Thanks to grant money, the college will continue assisting Indiana middle and high school students in understanding mathematics and science principles.


Most Popular Stories

Homework Hotline receives $2.85 million grant
Search for "math OR mathematics"11 Dec 2017  7:32 am 
Justin Curry's Favorite Theorem
Scientific American  Math9 Dec 2017  7:00 amThe University at Albany mathematician talks about why he just can’t get enough of those Platonic solids  Read more on ScientificAmerican.com 
Tips for Deploying your Work
Loren on the Art of MATLAB28 Nov 2017  8:31 amThere are a lot of ways of sharing your ideas with MATLAB these days. IncludingMATLAB scripts and functionsLive scriptsMATfilesAppsCode generation of various kinds, e.g., C/C++ and GPU via Coder productsMATLAB Compiler and SDK (standalone apps and code suitable for integrating into other environments)MATLAB Production ServerToday I want to remind you of some tools in MATLAB that can facilitate the transition to code you want to deploy via the MATLAB Compiler and SDK.ContentsUseful Functions for DeploymentOther Helpful Functions?Useful Functions for DeploymentHere's a list of the functions I… 
Missing numbers in addition
Homeschool Math Blog8 Dec 2017  12:24 pmSeveral people have asked me about this... what to do when a 1st grader is struggling to grasp the concept of missing numbers in addition problems, such as 3 + ___ = 8. I wrote the solution and posted it on my site... what to do when a child has a hard time finding the missing addends? 
Holiday Math and More: Math Teachers at Play #114
Denise Gaskins' Let's Play Math6 Dec 2017  4:13 amDo you enjoy math? I hope so! If not, the links in this post just may change your mind. Welcome to the 114th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of articles by bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to precollege. If you would like to jump straight to our featured blog posts, click here to see the Table of Contents. By the way, I found a cool, semiselfreferential trivia tidbit about our carnival number: 27 − 14 = 114. And if you put 114 dots into a…




Search for "math OR mathematics"

Homework Hotline receives $2.85 million grant
11 Dec 2017  7:32 amThanks to grant money, the college will continue assisting Indiana middle and high school students in understanding mathematics and science principles. 
Historic French chateau now has 13,000 owners from crowdfunding
11 Dec 2017  7:28 amThe Chateau de la MotheChandeniers has had many owners since its construction in the 13th century. Now more so than ever. 
Teacher Who Was Fired For 'Misgendering' A Student Slaps School With Lawsuit
11 Dec 2017  7:24 amA teacher who was fired for calling a transgender student by her biological gender hit back at the school with a lawsuit. After math teacher Joshua Sutcliffe, 27, allegedly said "well done girls" to two students at an Oxfordshire secondary school in England, the school suspended him and called for a disciplinary hearing. 
ViceChancellor builds bridges between Sheffield and China
11 Dec 2017  7:19 amPresident and ViceChancellor of the University of Sheffield Professor Sir Keith Burnett will this week visit Beijing and Xi'an as part of the University's efforts to cement academic and industrial collaborations in China. The weeklong visit will begin in Xi'an with Sir Keith addressing the global conference of the Confucius Institutes, including a private speech to the Chinese VicePremier and Minister for Education on the future of international collaboration with China. 
Proposals from Cuyahoga and Lorain community colleges to offer bachelor's degrees move forward
11 Dec 2017  7:13 amPlans for Cuyahoga Community College and Lorain County Community College to offer bachelor's degrees have gained initial approval from the Ohio Department of Higher Education. TriC's proposed bachelor in applied science in data integration/database administration and LCCC's proposed bachelor's of applied science in microelectronic manufacturing will be submitted for approval to the Higher Learning Commission following a public comment period that ends Dec. 22, the education department said in a statement.



Scientific American  Math

Justin Curry's Favorite Theorem
9 Dec 2017  7:00 amThe University at Albany mathematician talks about why he just can’t get enough of those Platonic solids  Read more on ScientificAmerican.com 
Fractions: Where It All Goes Wrong
28 Nov 2017  9:00 amWhy do Americans have such trouble with fractions—and what can be done?  Read more on ScientificAmerican.com 
Bathroom, Mathroom
26 Nov 2017  12:00 pmFor World Toilet Day, an appreciation of the most mathematically interesting room in the house  Read more on ScientificAmerican.com 
Millions, Billions, Trillions: How to Make Sense of Numbers in the News
24 Nov 2017  7:00 amAnyone who can understand tens, hundreds and thousands can develop habits and skills to accurately navigate millions, billions and trillions. Stay with me, especially if you’re mathaverse  Read more on ScientificAmerican.com 
New Keys to Help Extraterrestrials Unlock Our Messages
20 Nov 2017  12:45 pmA 19thcentury proposal for contacting aliens is being rebooted in the latest transmission to nearby star  Read more on ScientificAmerican.com



Loren on the Art of MATLAB

Tips for Deploying your Work
28 Nov 2017  8:31 amThere are a lot of ways of sharing your ideas with MATLAB these days. Including<ul><li>MATLAB scripts and functions</li><li>Live scripts</li><li>MATfiles</li><li>Apps</li><li>Code generation of various kinds, e.g., C/C++ and GPU via Coder products</li><li>MATLAB Compiler and SDK (standalone apps and code suitable for integrating into other environments)</li><li>MATLAB Production Server</li></ul>Today I want to remind you of some tools in MATLAB that can facilitate the transition to code you want to deploy via the MATLAB Compiler and SDK.Contents<ul><li>Useful Functions for Deployment</li><li>Other Helpful Functions?</li></ul>Useful Functions for DeploymentHere's a list of the functions I find most useful to aid in deployment.<ul><li>fullfile</li><li>fileparts</li><li>pathsep</li><li>filesep</li><li>mfilename</li><li>ctfroot</li><li>matlabroot</li><li>ismcc,...</li></ul> 
Color Your World: More with Maps, Graphs, and Polygons
27 Oct 2017  4:22 amToday, guest blogger Matt Tearle continues his investigation of the new polyshape type (added in R2017b) as a mapping tool.Contents<ul><li>Where were we?</li><li>Start simple: a greedy coloring algorithm</li><li>Greed is good?</li><li>Adding a little intelligence (but with no guarantees)</li><li>How far can this go?</li></ul>Where were we?In a previous post, I used the new polyshape variable type in MATLAB to determine connections between states. You can see the code in that post. I'll just load in the polygons and matrix of connections that came from that:load stateborders % Make a graph of state connections G = graph(border,stnames,'lower'); % Obtain centroid locations for states [x,y] = centroid(p); % Plot map and connections plot(p) hold... 
Loren’s Excellent Adventure: Maps, Graphs, and Polygons
12 Oct 2017  4:21 amR2017b was released recently. Today's guest blogger, Matt Tearle, discovered a fun application of one of the many new features  solving a mapbased puzzle.Contents<ul><li>A traveling MathWorker problem</li><li>Enter MATLAB</li><li>Problem: who is my neighbor?</li><li>Solution: the fat of the land</li><li>Visualizing the results</li><li>Where to next?</li></ul>A traveling MathWorker problem"Car Talk" recently featured a brain teaser submitted by a former MathWorker. The short, slightly modified version is: Loren has to drive from Delaware to every state in the contiguous US, visiting each state exactly once; Loren's boss  let's call him Jack  offers to meet her in the last state, which turns out to be his birthplace; but how can Jack know what the last state will be,... 
Math with Words – Word Embeddings with MATLAB and Text Analytics Toolbox
21 Sep 2017  6:32 amText data has become an important part of data analytics, thanks to advances in natural language processing that transform unstructured text into meaningful data. The new Text Analytics Toolbox provides tools to process and analyze text data in MATLAB.Today's guest blogger, Toshi Takeuchi introduces some cool features available in the new toolbox, starting with word embeddings. Check out how he uses sentiment analysis to find good AirBnB locations to stay in Boston! Contents<ul><li>What is a Word Embedding?</li><li>Ingredients</li><li>Loading a PreTrained Word Embedding from GloVe</li><li>Vector Math Example</li><li>Visualizing the Word Embedding</li><li>Using Word Embeddings for Sentiment Analysis</li><li>Word Embeddings Meet Machine Learning</li><li>Prepare Data for...</li></ul> 
MATLAB and the 2017 Eclipse – Part 4: Imaging the Eclipse
29 Aug 2017  3:57 amToday our guest blogger, David Garrison, will continue his series on MathWorks involvement in the 2017 solar eclipse.<ul><li>Part 1: The Citizen CATE Experiment</li><li>Part 2: Training the Volunteers</li><li>Part 3: Rehearsing for the Eclipse</li><li>Part 4: Imaging the Eclipse</li></ul>Here is Part 4 of the Series.Contents<ul><li>Recap of Parts 1  3</li><li>Getting Ready for the Eclipse</li><li>The Partial Phase</li><li>Totality</li><li>Any Questions?</li></ul>Recap of Parts 1  3In Part 1 of this series, I discussed MathWorks participation in the Citizen CATE Experiment  a citizen science project to image the 2017 solar eclipse. In Part 2 of this series, I described the volunteers, the equipment they will be using, and how they are being trained. In Part 3 of this series, I talked about how the...



Homeschool Math Blog

Missing numbers in addition
8 Dec 2017  12:24 pmSeveral people have asked me about this... what to do when a 1st grader is struggling to grasp the concept of missing numbers in addition problems, such as 3 + ___ = 8. I wrote the solution and posted it on my site... what to do when a child has a hard time finding the missing addends? 
Card game for math facts
30 Nov 2017  10:39 amI found this link when looking through some "OLD" stuff (my newsletter 10 years ago... in this Internet day and age, 10 years seems like an eternity ago!). It's a neat little "game" for math facts:http://littleblueschool.blogspot.com/2007/09/mathcardgameforadditionsubtraction.htmlTo be more precise, it is a way for kids to write some of their own math problems using a deck of cards. 😃 But it can definitely FEEL like a game for little ones! 
Math Mammoth Thanksgiving sale
16 Nov 2017  4:59 amMath Mammoth THANKSGIVING sale is here!Get 25% off of all the downloads/CDs sold at MathMammoth.com site! Use the coupon code THANKS2017.The offer is valid till December 3, 2017.Start browsing! 
Four principles of deeply effective math teaching
9 Oct 2017  5:42 amI went through and thoroughly updated this article of mine... have you read it in the past?Four basic principles of deeply effective math teachingIf you were asked what were the most important principles in mathematics teaching, what would you say? I wasn't really asked, but I started thinking, and came up with these basic habits or principles that can keep your math teaching on the right track.Principle 1: Let It Make SensePrinciple 2: Remember the GoalsPrinciple 3: Know Your ToolsPrinciple 4: Living and Loving Math 
Play With Your Math puzzles
2 Oct 2017  9:13 amAn intriguing website.... problems, but not solutions (not that I can see... but maybe, if you subscribe to get email updates, you'd get the solutions?)https://playwithyourmath.com/Their idea is,We take problems that we love, and we adapt them so that everyone (and anyone) can play. We design posters and handouts that hook you visually and explain the problem in just enough words. The problems that we’ve picked require trying, struggling, failing, adjusting, and trying again until, finally, a discovery is made.I definitely agree... that's what TRUE problem solving is all about! Doing it with math can prepare students for REAL LIFE, where often, the problems they will be facing at the workplace will NOT...



Denise Gaskins' Let's Play Math

Holiday Math and More: Math Teachers at Play #114
6 Dec 2017  4:13 amDo you enjoy math? I hope so! If not, the links in this post just may change your mind. Welcome to the 114th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of articles by bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to precollege. If you would like to jump straight to our featured blog posts, click here to see the Table of Contents. By the way, I found a cool, semiselfreferential trivia tidbit about our carnival number: 27 − 14 = 114. And if you put 114 dots into a 1←7 Exploding Dots machine, you’ll get the code 222. Pretty neat! As you scroll through the links below, you find several puzzle... 
Advent Math Activity Calendars
3 Dec 2017  4:36 amOnce again, some of my favorite websites offer a seasonal selection of activities to encourage your children’s (and your own!) mathematical creativity, one for each day in the runup to Christmas. Including an especiallytough Advent metapuzzle for truly determined problemsolvers… Click the images below to visit the corresponding December Math Calendar home pages. For Primary Students Easier activities for elementary and middle school. Math puzzle fun, plus a printable coloring page. 2017 Primary Advent Calendar When you get to the Nrich website, click a number to go to that day’s math. For Secondary Students Activities for middle and high school. Each day features a challenge from the Short Problems... 
Check Out These Cool Math Sales
2 Dec 2017  10:09 amI’ve been following Sonya’s Arithmophobia No More blog for a couple of years, and I love the work she is doing. But this month, she’s teamed up with Lacy at Play, Discover, Learn (another great blog to follow!) to offer a humongous bundle of playful math. You get math journaling pages, games, creative task cards, thoughtprovoking worksheets, and video training resources to help you build your child’s understanding of math from arithmetic to early algebra. Wow! These activities are perfect for homeschooling families or anyone looking to supplement their child’s current math curriculum with effective discoverybased activities. If you’ve ever wondered what to do with those Cuisenaire rods you picked up on... 
Math Teachers and Homeschool Bloggers: We Want You!
26 Nov 2017  11:16 pmSketch by Olga Berrios Do you have a favorite blog post about math activities, games, lessons, or handson fun? The Math Teachers at Play (MTaP) math education blog carnival would love to feature your article! We welcome math topics from preschool through the first year of calculus. Old posts are welcome, as long as they haven’t been published in past editions of this carnival. Click here to submit your blog post Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers. Don’t procrastinate: The... 
How You Can Play with Math #113 at Three J’s Learning
27 Oct 2017  12:31 pmCheck out the new carnival of playful math for all ages! <ul> <li>Math Teachers at Play Blog Carnival #113</li> </ul> Each carnival brings you a great new collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun. This month we have wholebody math, noticeandwonder puzzles, a game to build math vocabulary, intransitive dice, making sense of trig identities, and playing Go on a hundred chart. And plenty more! Click Here to Read the Carnival Blog Hey, Blogger, Can You Spare a Time? We need help! Do you write an education or family blog? Classroom teacher, math coach, homeschooler, parent, college professor, unschooler — anyone interested in helping kids play around with math? Please...



Basic mathematics blog

How to estimate fractions
11 Dec 2017  5:45 amLearn how to estimate fractions with this easy to follow lesson. 
Linear Parent Function
20 Nov 2017  8:18 amWhat is a linear parent function? Crystal clear explanation. 
Prove that the Diagonals of an Isosceles Trapezoid are Congruent
19 Nov 2017  12:54 pmProve that the diagonals of an isosceles trapezoid are congruent 
Prove that the Diagonals of a Rectangle are Congruent
19 Nov 2017  7:04 amProve that the diagonals of a rectangle are congruent 
Define and Identify Polygons Worksheet
17 Nov 2017  9:09 amDefine and identify polygons worksheet  great worksheet for students



Computational Complexity

Razor's Edge
7 Dec 2017  7:21 amInformally the sensitivity conjecture asks whether every hard Boolean function has a razor's edge input, where flipping a random bit has a reasonable chance of flipping the output. Let's be more precise. We consider functions f mapping {0,1}n to {0,1}. For every input x, the decision tree complexity at x is the least number of bits of x you would need to query to decide whether the function outputs 0 or 1. The decision tree complexity of a function is the maximum decision tree complexity over all possible x. Most interesting functions have high decision tree complexity, even the lowly OR function requires querying every bit on the input of all zeroes. The decision tree complexity is... 
Fireside chat with Simons Inst Director Dick Karp
4 Dec 2017  8:00 pmFireside chat with Dick Karp Above link is Samir Khuller interviewing Dick Karp, though its labelled as a fireside chat with Dick Karp. Very interesting to hear how TCS has evolved. More generally its good to know where you've come from to have a better idea of where you're going. bill g. 
Kolmogorov Complexity and the Primes
30 Nov 2017  4:35 amBill's post on how to derive the nonfiniteness of the primes fromVan der Waerden's theorem reminds me of a nice proof using Kolmogorov complexity. A quick primer: Fixed some universal programming language. Let C(x), the Kolmogorov complexity of x, be the length of the smallest program that outputs x. One can show by a simple counting argument for every n there is an x such that C(x) ≥ n. We call such x "random". Suppose we had a finite list of primes p1…pk. Then any number m can be expressed as p1e1···pkek. Pick n large, a random x of length n and let m be the number x expresses in binary. We can compute m from e1,…,ek and a constant amount of other information, remembering that k is a... 
Van der Waerden's theorem implies the infinitude of the primes
27 Nov 2017  10:18 am(Sam Buss and Denis Hirschfeld helped me on this post.) I was reading the table of contents of the American Math Monthly and saw an article by Levent Alpoge entitled Van der Waerden and the primes in which he showed from VDW's theorem that the set of primes is infinite. The article ishere and here. My writeup of it is here. Prof K saw me reading the paper. K: I see you are interested in proving the set of primes is infinite from VDW's theorem. BILL: Yes, who wouldn't be!!!! K: Well, lots of people. Including me. Can't you just state VDW's theorem and then give the normal proof? Would that count? Besides, we already have an easy proof that the set of primes is infinite without using VDW's... 
The Grad Student Tax
20 Nov 2017  5:15 amBy now as you've read from Luca or Scott or PhD Comicsor a variety of other sources on the dangerous changes to the tax code that passed the US House of Representatives last week. Among a number of university unfriendly policies, the tax code will eliminate the tax exemption for graduate student tuition for students supported with teaching or research duties, nearly every PhD student in STEM fields. The CRA, ACM, IEEE, AAAI, SIAM and Usenix put out a joint statementopposing this tax increase on graduate students.This is real. Without other changes, a tax on tuition will make grad school unaffordable to most doctoral students. In computer science where potential PhD students can typically get lucrative...



Mathematics and Computation

Spartan type theory
11 Dec 2017  5:52 amThe slides from the talk “Spartan type theory”, given at the School and Workshop on Univalent Mathematics. Download slides with speaker notes: Spartan Type Theory [PDF] 
A modular formalization of type theory in Coq
29 May 2017  8:01 amHere are the slides for the talk I just gave at TYPES 2017 in Budapest. It is joint work with Philipp Haselwarter and Théo Winterhalter. The abstract for the talk is available online. It describes a complete formalization of dependent type theory which allows you to turn various features of type theory on and off, and it proves several basic formal theorems. GitHub repository: formaltypetheory Slides: TYPES 2017 – A modular formalization of type theory in Coq [PDF] 
Two PhD positions in Ljubljana starting October 2017
28 Mar 2017  4:27 amWe are looking for two PhD students at the Faculty of Mathematics and Physics, University of Ljubljana. The programme starts in October 2017 and lasts three years. The positions will be fully funded (subject to approval by the funding agency). The candidates should have a Master’s degree in mathematics or computer science. No knowledge of Slovene is required. The first PhD student will be advised by dr. Andrej Bauer. The topic of research is foundations of type theory. The candidate should have interest in mathematical aspects of type theory, and familiarity with proof assistants is desirable. The second PhD student will be advised by dr. Matija Pretnar. The topic of research is the theory of programming... 
Five stages of accepting constructive mathematics
10 Oct 2016  8:27 amIn 2013 I gave a talk about constructive mathematics “Five stages of accepting constructive mathematics” (video) at the Institute for Advanced Study. I turned the talk into a paper, polished it up a bit, added things here and there, and finally it has now been published in the Bulletin of the American Mathematical Society. It is not quite a survey paper, but it is not very technical either. I hope you will enjoy reading it. Free access to the paper: Five stages of accepting constructive mathematics (PDF) 
The new and improved Programming languages zoo
7 Sep 2016  1:39 amIt is my pleasure to announce the new and improved Programming languages Zoo, a potpourri of miniature but fully functioning programming language implementations. The new zoo has a decent web site, it is now hosted on GitHub, and the source code was cleaned up. Many thanks to Matija Pretnar for all the work. The purpose of the zoo is to demonstrate design and implementation techniques, from dirty practical details to lofty theoretical considerations: <ul> <li>functional, declarative, objectoriented, and procedural languages</li> <li>source code parsing with a parser generator</li> <li>recording of source code positions</li> <li>prettyprinting of values</li> <li>interactive shell (REPL) and noninteractive file processing</li> <li>untyped, statically and...</li></ul>



The Math Less Traveled

Euler’s Theorem: proof by modular arithmetic
30 Nov 2017  11:21 amIn my last post I explained the first proof of Fermat’s Little Theorem: in short, and hence . Today I want to show how to generalize this to prove Euler’s Totient Theorem, which is itself a generalization of Fermat’s Little Theorem: If and is any integer relatively prime to , then . Remember that is the function that tells us how many positive integers less than are relatively prime to (share no common factors with) . So, for example, suppose and . There are four positive integers among which are relatively prime to (namely, , , , and ), so the theorem says we should have , which we can verify: . Once again, we start by considering the set of multiples of up to : . However, in this more... 
Fermat’s Little Theorem: proof by modular arithmetic
13 Nov 2017  3:16 pmIn a previous post I explained four (mostly) equivalent statements of Fermat’s Little Theorem (which I will abbreviate “FlT”—not “FLT” since that usually refers to Fermat’s Last Theorem, whose proof I am definitely not qualified to write about!). Today I want to present the first proof of FlT. We’re going to prove statement (2), that is, If is a prime and is any integer not divisible by , then . We already saw that statements (1), (2), and (3) are logically equivalent, so proving (2) is sufficient to prove all of them. (As I’ll show in a future post, we can also generalize this proof to prove the corrected version of statement (4).) So, suppose is a prime, and is any integer not... 
Four formats for Fermat: correction!
1 Nov 2017  9:32 amIn my previous post I explained three variants on Fermat’s Little Theorem, as well as a fourth, slightly more general variant, which it turns out is often called Euler’s Totient Theorem. Here’s what I said: If and is any integer, then . However, this is wrong! We can easily find a counterexample. For example, let and . Then , since there are only two numbers less than that are relatively prime to it (namely, and ; each of , , and shares a common factor with ). But then which has a remainder of , not , when divided by . What’s wrong? It turns out I missed a small but important restriction: this is only true when is relatively prime to . Note this is stronger than saying isn’t divisible... 
Four formats for Fermat
14 Oct 2017  11:35 amIn my previous post I mentioned Fermat’s Little Theorem, a beautiful, fundamental result in number theory that underlies lots of things like publickey cryptography and primality testing. (It’s called “little” to distinguish it from his (in)famous Last Theorem.) There are several different forms in which it is commonly presented, so I wanted to start by introducing them and showing how they are related. Statement 1 Let’s start with the statement that looks the least general: If is prime and is an integer where , then . (Recall that means that and have the same remainder when you divide them by .) For example, is prime, and we can check that for each , if you raise to the th power, you get... 
New baby, and primality testing
30 Sep 2017  1:12 pmI have neglected writing on this blog for a while, and here is why: Yes, there is a new small human in my house! So I won’t be writing here regularly for the near future, but do hope to still write occasionally as the mood and opportunity strikes. Recently I realized that I really didn’t know much of anything about fast primality testing algorithms. Of course, I have written about the LucasLehmer test, but that is a specialpurpose algorithm for testing primality of numbers with a very special form. So I have learned about a few generalpurpose primality tests, including the RabinMiller test and the BaillePSW test. It turns out they are really fascinating, and not as hard to understand as I was...



WordPress Tag: Mathematics

Libra
11 Dec 2017  7:53 am{“contentType”:”NEWS_STORY”,”id”:{“value”:”edc 
Good, bad and ugly from Packers' overtime win over Browns
11 Dec 2017  5:52 amAnother week, another nailbiting victory for the Green Bay Packers. Heading into the Dawg Pound to face off against the winless Browns, the Packers were nearly embarrassed by Cleveland, but a surprising fourthquarter rally and overtime heroics gave the Packers their second straight overtime win. The victory pushed them to 76, and the team might have done just well enough in riding the wave with Brett Hundley to have their franchise quarterback return to the lineup. As always, here’s a look at the good, the bad, and the ugly from Week 14: The Good <ul> <li>Davante Adams: If Aaron Rodgers is the best player on this Packers team, then Davante Adams can’t be too far behind. The receiver has become the clearcut,...</li></ul> 
Actuarial Analyst Interview
11 Dec 2017  4:29 amPlease tell us about yourself. How did you end up in such an offbeat, unconventional and unusual car 
Boy or Girl?
11 Dec 2017  4:00 amYou’re friends with someone (let’s call him Mr Smith) who has two children. You know that the older child is a girl. What’s the probability of the younger child also being a girl? This is one of a set of probabilityrelated problems which are known by various names, such as the ‘two child problem’ or the ‘boy or girl paradox’. This first problem that I’ve outlined is certainly quite a simple one to solve: there is a 50% chance that the younger child is a boy, and a 50% that the younger child is a girl. The answer is therefore 50%, or 1/2. We can also solve this problem in a more analytical way by examining the sample space, a list of all the possible outcomes. For two children, the sample... 
Hidden Numbers, Brought Into Daylight
11 Dec 2017  3:28 amThe mission of the Flatiron Institute is to advance scientific research through computational methods, including data analysis, modeling and simulation. The institute, an internal research division of the Simons Foundation, is a community of scientists who are working to use modern computational tools to advance our understanding of science, both through the analysis of large, rich datasets and through the simulations of physical process. If you are seeing the name above for the first time, so are we. It has come to our attention through this profile below. The questions raised are important. The answers, to the degree there are any, are fascinating. Thanks to longform journalism, which we need now more...



Neoformix

Toronto Coffee Shop Territories
18 Nov 2017  3:30 amA week or so ago I put together a simple project illustrating the locations of coffee shops within the Toronto area. I was curious about the density of coffee shops within the city and also the distributions of the larger coffee chains. In the image below the small dots are locations and the areas are coloured based on the closest location. The colours are Red  Tim Hortons, Green  Starbucks, Yellow  Second Cup, Purple  Coffee Time, Orange  Country Style, Blue  Other. The Tim Horton's red dominates much of the geography outside of the city and the location density is obviously much higher in the downtown area. Zooming in to downtown shows a more fractured landscape with strong... 
Ten Years
8 Apr 2016  4:30 amToday is the tenth anniversary of my first post on Neoformix! Thank you all for your attention and feedback over the years. I never dreamed I would be doing this for so long but it's been great fun. Thank you also to all the creators of interesting and informative work in the field of data visualization and creative coding. I have written 368 posts over the ten year span and they are all available in the Archive. The pace of new posts has slowed down lately but I'm very active on Twitter and Pinterest. 
Pinterest Boards
17 Dec 2015  2:30 amI have been using Pinterest for the last few years to collect images related to my areas of interest. There are over 1000 images pinned so far and you may find them interesting. Take a look! 
Stars and Stones
5 Nov 2014  3:00 amI just launched my first mobile app. It's a game, called Stars and Stones, and you can download it now on the Apple App Store for free. I enjoy games that have a simple natural user interaction, are easy to learn, but have a rich depth of play  an elegant complexity. That's what I attempted to create and I think I came close in many respects. Stars and Stones is a series of dynamic puzzles that get progressively more challenging. There are over 100 levels and the first 50 are free. In each puzzle you drag a token around to try and capture five stars while avoiding stones. The stones move as you move and their speed is relative to your own  the faster you move, the faster they... 
A Short Reflection on Storytelling in Data Visualization
28 Apr 2014  6:15 amThe role of storytelling in Data Visualization has become much discussed over the last year or so. One reason I find this aspect of Data Visualization so interesting is that my own natural tendencies are to focus on exploratory visualization. Much of my own past data visualization work is weak in the storytelling side of things. Coming from a scientific background and personally enjoying the act of discovering patterns in data means my default approach is to build exploratory tools. For me, personally, this whole storytelling aspect seems a rich area to mine in order to improve my work. I just finished listening to the latest Data Stories podcast called Visual Storytelling which is a discussion...



mathrecreation

Constructing Portia's Caskets
7 Dec 2017  7:39 pmIn Shakespeare's The Merchant of Venice, Portia tested her suitors by asking them to discover which of three caskets concealed her portrait. Inscriptions on the caskets presented riddles that would challenge the virtue of her potential mates. In his classic What is the Name of this Book? logician Raymond Smullyan, imagined several generations of clever Portias, who presented potential suitors with caskets inscribed with logic puzzles that provided the key to finding her hidden portrait.On this page I have set up interactive puzzle generators that correspond (roughly) to Smullyan’s first three generations of Portias. In this post I thought I would describe what I find interesting about the way the puzzles... 
the island of knights and knaves
18 Nov 2017  6:16 amThere is classic type of logic problem where we are asked to imagine an island consisting of two types of people: those that always tell the truth (knights), and those that always tell lies (knaves). In puzzles based on this trope, the islanders make statements, and we have to figure out which islanders are knights and which islanders are knaves.This pagewill generate knight and knave puzzles of varying difficulty. Here’s an example: An "easy" puzzle from https://dmackinnon1.github.io/knaves/ The grandfather of all these puzzles is an actual islander who referenced an actual island  around 600 BCE, the Cretan Epimenides is credited with the statement “All Cretans are liars.” The fun has not... 
trihexagonal & rhombille tilings
10 Nov 2017  12:14 pmThe image above is the superposition of two tessellations. The dark bold lines show a tiling of the plane that is made up of regular hexagons and triangles (thetrihexagonal tiling).The light lines show portions of the reciprocal (or dual) of the darklined tessellation.To create a reciprocal tessellation, for every two adjacent tiles in the original tessellation, join the centers of the two tiles by a line segment perpendicular to their shared side. This line segment becomes the edge of one of the tiles in the reciprocal tessellation.The reciprocal of trihexagonal tiling is made up entirely of rhombs, the rhombille tiling. 
Diophantine Desmos
23 Oct 2017  11:58 amIt may happen that you have a real valued function, but only want to find those points where both the input and output are integers.For example, consider y = sqrt(x). Suppose you had a graph of sqrt(x) and wanted to show which values of x give an integer result for y, i.e. which values of x are perfect squares:y = sqrt(x) with only integer solutions shownI recently learned how you can find and display integer solutions for certain types of equations in Desmos, and thought I would write a post about how to do this.When we care only about the integer solutions of an equation, we refer to it as a Diophantine equation. In general, Diophantine equations can take many forms  the technique described here can be... 
a Truchet puzzle mystery
3 Oct 2017  6:53 pmI thought it would be fun to create a page of Truchet puzzles, and while doing this I noticed something that surprised me: even though they were randomly generated, all puzzles of the same size had the exact same level of complexity.a single puzzle piecethat can be rotated into 4 positionsIn these puzzles, Truchet tiles like the one above are used to create a specific pattern. All the pieces are the same  it is just a question of rotating them correctly to make the pattern you are aiming for.a Truchet puzzle: can you make this patternusing only Truchet tiles?We can make these Truchet puzzles a bit more interesting if we have a specific starting arrangement, and add the restriction of using the smallest...



Math ∞ Blog

Review: Problem Solving and Reasoning With Discrete Mathematics
21 Nov 2017  2:45 pmBook Review: PROBLEM SOLVING AND REASONING WITH DISCRETE MATHEMATICS by Dr. Joseph G. Rosenstein US K12 mathematics has long been dominated by the notion that any legitimate pathway through high school and into college requires passing over Calculus Mountain. It isn’t a real mountain, but it might as well be for those who wish to pursue certain professions, not all of which actually make use of calculus at the graduate or professional school level or indeed in those professions in the field. In particular, medicine, dentistry, veterinary medicine, and other prestigious branches of “the healing arts” make calculus an absolute hurdle for those who wish to qualify for professional training. And... 
Joe Rosenstein: The Art of Being Discrete
21 Nov 2017  2:02 pmJoseph G. Rosenstein It’s our pleasure to welcome Professor Joseph G. Rosenstein to the Math Blog. He is Distinguished Emeritus Professor of mathematics at Rutgers University. His biography is extensive and you may read about his accomplishments on his web page . Michael Paul Goldenberg: Welcome, Joe. It’s a pleasure to be speaking with you again. I know you from attending a summer program for high school teachers in applied graph theory at DIMACS in the summer of 2001. You were running a parallel program for middle and elementary school teachers. You were quite a legend among the high school teachers who were returning from previous years. I was told to be on the lookout for someone with a... 
Finding Square Roots Without Estimating
23 Aug 2017  9:59 amTypical algorithms for doing square roots by hand require estimation. I have taught a different algorithm that does not rely on estimation but instead uses subtraction of successive odd integers. First, I offer examples that illustrate two situations that may arise. Then I present a third situation (as well as how to deal with the square roots of nonperfect squares). This approach is based on the fact that the nth perfect square is the sum of the first n odd integers. This fact can be used to subtract successive odd integers from a given number for which one wishes to find the square root. If the number isn’t a perfect square, this method can be extended by adding pairs of zeroes to the original... 
James Grime: FOOL FOR MATHS*
8 Aug 2017  11:41 amJames Grime is a mathematician with a personal passion for maths communication and the promotion of mathematics in schools and to the general public. He can be mostly found doing exactly that, either touring the world giving public talks or on YouTube. James has a Ph.D. in mathematics and his academic interests include group theory (the mathematics of symmetry) and combinatorics (the mathematics of networks and solving problems with diagrams and pictures). James also has a keen interest in cryptography (the mathematics of codes and secret messages), probability (games, gambling and predicting the future) and number theory (the properties of numbers). James went on to study mathematics at Lancaster... 
Subtraction: What is “the” Standard Algorithm?
31 Jul 2017  5:57 pmSubtraction: What is “the” Standard Algorithm? One common complaint amongst antireform pundits is that progressive reform math advocates and the programs they create and/or teach from “hate” standard arithmetic algorithms and fail to teach them. While I have not found this to be the case in actual classrooms with real teachers where series such as EVERYDAY MATHEMATICS, INVESTIGATIONS IN NUMBER DATA & SPACE, or MATH TRAILBLAZERS were being used (in fact, the socalled “standard” algorithms are ALWAYS taught and frequently given pride of place by teachers regardless of the program employed), the claim begs the question of how and why a given algorithm became “standard” as well as how being “standard”...



Math for all Grade blog

Nov 22, 1stgrademath
21 Nov 2017  10:39 pm1stgrademath. 
Oct 12, multiplying polynomials
12 Oct 2017  6:48 ammultiply each term of a polynomial with each of the other and combine like terms. 
Oct 8, Subtracting Fractions
8 Oct 2017  5:58 amsubtracting fractions having same and different denominators and mixed numbers. 
Oct 7, SET THEORY
7 Oct 2017  1:47 amset theory includes set notation, types of sets and operations on sets. 
Oct 5, Basic Algebra
5 Oct 2017  8:04 pmbasic algebra is also called high school algebra.



MIND Research Institute Blog

Cisco Spotlights MIND as a Global Problem Solver
7 Dec 2017  9:00 amCisco’s Global Problem Solvers initiative is fueled by the belief that "the world needs people who can innovate as technologists, think as entrepreneurs, and act as social change agents." As part of the initiative, Cisco works with individuals and organizations around the globe to leverage the power of technology in addressing issues like poverty, unemployment and inequality. Cisco Systems, Inc. has been a supporter of MIND Research Institute and the ST Math visual instructional program for over ten years now. Not only did Cisco’s investments in MIND help ST Math become webbased, but their networking solutions have helped MIND bring ST Math to over 1.2 million students in 47 states across the... 
Profiles in Success: Growing Mathematical Mindset in Early Learning
5 Dec 2017  9:00 amAt Pomona Unified School District in southern California, educators knew they needed a better way to reach all of their students when it came to math education. With a high English Language Learner (ELL) population, including many prekindergarten students, Pomona USD searched for a way to make math more accessible. They decided on ST Math, a visual learning program that builds a deep conceptual understanding of math. Without language barriers, ELLs are now making the same strides as their peers. The district is also seeing these results extend beyond early learning. "Elementary teachers can tell which students have gone through ST Math because of their confidence and lack of hesitation to take... 
Tom Vander Ark Supports MIND Research Institute on #GivingTuesday
30 Nov 2017  9:00 amTom Vander Ark is one of the leading voices in education today. As the CEO of Getting Smart, he is a tireless advocate for innovation in learning. He’s also a longtime supporter of MIND Research Institute, and demonstrated that support once again on Giving Tuesday, a yearly event centered around the encouragement and celebration of giving. Giving Tuesday was founded in 2012 by New York’s 92nd Street Y in partnership with the United Nations Foundation. The hashtag #GivingTuesday is used on a variety of social media platforms to highlight stories of individuals, communities and organizations who are supporting nonprofits. Cisco Systems, Inc. asked Tom and two other social media influencers to make... 
Highperforming District Emphasizes Personalized Learning
28 Nov 2017  9:00 amHigh performing districts face unique problems, such as how to keep top students engaged and challenged at school. Marlboro Township Public Schools in New Jersey introduced ST Math as part of its overall strategy to personalize learning through the use of digital tools, datadriven instruction, small group instruction and studentowned learning goals. See for yourself how they did it and how it’s worked. ST Math allows students to work at their own pace through intentionally sequenced learning paths. The adaptive animated feedback and mastery based objectives personalizes their exposure to each concept according to their unique needs. Interested in trying ST Math? Request a free... 
Profiles in Success: Evaluation Links ST Math to Improved Growth Mindset
21 Nov 2017  9:00 amAt Robeson Elementary, a school in Champaign Unit 4 School District in Illinois, educators take pride in fostering a growth mindset in their students and providing them with the right tools for success. Robeson's principal, Nick Gaines, brought in ST Math to give students access to engaging, personalized instruction and encourage them to become fearless problem solvers. Having seen the impact at other schools, Gaines knew that the program would fit right in with Robeson's culture. “I’m a big believer in growth mindset and that’s part of our culture. The aspect of ST Math where you put in the effort, try hard, make mistakes, learn from your mistakesthat really resonated with our teachers,...
