ## Mr. L's Math

• ### Polygonal Portal – Math and Art Power with GeoGebra

19 Jul 2014 | 11:54 am
Here’s a beautiful combination of math and art as well as demonstration of power and versatility of GeoGebra created by John Golden. He writes: “Thinking about ways to make a nice polygon spiral. This one is created by rotating and dilating the point that determines the first rotated polygon. (Using matrix exponentiation to rotate around the origin.) I love the spiral and 3-D effect of the transformation.” This is found on the GeoGebra Tube site. Here’s the direct link to John’s creation. NOTE: the double arrow at the upper right of the app resets the figure.
• ### Factoring Trinomials Using a Simple GeoGebra Applet

16 Jul 2014 | 10:36 am
Here’s a simple GeoGebra applet created using the “RandomBetween” function. You can refresh the screen with a new problem by using the double arrow in the upper right hand corner. Credit for this idea is due Steve Phelps from the Ohio GeoGebra Institute.
• ### Welcome to GeoGebraTube – a Common Core Technology Source

12 Jul 2014 | 1:08 pm
Here’s a quick intro to GeoGebraTube, a nice resource for Common Core teaching materials. GeoGebra is dynamic mathematics & science software for learning and teaching from elementary school to university level, which contains interactive geometry, algebra, statistics, and calculus abilities. There are, as of July, 2014, almost 100,000 free materials available. You can search by type of material, age, and language. After using the search function, you can select an entry, find some info about the sketch, see related sketches, and check out the author. If you find an author you…
• ### Voronoi Diagram Animation using GeoGebra

12 Jul 2014 | 11:58 am
Here’s a GeoGebra animation shared by Michael Borcherds on GeoGebraTube. It’s the type of visual imagery that stimulates students to want to be able to create the same thing, and asks them to uncover the coding steps behind the colorful patterns. You can stop/start the animation using the button at the lower left of the diagram, and relocate the starting (seed) points for more creativity. Reset the animation using the double arrow at the upper right. Enjoy!   For those looking for a little more of the mathematics behind this, here’s what Wikipedia has to say:…
• ### Here’s a great reason to use KenKen Puzzles

21 Nov 2013 | 4:42 pm
Here’s an edited version of an email I received today: This month, KenKen is being featured by the National Council of Teachers of Mathematics (NCTM) for its powerful attributes as a math learning tool. The NCTM’s December 2013 Mathematics Teacher Journal explains how KenKen puzzles allow students to explore basic operations, factors, parity, symmetry, algebraic thinking and various problem-solving strategies….all while keeping students interested and making math fun! Here’s the link to the seven page…
• ## MathNotations

• ### 45 Free SAT MATH Problems Tweeted in 21 Days! Enjoy!

29 Jul 2014 | 11:08 am
Just Follow me at twitter.com/dmarain Pls remember that all of these are based on actual SAT questions but are completely original and therefore subject to the Creative Commons License in sidebar. Essentially, use them for your students or for yourserlf but no commercial reproduction. Thanks... Perhaps my favorite is one I tweeted today: How many combos of 2 pizza toppings can be selected from 10 choices? Note: S,P is same as P,S; P,P is allowed (A)100 (B)90 (C)55 (D)54 (E)45 Respond with answer and solution via Contact Form near top of sidebar. VISIT ME DAILY ON TWITTER AT…
• ### THREE MORE SAT/COMMON CORE MATH PROBLEMS - FEED YOUR BRAIN!

21 Jul 2014 | 4:31 am
See them on my twitter feed at twitter.com/dmarain Did you submit your solution to the Geometry Puzzle from 7-20-14 via the Contact Form? VISIT ME DAILY ON TWITTER AT twitter.com/dmarain
• ### Best Geometry Puzzle Ever?

20 Jul 2014 | 7:02 am
• ### Dozens of Free Common Core, SAT Practice Problems

13 Jul 2014 | 11:00 am
I've been posting numerous challenge problems on Twitter of late, some with answers. You can see these at twitter.com/dmarain. Teachers: Feel free to use these to irritate your students. Students: Feel free to use these to irritate your teachers. Lol If you want to check your answers to these or you disagree with my answers or if you have any questions, use the new Contact Form in the sidebar. VISIT ME DAILY ON TWITTER AT twitter.com/dmarain
• ### And the winner is...

3 Jun 2014 | 9:03 am
Our winning submission for the June 1st Challenge came from KALEB LABBE Kaleb is a freshman at Fort Kent Community High School in Fort Kent, Maine. Congratulations Kaleb! Here are his answers: A)64 B)64, 16, 8, 4, 2 VISIT ME DAILY ON TWITTER AT twitter.com/dmarain

• ## Institute for Mathematics and Computer Science

• ### The Negative Effects of Homework Help

9 Jul 2014 | 10:00 pm
In The New York Times article, “But I Want to Do Your Homework,” author Judith Newman describes how she was driven, over her 12-year-old son’s objections, to help him ace his literature essay, only to earn a dismal grade. Her admission may sound familiar to many well-intentioned parents who believe they are doing what’s best for their child’s long-term success. Unfortunately, that’s not the case as Newman points out: “Sociologists at the University of Texas at Austin and Duke University assessed the effect of more than 60 kinds of parental involvement…
• ### Every Career Field Needs People Who Are Good At Math

11 Jun 2014 | 10:00 pm
If you’re not planning on pursuing a so-called STEM career, do you really need to be good at math? Yes, but not just for the often-stated reason that people encounter math regularly throughout their lives. Being able to handle everyday math is certainly important. For example: If you’ve been offered varying aid packages by different universities, which one makes the most financial sense for your family? If you’re deciding between leasing or buying a car, which is the best deal in the long run? While no one doubts that being better at money arithmetic would benefit…
• ### College Checklist: What Really Matters

14 May 2014 | 10:00 pm
It’s graduation time! The summer ritual of getting kids ready to send to college is around the corner. Mini-fridge, check. Shower caddy, check. Good study habits, hmmm. Surprisingly, developing good study habits before entering college is something that many talented children and their parents overlook. It’s easy to understand how this oversight happens when you realize that bright students often don’t need to study. That’s because their schoolwork isn’t challenging and requires minimal effort to receive high grades. Kids who are used to coasting like this hit…
• ### What Does It Mean to be Genuinely Good at Math?

17 Apr 2014 | 5:35 am
Have you seen the latest video of a young child reciting multiplication tables or the digits of pi? Or maybe you know a kid who has always gotten straight A’s. Pretty neat, but does it equate to being genuinely good at math? No. Bright students often do well in school with little or no effort. And an airtight memory facilitates excellent grades, especially when those grades depend on regurgitating information that’s already been provided. Being genuinely good at math is more about having a deep understanding of how and why things work. It also means being able to take that…
• ### From Public School to the Ivy League

19 Mar 2014 | 10:00 pm
The following excerpt is from the new book by Mandee Heller Adler, From Public School to the Ivy League: How to get into a top school without top dollar resources, which is available at Amazon.com. Ms. Adler is the founder and principal of International College Counselors, a Florida-based firm that provides expert strategies for admission to undergraduate colleges, graduate programs, business schools, law schools, medical schools, dental schools and other postgraduate schools. From Chapter 4: Writing Essays … ANSWERING THE QUIRKY QUESTIONS In recent years, a number of colleges have…
• ## Math-Blog

20 Jul 2014 | 7:01 pm
A group of researchers in philosophy, psychology and mathematics are requesting the assistance of the mathematical community by participating in a survey about mathematicians’ philosophical intuitions. The survey is available here: http://goo.gl/Gu5S4E. For the purposes of this survey, a mathematician is someone who holds an advanced academic degree in mathematics, teaches mathematics on a college or university level, uses advanced mathematics in the course of their work, or has published mathematical work in scholarly venues. Possibly related articles: Help us with your feedback by taking…
• ### Martin Fowler’s Design Stamina Hypothesis and Video Compression

14 Jul 2014 | 7:00 am
Martin Fowler’s Design Stamina Hypothesis expresses a widely held belief among practicing software engineers and other technical professionals that is also taught in computer science curricula. Basically, the idea is that “good software design,” a vaguely defined concept, fairly quickly pays for itself through faster, better, cheaper software development in the long run. Martin Fowler, Chief Scientist for ThoughtWorks and a noted writer on agile software development, software design and refactoring, encapsulates this concept in this “pseudo-graph”: The remarkable…
• ### Eugene Goostman, Teenaged AI, and the Definition of Number

16 Jun 2014 | 7:00 am
Eugene Goostman, an artificial intelligence program purporting to be a thirteen year old boy from the Ukraine, recently prompted a spate of breathless news articles reporting that an AI had finally and for the first time passed the famous Turing Test, fooling humans into thinking they were conversing with another human being and not with an AI program. This in turn prompted a number of critical responses, notably one by AI pioneer Ray Kurzweil who reported the following rather unconvincing exchange with Eugene: Question: How much is two plus two? Eugene: Now I’m sure that you are one of…
• ### The Mathematics of Terminators

27 May 2014 | 7:00 am
Can we make computers that think like or even better than human beings? If we can, will these computers make the world a better place as in Isaac Asimov’s I, Robot science-fiction stories or try to wipe us out as in James Cameron’s dystopian Terminator movie series? Classic Terminator Artificial intelligence (AI), currently rebranded as “Machine Learning” and “Deep Learning” (neural networks), is the attempt to use computers, sophisticated algorithms and mathematics to duplicate or exceed human intelligence. Artificial intelligence has had some successes:…
• ### The Refactoring

5 May 2014 | 7:00 am
• ### “The 12 Touchstones of Good Teaching” is Not So Good

29 May 2014 | 2:44 pm
I just found a list on Pinterest called “The 12 Touchstones of Good Teaching” based on the book of the same title. Of course I had to read it. And of course, I was incensed. One third of the list is good. One third is okay. And one third is deplorable. And all of it is centered on the wrong person. The Good Parts Apparently the list is broken up into three sections: Be Demanding Be Supportive Be Intentional The “Be Supportive” section is the good part. (Note: I’m discussing these out of order.) Item 5 – I engage student interest with every lesson. Item 6 – I interact…
• ### Confidence is More Important than Knowledge

19 May 2014 | 5:12 am
I tell fearful students all the time, “The difference between you and me is confidence.” I watched The Wizard of Oz this weekend and noticed the “math” that Scarecrow says when he gets his brains: What he says is that the sum of the square roots of any (any!) two sides of an isosceles triangle is equal to the square root of the other side: Utter nonsense. But amazingly confident! Knowledge is underrated. I’m not any better at math than anyone else. But what I do have is confidence in three areas: Confidence in my ability to think (about anything) Confidence…
• ### Summer Slide – The Big Myth

1 May 2014 | 12:58 pm
Every summer I get asked the same question, “How can I prevent the summer slide?” I’ve been rocking and rolling along with my same answers for a while: Engage your kids Talk about math in the summer activities Have fun with it And now I’m wondering about those answers. Actually, I’m wondering about the question. What is this “summer slide”? According to the National Summer Learning Association, “All young people experience learning losses when they do not engage in educational activities during the summer.” Wow! Okay, sounds terrible.
• ### Learning is Hard – And Scary!

26 Mar 2014 | 4:43 am
I’m learning how to write a business plan. And it’s hard! But I’m not just doing it to see if I can. There’s real meaning to learning this: I’m writing the business plan for Math Philanthropy, Inc. And when I’m done, I’ll submit it into a business plan competition. In this process, I’m discovering a few things: I’m scared that what I write will sound dumb. I worry that I’m not putting in enough. I wonder if I’m putting in too much. And what if everything I write is wrong? Sound familiar? If you’ve ever learned math (or…

• ## CSE Blog - quant, math, computer science puzzles

• ### 3D Tic Tac Toe Puzzle

10 Jul 2014 | 12:19 pm
Source: Shared by Alok Mittal (Cannan Partners) Problem: A 3x3 tic tac toe has 8 "winning lines" (3 horizontal, 3 vertical and 2 diagonals). How many "winning lines" does the 3x3x3 3D tictactoe have? There is a brute force solution, and then there is the aha! solution.

3 Jul 2014 | 8:16 am
Source: http://nrich.maths.org/ Problem: A mad robot sets off towards the North East on a journey from the point (0,0) in a coordinate system. It travels in stages by moving forward and then rotating on the spot. It follows these pseudo-code instructions: SUB JOURNEY     DISTANCE = 1000     WHILE (DISTANCE > 0.001)         MOVE DISTANCE         STOP         ROTATE(90, DEGREES, CLOCKWISE)         DISTANCE = DISTANCE / 2     END WHILE     EXPLODE END SUB Where does the…
• ### Social Network Friendship Paradox

1 Jul 2014 | 4:39 am
Problem / Observation: The friendship paradox is the phenomenon first observed by the sociologist Scott L. Feld in 1991 that most people have fewer friends than their friends have, on average. Prove it mathematically.
• ### Expected length of Last Straw - Breaking the back of a camel

16 Jun 2014 | 12:08 pm
Source: Puzzle Tweeter who took it from Mind your decisions Problem: A camel is loaded with straws until it's back breaks. Each straw has a weight uniformly distributed between 0 and 1, independent of other straws. The camel's back breaks as soon as the total weight of all the straws exceeds 1. Find the expected weight of the last straw that breaks the camel's back. Update (18th June 2014): Solution posted by me (Pratik Poddar) in comments
• ### Cards on a Square Turntable

16 Jun 2014 | 10:44 am
Source: Steve Miller's Math RiddlesProblem: A square has a quarter in each corner. You are blindfolded and must get all quarters to be heads up or all to be tails up. You will be told when you have done this. You may flip however many you want, then ask if you are done (this constitutes a turn). The square is then rotated/spun an undisclosed number of times. You then get another turn and so on…Is there a strategy that is guaranteed to work in a finite number of moves, and if so, what is that smallest number of moves you need to be 100% you’ll be able to have all heads up or all tails up?
• ## Math for all Grade blog

• ### Jul 29, First grade math worksheets

29 Jul 2014 | 2:06 am
• ### Jul 28, Compound Interest

28 Jul 2014 | 1:21 am
Interest calculated on principal is simple interest. Regularly adding interest to principal at agreed time periods is called compounding. The sum of principal and simple interest or compound interest is called Amount.
• ### Jul 17, Geometry Formulas

17 Jul 2014 | 2:35 am
Geometry Formulas
• ### Jul 17, Math Formulas

17 Jul 2014 | 1:35 am
Math Formulas
• ### Jul 17, Trigonometry Formulas

17 Jul 2014 | 1:17 am
Trigonometry Formulas