• Most Topular Stories

  • Another Common Core Rant - not a video...

    Dave Marain
    15 Apr 2014 | 5:31 am
    While I agree with the concerns of many parents that over-testing is damaging to children and subverts the purpose of education, I don't believe that the Common Core has set the bar too high, at least in math, my area of expertise. I know from direct experience with children that we can expect far more thinking of them than is commonly held. That is the Core Belief of my blog. The problem is that teachers have not received the necessary preparation and the testing has been rushed and lacking in quality control. We're trying to set the bar higher for children without raising the bar…
  • Re: Application of Quantum dot enabled displays

    Search for "math OR mathematics"
    20 Apr 2014 | 4:32 am
    If the costs can be brought down and such panels can be installed in the window pans then it will bring down the electricity costs and scarcity by some level.
  • 'Body hack' app by math researchers shortcuts jet-lag recovery

    Mathematics News -- ScienceDaily
    10 Apr 2014 | 4:46 pm
    A different kind of jet-lag mobile app released today by mathematicians reveals previously unknown shortcuts that can help travelers snap their internal clocks to new time zones as efficiently as possible.
  • A Month of Math, Magic and Mystery

    Scientific American - Math
    16 Apr 2014 | 8:52 am
    Haven't got the Math Awareness Month bug yet? Here are three teasers to get you started: 1. What read the same right side up and upside down, and combine mathematics, art, and language? -- Read more on
  • The 16th Century’s Line of Fire

    NYT > Mathematics
    7 Apr 2014 | 10:00 pm
    Mathematics would seem to be immune to ideology. But not always, as a look back at a controversy from the dawn of the modern era makes clear.
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    Mathematics News -- ScienceDaily

  • 'Body hack' app by math researchers shortcuts jet-lag recovery

    10 Apr 2014 | 4:46 pm
    A different kind of jet-lag mobile app released today by mathematicians reveals previously unknown shortcuts that can help travelers snap their internal clocks to new time zones as efficiently as possible.
  • Virus structure inspires novel understanding of onion-like carbon nanoparticles

    10 Apr 2014 | 9:22 am
    Symmetry is ubiquitous in the natural world. It occurs in gemstones and snowflakes and even in biology, an area typically associated with complexity and diversity. There are striking examples: the shapes of virus particles, such as those causing the common cold, are highly symmetrical and look like tiny footballs.
  • Should you trust your financial advisor? Pseudo-mathematics and financial charlatanism

    10 Apr 2014 | 7:30 am
    Your financial advisor calls you up to suggest a new investment scheme. Drawing on 20 years of data, he has set his computer to work on this question: If you had invested according to this scheme in the past, which portfolio would have been the best? His computer assembled thousands of such simulated portfolios and calculated for each one an industry-standard measure of return on risk. Out of this gargantuan calculation, your advisor has chosen the optimal portfolio. After briefly reminding you of the oft-repeated slogan that "past performance is not an indicator of future results," the…
  • Technical tests of biodiversity: When physicists play with genetics of populations

    9 Apr 2014 | 6:39 am
    The effect of migration on biodiversity (intended as the coexistence of different genetic traits) is an open question: does migration increase or decrease the genetic variability of populations? Or is the relationship more complex than that? A team of physicists has developed and analyzed a model that simulates the effect of migration on the genetic biodiversity of populations, and discovered that the effect is all but trivial.
  • Method offers potential for understanding anti-bacterial resistance

    8 Apr 2014 | 4:48 am
    Biologists could gain a deeper understanding about how species have evolved -- and even find ways to address antibiotic resistance -- using tools that were recently developed. By basing their methods on mathematical models and Bayesian analysis, the researchers succeeded in producing tools for biologists who are interested in jumping genes and the traits they carry with them.
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    Wild About Math!

  • Visually stunning math concepts which are easy to explain

    10 Apr 2014 | 9:01 am
    Math StackExchange has a great list of "visually stunning math concepts which are easy to explain."
  • Tim Chartier – Inspired by Math #34

    6 Apr 2014 | 10:35 pm
    My favorite kind of Math challenges are those that children can understand and professional mathematicians can't solve easily (or at all.) Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing is a brand new book from Princeton University Press that has a great collection of fun problems that kids (middle school and above) and their parents can work on together. Author Tim Chartier does a fantastic job of weaving some wonderful stories into his sharing of a number of challenges that are either original or new spins on old problems. And, many (all?) of the puzzles in…
  • Chuck Adler – Inspired by Math #33

    13 Feb 2014 | 6:27 pm
    I've admitted before that Physics and I have never gotten along. But, science fiction is something I enjoy. So, when Princeton University Press sent me a copy of Physics Professor Chuck Adler's new book "Wizards, Aliens, and Starships," I was intrigued enough that I wanted to interview the author. This interview rambled, but in a good way. Chuck is a great guest, he's passionate about physics and math as well as fantasy and science fiction. We flowed through a number of subjects and had a grand time. Enjoy! About Chuck Adler Chuck Adler grew up in the DC suburbs, and went to a very good…
  • Martin Gardner undiluted

    22 Nov 2013 | 11:54 am
    Princeton University Press recently published "Undiluted Hocus-Pocus: The Autobiography of Martin Gardner." I've not reviewed the book since these days I pretty much only interview authors and living authors at that. So, no review from me, but I highly recommend Shecky's review and Shecky's first impressions at Math Tango. What inspired to blog this afternoon was an email I received from Andrew S. DeSio, Director of Publicity for Princeton University Press. Andrew has asked me to help spread the word that Martin Gardner really did write his own autobiography. Here's an excerpt from Andrew's…
  • Colm Mulcahy – Inspired by Math #32

    21 Sep 2013 | 10:56 am
    I had the pleasure of interviewing mathematician and mathematical card magic innovator Colm Mulcahy. Dr. Mulcahy just published a book, Mathematical Card Magic: Fifty-Two New Effects. We spent a delightful hour discussing his book, his love of math and magic, and the inspiration behind writing the book. Plus, Dr. Mulcahy shares a few challenges listeners might enjoy chewing on, sprinkled throughout the interview. And, we discuss Martin Gardner, who Colm Mulcahy knew for the last decade of his life and met with several times. You may also enjoy Shecky's text interview with Colm Mulcahy at Math…
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    Loren on the Art of MATLAB

  • Debunking Bad News Analysis with MATLAB

    Loren Shure
    7 Apr 2014 | 8:28 am
    With spring comes the tax filing deadline. This post is also about taxes. I'd like to introduce this week's guest blogger, Toshi Takeuchi. Toshi analyzes web data and runs online ad campaigns here at MathWorks.Hi, I am Toshi. I am a big fan of Nate Silver who made analyzing data very cool and mainstream. Because I analyze data a lot, it bugs me when I see questionable analyses passed around in the news media.So when I saw this CNBC post on Google+, my “bogus data analysis” radar started sending high alerts.This map shows you the ranking of states based on average tax amount,…
  • MATLAB Virtual Conference 2014

    Loren Shure
    17 Mar 2014 | 10:47 am
    We are hosting another worldwide conference this month, on-line. Its coming Marcn 26, and has special tracks includingDiscover MATLAB and SimulinkFind Out What's NewSee What Industry Experts Are DoingExplore MATLAB and Simulink in AcademiaContentsRegisterTimezonesKeynoteHope to See You ThereRegisterYou can register on-line here.TimezonesThere are two timezones for the conference, one for the Americas (with four sessions in Spanish), and one for India/Europe.KeynotePlease be sure to attend Roy Lurie's keynote entitled "Embracing Technical Computing Trends with MATLAB: Accelerating the Pace of…
  • Integer Programming and Hyper Sudoku

    Loren Shure
    14 Mar 2014 | 9:53 am
    I'd like to introduce this week's guest blogger Alan Weiss. Alan writes documentation for mathematical toolboxes here at MathWorks.Hi, folks. While I have not written a blog post for Loren before, if you use Optimization Toolbox™ or Global Optimization Toolbox then you might have read my work.I am excited to describe how to use a new solver. Beginning with Release 2014a, Optimization Toolbox has mixed-integer linear programming. The intlinprog solver attempts to solve problems with linear objective functions, linear constraints, and (this is the new part) the constraint that some…
  • Arithmetic Associativity – Not So Fast

    Loren Shure
    26 Feb 2014 | 7:07 am
    Arithmetic is associative, right? Well, in the world of paper and pencil, where you can often do calculations exactly, that can be true. However, in the computing world, where real numbers can't always be represented exactly because of working with finite precision datatypes, it turns out that you can't depend on the arithmetic to behave the way you were taught in grade school.ContentsLet's Do Some MathLet's Try Another ExampleHave You Rewritten Expressions to Get Better Accuracy?Let's Do Some MathSuppose I want to check the following:$$ \sqrt {2} = 2/\sqrt {2} $$I can do this analytically…
  • Double Integration in MATLAB – Methods and Handling Discontinuities, Singularities, and More

    Loren Shure
    12 Feb 2014 | 7:06 am
    In our recent post, Mike Hosea and I talked about adjusting both the absolute and relative tolerances for getting more accurate results when calculating a double integral. Today we'd like to talk about choosing the method of integration as well as which order to choose for the first dimension (direction) of integration.ContentsSet the StageChanging the Order of IntegrationSingularitiesCan You Take Advantage of these New Integration Routines?Set the Stageintegral2 has, at present, two different integration methods, 'tiled' and 'iterated', not counting the 'auto' method that chooses between…
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    Homeschool Math Blog

  • Giveaway - Math Mammoth!

    15 Apr 2014 | 7:50 am
    It is time for a giveaway for my own products (Math Mammoth)! 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…
  • Fraction lessons updated

    2 Apr 2014 | 11:18 am
    These fraction lessons on my site have been updated! They are complete lessons with varying exercises and word problems, and give you a great preview to my books Math Mammoth Fractions 1 and Math Mammoth Fractions 2.Understanding fractionsA fractional part of group Mixed numbersFractions to mixed numbers and vv.Adding like fractionsEquivalent fractionsAdding unlike fractions 1Adding unlike fractions 2: Finding the common denominatorAdding mixed numbersSubtracting mixed numbersSubtracting mixed numbers 2Measuring in inchesComparing fractions Simplifying fractionsMultiply fractions by…
  • Giveaways at Educents

    1 Apr 2014 | 1:26 pm
    Educents is celebrating their 1-year anniversary... with a SLEW of giveaways! You will want to see this -- dozens on giveaways on the same page (including one for Math Mammoth)!
  • Grading tests and math homework

    31 Mar 2014 | 7:27 am
    A few days ago I got a question from Jennifer concerning GRADING a child's math work, and I think it's a good question! How do recommend that parents grade when using Math Mammoth? Should I score every assignment? Or just tests? Before we pulled our children out of public school, only tests were being counted for their grade. What do you recommend? Thanks Jennifer I don't actually give any exact grading recommendations regarding Math Mammoth but leave it up to parents/teachers. I do include a grading rubric for the tests, but that's all.Personally, I feel that grading needs to be such that it…
  • The missing $1 puzzle and more

    27 Mar 2014 | 4:56 pm
    Have you ever encountered this well-known puzzle about the missing $1? Three people rent a room at $30. They pay $10 each and go up to the room. The owner realized he charged too much and it was only supposed to be $25. He sends the bell hop up with the $5. Each of the people keeps $1 and they give the bellhop $2 as they can't share it. So now each person has paid $9 for the room (total $27) and the bell hop has $2... where is the other $1??? See the solution to this and find many more puzzles on my new page of favorite challenging…
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  • Easter Egg Hunt

    17 Apr 2014 | 11:00 am
    Are you read for a quadratic equation word problem that relates to Easter? I can't think of anything more entertaining to do this Easter that links the holiday with Math! Jennifer Ledwith provides us with this entertaining set of questions for a fun filled 'mathy' Easter.  See the exercise questions here. (All questions are supported with answers.)
  • Measures of Central Tendancy

    9 Apr 2014 | 8:48 am
    This concept is taught as early as the 3rd grade and refers to the law of averages. When the term average is used, most of us mean the 'mean' average. However, there are other averages which are the median and the mode.  If you are looking for a 101 on the Mean, the Median and the Mode, you'll find a quick overview here....Read Full Post
  • Beginning of Base 10

    5 Apr 2014 | 5:52 am
    Base 10 concepts begin in Kindergarten. At this early age, base 10 refers to the ability to understand that in a number like 12, the one represents 1 ten or 10 ones, it no longer is the same as 1 when 1 is in isolation. It is also showing the ability to count onward when 10 is recognized, looking at a group of 10 and automatically knowing to count up to determine how many there are when there is a group of 10 and 5 more or 6 more....Read Full Post
  • Best Graduate Level Math Programs

    2 Apr 2014 | 11:43 am
    Are you ready to move on to a graduate degree in math? Whether you're looking to pursue graduate level in Algebra, Number Theory, Algebraic Geometry, Analysis, Applied Math, Discrete Math, Topology, Logic or Geometry, you might just find this list of the top schools to pursue graduate level math to be quite helpful. You'll find score levels and useful information to help you guide your decision....Read Full Post
  • Algebraic Reasoning in Kindergarten?

    30 Mar 2014 | 1:53 am
    When you think of algebraic reasoning, I'm sure that kindergarten is the last thing on your mind. However, algebraic reasoning occurs as early as kindergarten and is certainly one of the benchmarks in the Common Core Standards. This week, I've written an article about how to address subtraction to five, addition to 10 and what it means to reason algebraically in kindergarten. The strategies in this article address K.0A in the Common Core Standards....Read Full Post
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    Let's Play Math!

  • Reblog: Putting Bill Gates in Proportion

    Denise Gaskins
    17 Apr 2014 | 4:34 pm
    [Feature photo above by] Here’s a blast from the Let’s Play Math! blog archives: Seven years ago, one of my math club students was preparing for a speech contest. His mother emailed me to check some figures, which led to a couple of blog posts on solving proportion problems. I hope you enjoy… Putting Bill Gates in Proportion and Bill Gates Proportions II Putting Bill Gates in Proportion A friend gave me permission to turn our email discussion into an article… Can you help us figure out how to figure out this problem? I think we have all the information we…
  • Do You Blog About Math?

    Denise Gaskins
    14 Apr 2014 | 1:50 pm
    by Mike Licht, It’s carnival time again. Activities, games, lessons, hands-on fun — if you’ve written a blog post about math, we’d love to have you join our Math Teachers at Play (MTaP) math education blog carnival. Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up through first-year 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. Browse all the past editions of the Math Teachers at Play blog…
  • Reblog: The Handshake Problem

    Denise Gaskins
    3 Apr 2014 | 5:49 am
    [Feature photo above by Tobias Wolter (CC-BY-SA-3.0) via Wikimedia Commons.] Here’s a blast from the Let’s Play Math! blog archives: Seven years ago, our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned. I threatened to hand out a ten question pop quiz on integer arithmetic, but instead my pre-algebra students voted to perform a skit. I hope you enjoy… Skit: The Handshake Problem If seven people meet at a party, and each person shakes the hand of everyone else exactly once, how many handshakes are there in…
  • Reblog: In Honor of the Standardized Testing Season

    Denise Gaskins
    24 Mar 2014 | 11:16 am
    [Feature photo above by Alberto G. Photo right by Renato Ganoza. Both (CC-BY-SA-2.0) via flickr.] Here’s a blast from the Let’s Play Math! blog archives: Quotations and comments about the perils of standardized testing, now part of my book Let’s Play Math. I hope you enjoy… In Honor of the Standardized Testing Season The school experience makes a tremendous difference in a child’s learning. Which of the following students would you rather be? I continued to do arithmetic with my father, passing proudly through fractions to decimals. I eventually arrived at the…
  • Math Teachers at Play #72 via Christy’s Houseful of Chaos

    Denise Gaskins
    20 Mar 2014 | 9:15 am
    [Feature photo above is 72 Pencils by fdecomite via flickr.] Math Teachers at Play is a traveling blog carnival. It moves around from month to month, and the March edition is now posted at Christy’s Houseful of Chaos. What a fun list of math posts to browse! This is the 72nd Edition of the Math Teachers at Play (MTaP) blog carnival! The number 72 is a Harshad number in number bases from binary up to but excluding base 13. Harshad numbers are numbers that are divisible by the sum of their numbers. They are base-dependant. In binary 72 is expressed 1001000. Add the digits together to get…
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  • 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…
  • Decision time: MacPorts vs Homebrew vs Fink

    7 Mar 2014 | 8:12 pm
    My work macbook pro recently crapped out on me during an update of the OS (apparently something has a tendency to go wrong with the video card or its driver or something similar during this particular update for this particular model … sigh) so I’ve had the joy of reinstalling my personal ecosystem of software again. One of the crucial decisions for me is whether to use MacPorts, HomeBrew, or Fink to allow me to manage the installation of non-trivial Unix packages. This post is really just to remind myself that at this go-round, I chose MacPorts because of these posts.
  • Adagrad and projections onto ellipsoids

    6 Feb 2014 | 10:16 pm
    ((Caveat! I am not sure the manipulations done in this post are correct, but the gist is certainly there.)) One of my favorite optimization techniques is Adagrad, a first-order technique that approximates the Hessian by using all the gradients up to that point. It calls for updates of the form: \[ x_{t+1} = \Pi_{\mathcal{X}}^{G_t^{1/2}} (x_t - \eta G_{t}^{-1/2} g_t), \] or more practically for high-dimensional problems, \[ x_{t+1} = \Pi_{\mathcal{X}}^{\text{diag}(G_t)^{1/2}} (x_t - \eta \text{diag}(G_{t})^{-1/2} g_t). \] Here, \(g_t\) denotes the gradient at step \(t\), \(\eta\) is a fixed…
  • Back of the envelope calculations of how fast your computer can do linear algebra operations

    23 Jan 2014 | 3:28 pm
    Let’s talk about CPU speed, practically. By practically, I mean, how fast can your CPU do linear algebra operations. And by linear algebra operations, I mean matrix-matrix multiplies. First, you need to calculate how many FLOPS your computer can do. The following formula comes in handy: \[ \text{nFLOPS} = \text{cores} \cdot \frac{\text{clock cycles}}{\text{second}} \cdot \frac{\text{FLOPS}}{\text{cycle}}. \] You probably already know the number of cores in your computer, and the number of clock cyles. The interesting thing here is the number of FLOPS per cycle: this depends on the…
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    Computational Complexity

  • Announcements

    18 Apr 2014 | 8:25 am
    Time for a short rundown of announcements. STOC will be held May 31-June 3 in New York City. Early registration and hotel deadline is April 30. Student travel support requests due by this Monday. The newly renamed ACM Conference on Economics and Computation (EC '14) will be held in Palo Alto June 8-12. Early registration deadline is May 15. Hotel deadline is May 19th but the organizers suggest booking early because Stanford graduation is June 13. The Conference on Computational Complexity will be held June 11-13 in Vancouver. Local arrangements information will be posted when available.
  • Should you reveal a P = NP algorithm?

    17 Apr 2014 | 5:13 am
    A reader asks What would you do if you could prove that P=NP with a time-complexity of n2 or better... moreover, would you publish it?   There are all these statements of the good that could come of it. But how would the government react in its present state? Would it ever see the light of day? How would a person be treated if they just gave it away on the internet? Could a person be labeled a threat to national security for giving it away?  I consider this a completely hypothetical and unlikely scenario. If you think this applies to you, make sure you truly have a working…
  • Factorization in coNP- in other domains?

    13 Apr 2014 | 7:40 pm
    I had on an exam in my grad complexity course to show that the following set is in coNP FACT = { (n,m) : there is a factor y of n with 2 \le y \le m } The answer I was looking for was to write FACTbar (the complement) as FACTbar = { (n,m) | (\exists p_1,...,p_L) where L \le log n for all i \le L we have m < p_i \le n and p_i is prime (the p_i are not necc distinct) n =p_1 p_2 ... p_L } INTUITION: Find the unique factorization and note that the none of the primes are < m To prove this work you seem to need to use the Unique Factorization theorem and you need that PRIMES is in NP (the…
  • Favorite Theorems: Extended Formulations

    9 Apr 2014 | 2:24 pm
    The first couple of favorite theorems took place at the beginning of the last decade, but recent years have brought exciting results as well, such as the limitations of using linear programs to solve hard problems. Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds by Samuel Fiorini, Serge Massar, Sebastian Pokutta, Hans Raj Tiwary and Ronald de Wolf, STOC 2012 (ArXiv). The matching polytope has exponential extension complexity by Thomas Rothvoß. To appear in STOC 2014. It all started with a paper by E.R. "Ted" Swart (the Deolalikar…
  • How free is Randomness?

    7 Apr 2014 | 5:50 am
    Matthew Green had a great post on the topic how do you know a random number generator is working.  Gee, I just look at the sequence and see if it LOOKS random. Probably not the best idea. Actually people often found pattersn where there aren't any. Reminds me of a the following apocryphal story which would have to have taken place before everyone had a computer: A teacher assigns the class a HW assignment to flip a coin 600 times and record H's and T's. He warns them that if they just try to come up with a random sequence without flipping he will know. Sure enough, a few of them had…
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    Natural Blogarithms

  • Review Activity Ideas

    Scott Franklin
    29 Mar 2014 | 12:11 pm
    During the Teacher Quality Grant class today, we began preparing for the Post-Test that will take place in two weeks. Class participants shared a variety of ways that they conduct reviews in their junior high and high school classrooms. This group of teachers shares some very interesting games that they have used to engage students and get them more excited about math. Here are the ideas they shared: Jeopardy®: This is a classic game where students compete for points by selecting a category and point value. The question (or answer) is revealed and they are given the opportunity to buzz in…
  • How to Insert Equation Numbers in Word 2010

    Scott Franklin
    3 Mar 2014 | 10:46 am
    How to Insert Equation Numbers in Word 2010.  In most cases, I’m using LaTEX to typeset my math docs but when I am in a hurry or I’m having my students write up reports, I need to use Word.  Here’s a quick demo for adding equation numbers in word that auto-number and can be referenced in the text.
  • Graphs of Sine and Cosine Functions

    Scott Franklin
    3 Mar 2014 | 7:52 am
    I just posted a new video to the Trigonometry Lecture Series.  This is the 11th in the series. In this video, I cover how to identify properties of sine and cosine graphs, determine the amplitude and period of sinusoidal functions, graph the sinusoidal functions using key points, and find an equation for a sinusoidal graph. View on YouTube
  • How to Insert an Excel Chart into a Blackboard Discussion Board

    Scott Franklin
    2 Mar 2014 | 8:44 pm
  • New Videos in the Trigonometry Video Series

    Scott Franklin
    10 Feb 2014 | 5:46 pm
    Just finished uploading five new videos to my online video lecture series in Trigonometry.  Here’s the first and a link to the playlist on YouTube: Link to Full Playlist Newly added: Lecture 6: Measuring Angles in Radians Lecture 7: Definition of Trigonometric Functions Lecture 8: Trig Values of Special Families of Angles Lecture 9: Properties of Trig Functions Lecture 10: Basic Identities of Trig Functions
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  • “Gods” make Comeback at Toyota

    10 Apr 2014 | 8:30 pm
    is the headline of this bloomberg piece that reports the strange phenomena that human beings are replacing robots in the manufacturing lines. The point is that by automating some of these production process, much of the skill learnt by the human worker is lost. Without these knowledge, the humans cannot innovate and improve on the current process. I see a close parallel between this and how students are losing their mathematical/computational ability because they are doing all their calculations on a calculator. Sure, if all the mathematics that you will do in future is to add some numbers on…
  • Come Together

    8 Apr 2014 | 6:22 pm
    is not the beatles song but the title of episode 16 of a tv program called discover science. I happened to catch it on local tv and the combination of quirky Japanese humour and the clever introduction to mathematics and science caught my attention. A preview of the episode is available at the above link but you need to watch the whole episode to find the link to parabolas.
  • Mathematics and poetry

    4 Apr 2014 | 2:59 pm
    A nice article by Ornes on slate and a paper by Glaz. My favourites has to be the Fermat Last Theorem Poetry Challenge which I have read about previously elsewhere. Here’s one entry by E. Howe, H. Lenstra, D. Moulton: “My butter, garcon, is writ large in!” a diner was heard to be chargin’. “I HAD to write there,” exclaimed waiter Pierre, “I couldn’t find room in the margarine.”
  • Maths & Fashion

    20 Mar 2014 | 3:21 pm
    That headline caught my eye and earned the newspaper article a more detailed look. It’s about a sub brand from Issey Miyake called 132.5, which apparently stands for 1 piece of material which forms a 3d dress but yet can be folded flat into 2d. The meaning of the .5 wasn’t that clear to me. Fashion’s not my thing but this is certainly cool enough to merit a link.
  • Advice to Young Mathematicians

    27 Jan 2014 | 8:25 pm
    The Princeton Companion to Mathematics contains a short section of sound advice to young mathematicans by Sir Micheal Atiyah and others. It is certainly worth reading. The section can be downloaded from here.
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    mathematics « Tag Feed

  • Missing Math: A Number Mystery

    Shirley Duke
    17 Apr 2014 | 6:00 pm
    Missing math : a number mystery MATHEMATICS (K-2) Missing Math: A Number Mystery by Loreen Leedy ATOS 2.7 460L Essential Question: Why are numbers important? Unit Summary: Students will examine the essential question, “Why are numbers important?” They will work in groups to locate numbers from five books from an assigned section of the library based on the Dewey Decimal System. The groups will find books holding specified number criteria and will fill out a chart to show the numbers they have located. They will use their numbers in number sentences to show greater and less than…
  • Arthur Benjamin: Lightning calculation and other "Mathemagic"

    17 Apr 2014 | 5:17 pm
    Speaker Arthur Benjamin is an American mathematician known for his stage and TV shows in mathemagic – showing off his skill in rapidly performing calculations with large numbers. He has published multiple books to teach these skills to others. Summary Arthur combines his love of magic and maths to do some extremely quick calculations – squaring and multiplying random 2-3 digit numbers instantly as they are called out by the audience. 4 digit numbers took a little longer, but still within a few seconds. His next ‘trick’ was to ask the audience to multiply a known 4…
  • In what manner do mathematical objects exist?

    17 Apr 2014 | 3:45 pm
    I mean it cant really be said they don’t exist,  as many of our models of the physical world use them, unless of course we take a uselessly literal and physical interpretation of existence. But in what sense do things like parabolas and circles and functions and cones and such actually exist? One interpretation is that of plato; the idea that mathematics exists on some higher plane which we ‘dip into’ now and then so as to better inform our perceptions of the physical world. However, this raises more questions than it answers; where is this plane of existence inhabited…
  • Math Part Two - Palindromes and Passwords

    the author
    17 Apr 2014 | 2:55 pm
    I’m a Math Nerd. I confess. I like numbers. It’s a weakness. I liked Math so much that I
  • Logic

    17 Apr 2014 | 1:01 pm
    In the true fashion of my exploratory spirit, I’ve decided to give the proper definition of ‘Logic’ a little try. Grab pen and paper, and here we go. Etymology First, what I always like to do is to look up the word itself. Any object that we occupy ourselves with that has a name, will have some origins in how our forefathers may have encountered it. Therefore, the etymologic description of an object’s name can already hint us towards what it may describe. – In the case of ‘Logic’, I happen to know by rote that it ultimately derives from the Old Greek…
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  • A Common Core Alg Activity Using Desmos - Piecewise Linear Functions and Squares

    Dave Marain
    20 Apr 2014 | 4:29 am
     This is my first attempt to use Desmos, the outstanding free online graphing calculator (and a free iPad app). I'm sure many of you have been utilizing this powerful resource. There are already many available teacher samples you can use. Let me know if you can view the graph (you may have to adjust the window slightly). More importantly, what do you think of the activity and do you see its potential for deepening understanding of algebra? If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar. 175 problems divided…
  • Another Common Core Rant - not a video...

    Dave Marain
    15 Apr 2014 | 5:31 am
    While I agree with the concerns of many parents that over-testing is damaging to children and subverts the purpose of education, I don't believe that the Common Core has set the bar too high, at least in math, my area of expertise. I know from direct experience with children that we can expect far more thinking of them than is commonly held. That is the Core Belief of my blog. The problem is that teachers have not received the necessary preparation and the testing has been rushed and lacking in quality control. We're trying to set the bar higher for children without raising the bar…
  • Developing Fraction Sense Using Egyptian Fractions

    Dave Marain
    5 Apr 2014 | 12:01 pm
    This MathCast describes a procedure for writing proper fractions as a sum of unit fractions, e.g., 5/6=1/2+1/3. This exploration is appropriate for Gr5 on up.A simplified form of the Greedy Algorithm.Watch "Developing Fraction Sense Using Egyptian Fractions" on YouTube: I'm experimenting with embedding these MathCasts directly into my blog post, however, the audio may not come out right. May work on your computer but not your tablets or smartphones. Please let me know. If there is a problem you can just click on the link to YouTube. VISIT ME DAILY ON TWITTER AT…
  • A Data-Based Percent Problem for the New SAT and Common Core

    Dave Marain
    30 Mar 2014 | 3:07 pm
    The MathCast below is a more sophisticated % problem which requires processing several pieces of data expressed in percent form. Students have to make sense of the information and  develop a model to represent the data. Both a tree model and a table/spreadsheet approach are demonstrated. These are the kinds of data-based applications which will become a central theme of the newer assessments from PARCC, SBAC and the College Board. Sorry, you'll have to watch the video to see the problem but I'll give you a glimpse: 70% of the left-handed students surveyed were boys... Watch…
  • 40% of 9th graders play sports...Math Challenges for the Old/New SAT and the Common Core

    Dave Marain
    24 Mar 2014 | 5:07 am
    David Coleman of the College Board has stated that ratios, percents, etc., will be an important focus of the new SAT, particularly in an applied setting.The MathCast below demonstrates a classic medium-hard percent word problem which should continue on all of our "new" assessments. Watch "40% of the 9th grade... Percents,New SAT and…" on YouTube-40% of the 9th grade... Percents, the New SAT and…: I encourage all my readers to offer constructive criticism re both the content and the technology of these videos and suggest…
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  • Markham Winter of 2014

    1 Apr 2014 | 4:30 am
    Winter has finally ended in Markham where I live and it has seemed a very long and cold season this year. I decided to take a look at the weather data from Environment Canada and see whether my impression is supported by the data. The result is the graphic below. Click on it to see a larger version. Yes, 2014 was the coldest winter in Markham since 1994. We had an average temperature during the winter of -8.2 C this year and in 1994 it was -9.2 C. Both last year and especially 2012 were warmer than usual so it likely felt that much worse in comparison. We also had the 4th most snow in the…
  • Toronto Visible Minorities

    27 Sep 2013 | 4:30 am
    Toronto is the most multicultural city in the world. According to the 2011 National Household Survey, 46% of the population were foreign-born immigrants and 47% are members of a visible minority. (ref) These immigrants come from a wide variety of places across the globe and their diversity makes the city a truly remarkable place. I have created a Dot Map that shows a single point for every person in the Toronto area, coloured by visible minority status. There are 5,700,628 in all and they are positioned at their place of residence and coloured based on the information from the 2011 census and…
  • Toronto 311 Visualization

    6 Sep 2013 | 4:20 am
    The calls people make into the 311 service line in Toronto give an interesting glimpse into the pulse of the city. The City of Toronto makes this data available through their Open Data initiative. I did some analysis and design work with it to produce a visualization for illuminating time-based patterns during 2012. The visualization is a set of small multiple calendar heatmaps, one for each data series. The one shown above is for reports about 'long grass and weeds'. I was inspired to use this visual form by this example: Vehicles involved in fatal crashes by Nathan Yau. I experimented with…
  • Visual Book Selector

    8 May 2013 | 5:00 am
    One common pattern I see in many interactive applications is to support a person who is selecting a few items from some larger set. Often these items have various characteristics that the person wants to use in some way to guide their selection process. The characteristics can be numeric quantities, dates, categories, or names of things. Showing all the items in a list and allowing the person to sort by one of the attributes is often a decent default solution. In other cases it's more useful to consider multiple attributes at a time during the selection process. Maybe you want items that are…
  • Star Wars Movie Fingerprints

    27 Mar 2013 | 4:35 am
    Recently YouTube had a video that showed all six Star Wars movies at once. They were placed in a 2 by 3 matrix and had an audio track of all the movies superimposed. It was an interesting experiment that has since been removed based on copyright grounds. Before it was removed I was able to do some simple analysis on the video and extract some details of the individual episodes of the Star Wars series. Basically, I produced something very similar to a classic work called Cinema Redux™ by Brendan Dawes, done in 2004. Each individual movie in the series was reduced to a collection of small…
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    Institute for Mathematics and Computer Science

  • What Does It Mean to be Genuinely Good at Math?

    IMACS Staff Writer
    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

    IMACS Staff Writer
    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 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…
  • IMACS Math Academy for Broward County Middle School Students

    IMACS Staff Writer
    19 Feb 2014 | 10:00 pm
    The IMACS Math Academy is an intensive one-week program for exceptional students currently attending middle school in Broward County, Florida. Broward County, Florida students currently attending grades 6-8 are invited to apply to the IMACS Math Academy, an intensive one-week program designed to stimulate talented students’ interest in mathematics beyond the traditional classroom. There is no cost to attend the IMACS Math Academy! There are two scheduled sessions. The first will be held March 24 – 28 during Spring Break. The second will be held June 23 – June 27 during…
  • AP Computer Science … Updating

    IMACS Staff Writer
    29 Jan 2014 | 10:00 pm
    Following a recent review of the AP Computer Science A course and exam, the College Board has decided to replace its case study requirement with a requirement to complete a minimum of 20 hours of hands-on lab experiences. This change, which will take effect for the 2014-2015 school year, is being implemented to more effectively support student learning of core concepts in computer science. IMACS continues to follow closely all communications from the College Board, as well as discussions within the APCS community, on the forthcoming changes and will act accordingly. From the beginning,…
  • Letters to a Young Math Teacher

    IMACS Staff Writer
    1 Jan 2014 | 10:00 pm
    The following letter is extracted from the new book, Letters to a Young Math Teacher, by Gerald Rising and Ray Patenaude, which is available from and other sources. Gerry Rising is Distinguished Teaching Professor Emeritus at State University of New York at Buffalo where he co-founded the university’s Gifted Math Program for highly-qualified regional students in grades seven through twelve. Gerry Rising was for many years associated with IMACS activities and is a strong supporter of our work. Letter Seventeen: A Bag of Tricks Paul Rosenbloom enjoyed an international…
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    Maths Tips From Maths Insider

  • How to Solve a Physics Problem (FUNNY!) plus Mental Math Tips

    Caroline Mukisa
    4 Apr 2014 | 8:14 am
    I saw the comic strip below last week on Facebook by the funny folks at Saturday Morning Breakfast Cereal (SMBC), and spent a good few minutes cry-laughing (is that a thing?) Even my daughter in the midst of wrangling with Quadratics in preparation for a math test, joined in. You see, even for seasoned math teachers, math lovers and professional scientists and mathematicians, arithmetical errors are all too common when problem solving.   As part of my role as Instructor for International Students at Tabtor Math, I was given 5 math worksheets at Grade 5 and 6 level to test and report…
  • Check out These Challenging Online Math Tools for Gifted Kids

    Caroline Mukisa
    3 Dec 2013 | 1:28 am
    This is a guest post by Joseph Rodriguez While many educators agree that it is essential to improve the quality of math education in our public schools, a debate persists about how it should be done. Do we work with the students who are struggling, so that they can do better? Or do we push the students who are excelling, so they can move on to even greater things? Budgets are tight and many schools are pushed to decide one path or the other. Fortunately, many online resources can challenge gifted math students with new coursework and an outlet for their ingenuity. Here’s what you…
  • Holiday Math and More

    Caroline Mukisa
    28 Nov 2013 | 1:12 am
    If you’ve read my Tabtor vs Kumon blog post a few months back, you’ll know that I’ve been working with Tabtor Math, the personalized iPad based math program. I’m Tabtor’s instructor for many of their international students, and I’m also recording instructional videos which accompany each of the Tabtor worksheets as well as writing articles for their blog. As a result, It’s been a bit quiet here at Maths Insider but after the holiday I’ll hopefully be back here with a vengeance. I’ve still got plenty of ideas to share with you on Maths…
  • – A Great Math Program for Self Motivated Teens

    Caroline Mukisa
    17 Oct 2013 | 6:11 am
     This is a guest post by Stephanie from For those who need a math education program that can allow high school students to work at their own pace, may be what you’re looking for. Subject material from basic math skills to more advanced forms of linear algebra are present and ready for you to explore, as well as science and computing courses. While there are some materials that can be tested for free, a subscription is needed in order to take advantage of the courses at this website. How Detailed are the Courses? Each course is divided among several…
  • Pretend Mind Reading – A Way Of Learning Algebra by Lawrence Ball

    Caroline Mukisa
    30 Sep 2013 | 11:49 pm
          This is a guest post by Lawrence Ball Here’s a way to pretend you read someone’s mind. It’s also a way to get familiar with algebra. I want you to do some calculations for me, are you ready?   Think of a number between 1 and 5, don’t tell me what it is, but remember it for later. OK? Got one? Now double it. OK? Now add 10. Now halve it (or divide it by 2 – same thing) Now take away the number you started with. Your answer is 5. Well it should be, if it isn’t you made a mistake! Lets try another one. Think of a number between 1 and 5 The reason I keep…
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  • 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…
  • Fibonacci Valentine

    29 Jan 2014 | 9:15 am
    Part of Wordless Wednesday… It’s time for math and love to intersect again! Want the instructions to build one yourself? Check it out over on cwist! And don’t forget to share on Twitter, Facebook and Pinterest!
  • Football vs. Furniture – A Tale of Probabilities

    22 Jan 2014 | 3:45 pm
    We have a local legend, icon and hero here in Houston, where I live. His name is Mattress Mack and he owns a furniture store. Okay, his real name is Jim McIngvale and his furniture store is a little more than just that. It’s THE furniture store. He’s built this amazing empire of furniture sales doing crazy, fun and remarkable things. This past weekend was no different. Gambling with Football and Furniture I got an email on Friday – two days before the AFC and NFC championship football games. They were running a(nother) bizarre promotion. Here’s the gist of the rules: 1. Purchase…
  • Symmetry in Christmas Ornament Crafts

    22 Dec 2013 | 10:38 pm
    The sweet ladies at got me into another fun round of crafty goodies – this time with symmetry! Unfortunately, I’m stuck in a hospital room with limited supplies. (No biggie – just fixing to give birth.) I did all of the following with tinsel cord, some blinds samples and a tiny pair of scissors. Christmas Tree This one looks like a Christmas tree. It was my first attempt and it turned out pretty good! Notice the vertical symmetry. Ribbon Candy I noticed that a single blind sample like this did neat things, so I put two together. They turned out looking a lot like…
  • Christmas Ornament Craft with Fractions!

    16 Dec 2013 | 3:00 am
    This weekend I had the privilege to collaborate with Heather Sanders, amazing homeschool teacher and blogger. She let me spin her Christmas tree debacle into a fun fraction experience over at Pioneer Woman’s homeschool blog. In the writing of that post, I was inspired to create this Christmas ornament craft. You can use these ornaments to describe the fractions happening in your Christmas tree. Print them on card stock and let your students find the fractions. Then have them write them down and color the ornaments to put on the tree! Supplies Scissors Hole Punch Sharpie Crayons, colored…
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    CSE Blog - quant, math, computer science puzzles

  • Value of Pi - Estimation using Dice

    Pratik Poddar
    30 Mar 2014 | 5:21 am
    Source: Asked to a friend at Goldman Sachs Quant Interview Problem: Estimate the value of pi using a dice
  • (2n choose n) is never a perfect power

    Pratik Poddar
    15 Feb 2014 | 11:22 pm
    Source: Cute problem sent by Sudeep Kanath Problem: Prove that (2n choose n) is never a perfect power
  • Coin Problem - Wolfram Mathematica Puzzle

    Pratik Poddar
    10 Feb 2014 | 3:29 am
    Source: The super awesome puzzle blog by Gowtham Kumar - Puzzle Tweeter - Coin Problem who got it from Wolfram Mathematica Problem: Suppose you have an infinite stock of $a bills and $b bills such that g.c.d(a,b)=1. Find the largest amount of money (integer) that cannot be represented using $a and $b denominations. Shameless plug: If you have not done it already, please like / +1 / follow on: Quora, Twitter, Facebook, G+
  • Determinant of Matrix (17-11)

    Pratik Poddar
    24 Dec 2013 | 12:53 am
    Source: Mailed by Sudeep Kamath (EECS PhD Student, UC Berkeley, EE IITB 2008 Alumnus) Problem:A is a 300 x 300 matrix with 17 on the diagonal, and the rest of the entries being 11. What is det (A) ?
  • Open Ended Search Problem

    Pratik Poddar
    20 Dec 2013 | 8:50 pm
    Disclaimer: It is a made up problem. Not to be attempted by light hearted. Problem: I have a 300 word text. I have a large list of indexed strings (Length of string ~ 20, Number of strings ~ 1M). I need to figure out phrases in the 300 word text that match exactly to one of the strings in the large list of strings I have. A naive approach: Taking all 45000 (300 C 2) phrases, search in the large list of strings. Can we do better than this? We need to minimize calls to list of indexed strings!
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  • SBI-PO Study Plan: Reasoning section

    20 Apr 2014 | 12:41 am
    SBI-PO MCQ exam is divided into four sections:General Awareness - 50 quesData Interpretation - 50 quesReasoning - 50 quesEnglish - 50 quesToday I will cover only Reasoning section thoroughly and soon I will cover other sections too. For SBI-PO and SSC too, reasoning is a scoring subject. So you should leave this section and try to cover its topics first and then proceed to other sections. ReasoningIn reasoning section, the major part is of verbal topics like inference conclusion, sullogism, data sufficiency etc. From last few years the weightage of section is almost same. Just little changes.
  • Important Questions of Mensuration: Quantitative Aptitude

    9 Apr 2014 | 4:46 am
    Mensuration is one the toughest topic of quantitative aptitude section. The only thing is it takes time to analyze the question. Rest is just clarification and formula learning ability of candidate. This chapter is a part of quantitative aptitude section of SSC CGL and SBI PO. Today I will discuss some questions related to basic terms of mensuration.Examples with Solution Example1: What will be the area and perimeter of triangular plot whose sides are 17 m, 8m and 15m long?Solution: Firstly, we will check which kind of triangle it is.Since, `8^2 + 15^2 = 17^2`.......  (`H^2 = P^2 +…
  • Syllabus of SBI-PO Recruitment 2014

    4 Apr 2014 | 7:29 am
    SBI-PO exam includes both multiple type questions and descriptive paper. Total marks including descriptive exam is 250.Objective type Paper : 200 MarksDescriptive Paper: 50 MarksObjective type exam consists of four sections:English LanguageData Analysis and InterpretationReasoningGeneral Awareness, Computers and Marketing. Descriptive ExamDescriptive exam is of half an hour and it can be about anything discussed Essay writingLetter writingParagraph writingPrecise writing English sectionThis section basically covers comprehensions, faulty sentences, jumbled sentences, closed passages etc.
  • SBI-PO Recruitment 2014 notification out

    4 Apr 2014 | 4:23 am
    SBI-PO Recruitment 2014 notification out. All the best to all the candidates.Important datesOnline registration : 07.04.2014Payment of fees- Online : 07.04.2014 to 25.04.2014  Payment of fees- Offline : 07.04.2014 to 25.04.2014  Eligibility criteriaAll graduates and third year students from recognized university are eligible.Age range: 21- 30 yearsDetails official notification: hereSoon, I will post syllabus, study plan and strategies to crack this exam.
  • How to prepare for Quantitative Aptitude section

    27 Mar 2014 | 1:59 am
    Quantitative aptitude section is one of the four sections of bank exams, SSC and others. Some candidates think that it is not possible to crack Quant section. But, I want to tell you that a perfect study plan and regularity can easily help you to score good in this section because in numerical ability questions level is moderate. Tough questions have never been asked earlier. So you just need to clear all the basics of quantitative aptitude section. Rest will depend on you time mangement.Tricks to crack Quantitative aptitude section  Attempt chapters of your interestWhen you start…
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