# Math

• ## Most Topular Stories

• ### Thorp on avoiding gambler’s ruin

Marauders of the Lost Sciences
31 Oct 2014 | 3:10 am
The famous mathematician turned speculator describes the importance of the Kelly Criteria for sizing bets in games of chance where you have an edge (i.e. a positive expectation of winning). The Kelly Criteria is widely used in the stock market today. The fundamental problem in gambling is to find positive expectation betting opportunities. The analogous problem in investing is to find investments with excess risk-adjusted expected rates of return. Once these favorable opportunities have been identified, the gambler or investor must decide how much of his capital to bet. This is the problem…
• ### Diminishing Differences Puzzle

CSE Blog - quant, math, computer science puzzles
18 Oct 2014 | 3:05 am
Source: Australian Mathematical Society Gazette Puzzle Corner 34 Problem: Begin with n integers x1, . . . , xn around a circle. At each turn, simultaneously replace all of them by the absolute differences Repeat this process until every number is 0, then stop. Prove that this process always terminates if and only if n is a power of 2. Shameless plug: Follow CSE Blog on CSE Blog - Twitter and CSE Blog on Quora. :-)
• ### Math anxiety and how to prevent it

Homeschool Math Blog
27 Oct 2014 | 1:46 pm
Photo courtesy of WecometolearnUpdated!7 Reasons behind Math Anxiety and How to Prevent ItThis article lists some of the major factors that contribute to math anxiety in students and gives helpful ideas for teachers to motivate children to study math and to prevent math anxiety. Including:- how teachers feel about math- whether mistakes are valued or not- tests and especially timed tests- whether math is presented to be a creative subject or not... and more! Check it out!
• ### The Top 10 Martin Gardner Scientific American Articles

Scientific American - Math
21 Oct 2014 | 7:32 am
The “Mathematical Games” column in Scientific American that began in January 1957 is a legend in publishing, even though it’s been almost 30 years since the last one appeared. -- Read more on ScientificAmerican.com
• ### This week's top new iPhone app is helping kids cheat on their math homework - Quartz

31 Oct 2014 | 10:37 am
KFYR-TVThis week's top new iPhone app is helping kids cheat on their math homeworkQuartzThe hottest recent iPhone app debut isn't about photo sharing or social networking: PhotoMath, which just launched last week, uses an iPhone's camera to read and solve math problems in real time. It led Apple's iOS store in overall US downloads last ...Smartphone App Solves Students' Math HomeworkKFYR-TVall 6 news articles »
• ## MATH - Google News

• ### This week's top new iPhone app is helping kids cheat on their math homework - Quartz

31 Oct 2014 | 10:37 am
KFYR-TVThis week's top new iPhone app is helping kids cheat on their math homeworkQuartzThe hottest recent iPhone app debut isn't about photo sharing or social networking: PhotoMath, which just launched last week, uses an iPhone's camera to read and solve math problems in real time. It led Apple's iOS store in overall US downloads last ...Smartphone App Solves Students' Math HomeworkKFYR-TVall 6 news articles »
• ### Hillsboro math classes comparing digital instructional materials in 8-week pilot - The Oregonian - OregonLive.com

31 Oct 2014 | 8:37 am
Hillsboro math classes comparing digital instructional materials in 8-week pilotThe Oregonian - OregonLive.comLast spring, the math study team conducted a six-week pilot study introducing students to Chromebooks to determine how the technology affected their learning, if digital devices were an effective tool for math lessons and what students and teachers needed.
• ### Zombie Math Awakens Student Interest in Algebra - Education World

31 Oct 2014 | 8:25 am
Zombie Math Awakens Student Interest in AlgebraEducation WorldIn New Mexico, teacher Brian Smith is using zombies to teach algebra in his classroom and students have "to use their math skills to figure out how to coordinate the perfect parabolic arc to launch accurate mortar fire at the walking dead," said an
• ### 10 Creative Careers That Rely on Science and Math - The Atlantic

31 Oct 2014 | 7:25 am
The Atlantic10 Creative Careers That Rely on Science and MathThe AtlanticBut they couldn't do so safely without an intimate knowledge of math and physics. For even the simplest plunges, divers need to calculate the rate at which they should rise to the surface to avoid decompression sickness. They also need to know the laws
• ### Improving DuPage scores show 'teaching math finally makes sense' - Chicago Daily Herald

31 Oct 2014 | 4:26 am
Improving DuPage scores show 'teaching math finally makes sense'Chicago Daily HeraldFry Elementary first-grade teacher Allison Schroeder leads a math lesson that is aligned to the Common Core state standards. Teachers in Indian Prairie Unit District 204 updated their math curriculum first to match the Common Core and have been Earth to Teachers. Come in, Teachers. You Can't Support Common Core But Reason (blog)all 2 news articles »

• ## Search for "math OR mathematics"

• ### What Happens When A Teacher Spends 2 Days As A Student

31 Oct 2014 | 10:57 am
A blog post published earlier this month is inciting an important debate about the structure of high school days and how classes should be taught. A blog post published earlier this month is inciting an important debate about the structure of a high school day and how classes should be taught.
• ### Should Alex Gordon have tried to steal home on Wednesday night?

31 Oct 2014 | 10:55 am
Nothing else is going on, and we're all sort of over asking whether Alex Gordon should've kept running in the ninth inning of Game 7, so let's throw this one out there. It's a reader email from Mark M.: I wonder if you'd write about whether Ned Yost should have called a straight steal of home in the 7th game, bottom of the ninth, after there was one strike on Salvador Perez .
• ### Beware Common Core Proponents Asking for Treats

31 Oct 2014 | 10:52 am
It always seems appropriate that Halloween comes just days before an election. Politicians are masters at dressing themselves up in ways that obscure reality, in particular their positions on tough issues.
• ### The Art of Planetary Science

31 Oct 2014 | 10:47 am
On October 17-19, 2014, the Lunar and Planetary Laboratory on the University of Arizona campus hosted the second annual Art of Planetary Science exhibition . I have always viewed scientific endeavors as having an artistic component.
• ### Transferring credit card balances to a new card

31 Oct 2014 | 10:45 am
Have you been approved for a new credit card with a 0% interest balance transfer offer? Here are the steps you'll want to take before you actually transfer a balance from an old credit card to a new one and the steps for completing the transfer. List all of your credit cards, their balances and their interest rates.
• ## Mathematics News -- ScienceDaily

• ### Model explains why HIV prevention dosing differs by sex

30 Oct 2014 | 7:15 am
A mathematical model predicts that women must take the antiretroviral medication Truvada daily to prevent HIV infection via vaginal sex, whereas just two doses per week can protect men from HIV infection via anal sex. This finding helps explain why two large clinical trials testing HIV pre-exposure prophylaxis, or PrEP, in women failed to show efficacy.
• ### Same votes, different voting districts would alter election results in NC: Math study bolsters call for non-partisan redistricting reform

29 Oct 2014 | 5:43 pm
Researchers have developed a mathematical model that shows how changes in congressional voting districts affect election outcomes. Focusing on the last election, they show the outcome of the 2012 US House of Representatives elections in North Carolina would have been very different had the state's congressional districts been drawn with only the legal requirements of redistricting in mind. The researchers hope the study will bolster calls for redistricting reform in 2016.
• ### Modeling Cancer: Researchers Prove Models Can Predict Cellular Processes

28 Oct 2014 | 6:38 pm
Mathematical models to predict the dynamics of cell transitions have been developed by researchers who compared their results with actual measurements of activity in cell populations. The results could inform efforts to treat cancer patients.
• ### Lack of A level maths leading to fewer female economists in England

28 Oct 2014 | 5:25 am
A study has found there are far fewer women studying economics than men, with women accounting for just 27 per cent of economics students, despite them making up 57 per cent of the undergraduate population in UK universities. The findings suggest less than half as many girls (1.2 per cent) as boys (3..8 percent) apply to study economics at university, while only 10 per cent of females enroll at university with an A level in maths, compared to 19 per cent of males.
• ### An effective, cost-saving way to detect natural gas pipeline leaks

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

• ## Scientific American - Math

• ### In Which Omar Khayyam Is Grumpy with Euclid

28 Oct 2014 | 5:30 am
My math history class is currently studying non-Euclidean geometry, which means we've studied quite a few "proofs" of Euclid's fifth postulate, also known as the parallel postulate. -- Read more on ScientificAmerican.com
• ### Snaking Staircase Nominated for Prestigious Engineering Award

25 Oct 2014 | 8:00 am
The Miles Stair uses stronger, lighter concrete -- Read more on ScientificAmerican.com
• ### The Top 10 Martin Gardner Scientific American Articles

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

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

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

• ### Preparing Your Child for Common Core Tests

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

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

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

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

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

• ## Loren on the Art of MATLAB

• ### Using MATLAB to Detect Cookies

23 Oct 2014 | 2:41 am
Today, I'd like to introduce a guest blogger, Tom Lowell, who is a program manager here at MathWorks. He works in our hardware connectivity group, and plays with Arduinos and Raspberry Pis in his spare time. He's relatively new to both MathWorks and MATLAB and decided to write a cookie detector as his first MATLAB project.ContentsMotivationSetupCodeTuningThe OutputNotificationDo You Have a Project that Uses an IP camera?MotivationWhen I joined MathWorks, one of the first traditions I learned was that a large plate of home made cookies is delivered every Friday to every floor of every building…
• ### Taking the Pulse of MOOCs

16 Oct 2014 | 5:45 am
Coursera is a technology platform that kickstarted the current MOOCs boom. Even though there are more MOOCs players now, it still remains one of the leading companies in this space. But how are they doing these days for delivering higher education to the masses online?Today's guest blogger, Toshi Takeuchi, would like to share an analysis using Courera's data.I am a big fan of MOOCs and I benefited a lot from free online courses on Coursera, such as Stanford's Machine Learning course. Like many websites these days, Coursera offers its data through REST APIs. Coursera offers a number of APIs,…
• ### MATLAB R2014b Graphics – Part 2: Using Graphics Objects

14 Oct 2014 | 7:55 am
Today, David Garrison, our guest blogger, will continue his series on the new graphics system in R2014b.Part 1: Features of the New Graphics SystemPart 2: Using Graphics ObjectsPart 3: Compatibility Considerations in the New Graphics SystemHere is Part 2 of the series.ContentsWhat have we learned so far?The MATLAB Graphics SystemPre-R2014b Numeric HandlesR2014b Graphics ObjectsGetting and Setting Object PropertiesUsing set and getHave you starting using graphics objects in R2014b?Next up -- Part 3: Compatibility Considerations in the New Graphics SystemWhat have we learned so far?In Part 1 of…
• ### Reversal of Sorts – New in Release R2014b

9 Oct 2014 | 5:36 am
I wanted to show you a glimpse of some of the new math functionality available in R2014b.ContentsThe QuestionMy Original AnswerSolution with R2014bWhat New Math Have You Enjoyed in R2014b?The QuestionRecently on the MATLAB newsgroup, Christoph asked this question:I have a vector A shown below, which has 6 elements. the elements are already sorted in descending order. now i want to create vector C by deleting elements from A, starting with element a1, until the sum of the vector equals or is smaller the value BA= 26 23 20 19 15 14 B=70So, the output should beC= 20 19 15 14Any idea how to do…
• ### MATLAB R2014b Graphics – Part 1: Features of the New Graphics System

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

• ### Math anxiety and how to prevent it

27 Oct 2014 | 1:46 pm
Photo courtesy of WecometolearnUpdated!7 Reasons behind Math Anxiety and How to Prevent ItThis article lists some of the major factors that contribute to math anxiety in students and gives helpful ideas for teachers to motivate children to study math and to prevent math anxiety. Including:- how teachers feel about math- whether mistakes are valued or not- tests and especially timed tests- whether math is presented to be a creative subject or not... and more! Check it out!
• ### Math teachers at play #79

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

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

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

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

• ### Math Teachers at Play #79

22 Oct 2014 | 7:00 am
[Feature photo above by Jimmie, and "79" image (right) by Steve Bowbrick via flickr (CC BY 2.0).] Do you enjoy math? I hope so! If not, browsing this post just may change your mind. Welcome to the 79th edition of the Math Teachers At Play (MTaP) math education blog carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college. Let the mathematical fun begin! By tradition, we start the carnival with a puzzle, game, or trivia tidbits. If you would like to jump straight to our…
• ### Horseshoes: A Place Value Game

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

15 Oct 2014 | 2:47 pm
[Photo by Olga Berrios via flickr.] Do you have a favorite blog post about math activities, games, lessons, or hands-on fun? The Math Teachers at Play (MTaP) math education blog carnival would love to feature your article! We welcome math topics from preschool through the first year of calculus. Old posts are welcome, as long as they haven’t been published in past editions of this carnival. Click here to submit your blog post. [Note: Sometimes the automated Google form refuses to load in my browser. If you have trouble, leave a link to your entry in the comments below.] Browse all the past…
• ### Math Storytelling Day: The Hospital Floor

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

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

• ## Basic mathematics blog

• ### How to Multiply Matrices

28 Oct 2014 | 5:17 am
Learn how to multiply matrices with crystal clear directions
• ### Add and Subtract Matrices

27 Oct 2014 | 9:34 am
Learn to add and subtract matrices with this great lesson
• ### Compute with Scientific Notation

23 Oct 2014 | 5:40 pm
Learn to compute with scientific notation. Add and subtract with scientific notation. Multiply and divide with scientific notation
• ### Online Matrix Calculator

16 Oct 2014 | 4:31 am
This online matrix calculator will do addition, subtraction, multiplication, determinant, and inverse of matrices
• ### Introduction to Matrices

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

30 Oct 2014 | 10:35 am
Congratulations to the San Francisco Giants, winning the World Series last night. In honor of their victory let's talk metrics. Baseball has truly embraced metrics as evidenced in the book and movie Moneyball about focusing on statistics to choose which players to trade for. This year we saw a dramatic increase in the infield shift, the process of moving the infielders to different locations for each batter based on where they hit the ball, all based on statistics. Metrics work in baseball because we do have lots of statistics, but also an objective goal of winning games and ultimately the…
• ### Sipser Symposium

28 Oct 2014 | 9:21 am
On Sunday we had the Symposium on Theoretical Computer Science on the Occasion of Michael Sipser's 60th birthday to celebrate what Mike has brought to research (seminal work on the complexity of randomness and circuits), service (ten years leading the MIT math department before recently becoming Dean of Science) and education (his great textbook and the corresponding popular course he still teaches). We had an incredible turnout for the symposium and banquet that followed. I counted five Turing Award Winners (Mike's advisor Manuel Blum, Leslie Valiant, Shafi Goldwasser, Silvio Micali and Ron…
• ### Guest Post by Dr. Hajiaghayi: A new way to rank departments

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

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

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

• ### TEDx “Zeroes”

16 Oct 2014 | 12:01 am
I spoke at TEDx University of Ljubljana. The topic was how programming influences various aspects of life. I showed the audence how a bit of simple programming can reveal the beauty of mathematics. Taking John Baez’s The Bauty of Roots as an inspiration, I drew a very large image (20000 by 17500 pixels) of all roots of all polynomials of degree at most 26 whose coefficients are $-1$ or $1$. That’s 268.435.452 polynomials and 6.979.321.752 roots. It is two degrees more than Sam Derbyshire’s image,  so consider the race to be on! Who can give me 30 degrees? The code…
• ### Reductions in computability theory from a constructive point of view

19 Jul 2014 | 5:50 am
Here are the slides from my Logic Coloquium 2014 talk in Vienna. This is joint work with Kazuto Yoshimura from Japan Advanced Institute for Science and Technology. Abstract: In constructive mathematics we often consider implications between non-constructive reasoning principles. For instance, it is well known that the Limited principle of omniscience implies that equality of real numbers is decidable. Most such reductions proceed by reducing an instance of the consequent to an instance of the antecedent. We may therefore define a notion of instance reducibility, which turns out to have a…
• ### Seemingly impossible constructive proofs

8 May 2014 | 7:15 am
In the post Seemingly impossible functional programs, I wrote increasingly efficient Haskell programs to realize the mathematical statement $\forall p : X \to 2. (\exists x:X.p(x)=0) \vee (\forall x:X.p(x)=1)$ for $X=2^\mathbb{N}$, the Cantor set of infinite binary sequences, where $2$ is the set of binary digits. Then in the post A Haskell monad for infinite search in finite time I looked at ways of systematically constructing such sets $X$ with corresponding Haskell realizers of the above omniscience principle. In this post I give examples of infinite sets $X$ and corresponding constructive…
• ### Brazilian type checking

6 May 2014 | 2:59 am
I just gave a talk at “Semantics of proofs and certified mathematics”. I spoke about a new proof checker Chris Stone and I are working on. The interesting feature is that it has both kinds of equality, the “paths” and the “strict” ones. It is based on a homotopy type system proposed by Vladimir Voevodsky. The slides contain talk notes and explain why it is “Brazilian”. Download slides: brazilian-type-checking.pdf GitHub repository: https://github.com/andrejbauer/tt Abstract: Proof assistants verify that inputs are correct up to judgmental…
• ### Intuitionistic Mathematics and Realizability in the Physical World

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

• ## WordPress Tag: Mathematics

• ### A new mathematics

28 Oct 2014 | 3:59 pm
Lately I’ve been thinking about how to differently present mathematics to my kids and ultimately to address my own discomforts. I’ve found a couple articles here and here and here that I’m planning to read thoroughly. I’ve also signed up for Devlin‘s MOOC that I think will be helpful to anyone with a similar interest. I haven’t read through them all yet. But plan to post more in the future about this exploration of mine. How do you think mathematical thinking can be brought into schools?
• ### Maths, active learning and metacognition

28 Oct 2014 | 2:30 pm
An interesting article about a new book which explains how we learn to learn, and how to teach students how to think: “Critical Maths for Innovative Societies: The Role of Metacognitive Pedagogies”. “College professors often point out that their students never learnt how to learn. Derek Cabrera was surprised to find that even the “cream of the crop of our education system” was not good at dealing with novel problems in unstructured assignments. As PISA shows, across OECD countries, about one in five students is able to solve only straightforward problems – if any –…
• ### Sub

28 Oct 2014 | 1:25 pm
Her sub plans were clear and the class a sea of smiling 12 year old faces. Crazy Sock Day, part of spirit week, had them in a particularly good mood, and it was a class I’d visited just the week before. It’s a fact that not everyone knows that if a substitute teacher is late, as today’s was (the result of a fender bender on the way to school), the principal or assistant principal takes the class. It doesn’t happen all that often, but when it does I take the opportunity to dive in and participate in the most important job in education: teaching. In my time as an administrator I’ve…
• ### Brian Hayes on clear climate models for the curious public

28 Oct 2014 | 10:20 am
American Scientst has a nice article by Brian Hayes recounting the basic physics of climate, and then recommending both public engagement with clear, simple climate models, at least by the curious and scientifically literate, and the development of models which can be thus understood. He goes on to offer a number of resources offering such models. This is great. However, this is both hardly a new phenomenon, especially with Python, and it doesn’t relieve the curious student of climate from the public of knowing some of the physics contributing to these calculations. Toward that end I…
• ### When Will My Beer Be Cold Enough?

28 Oct 2014 | 9:46 am
It’s Saturday afternoon, and your good friend brings over a six-pack of your favorite beer. Unfortunately, the beer is at room temperature. You throw the beer in the fridge, and after about 10 minutes, you pull one out to check it and find it is still warm. How long are you going to have to wait until the beer is the desired temperature to drink? Fortunately we have knowledge of Newton’s law of cooling, and how to solve differential equations. Here’s how we can figure it out. Newton’s law of cooling, in regards to this scenario, simply states that the change in…
• ## Mr. L's Math

• ### Programming with GeoGebra

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

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

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

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

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

• ### Implement The Core: No *Mean* Tricks!

31 Oct 2014 | 6:43 am
Halloween Twitter Problem (@dmarain)    Treats__Kids           1 ___4           2____5           3____4           4____4 M🎃an treats/child? M🎃dian? COREFLECTIONS (1) This question fits where in Common Core? Grade levels? (2) What questions could you ask before calculation to develop number sense/conceptual thinking? Some ideas... Why is this sometimes referred to as a frequency table? OR Which is easier to determine -- mean or median? OR If  frequency = 4 kids for all # of treats, mean = ? Mental Math!! OR Explain to your partner why mean >…
• ### A Dose of Reality -- My Latest Common Core Rant

22 Oct 2014 | 9:55 am
I'm reproducing my comment to the post, "Who Needs Algebra?"on Mr. Honner's outstanding blog... http://mrhonner.com/archives/14291#comment-10579. I strongly recommend you  read all of his excellent pieces. The current one is compelling for all math educators not to mention the public... MY COMMENTS... First of all requiring an in-depth conceptual understanding of algebra for all students shows complete insensitivity to special needs students and their longsuffering teachers and parents. Sure just modify the curriculum for them. Go ahead. Show me exactly what that looks like…
• ### Just How Common is our Core?

22 Oct 2014 | 7:54 am
Borrowing a problem from the comments in the excellent blog CorkboardConnections. Hope that's ok... http://corkboardconnections.blogspot.com/2014/08/common-core-math.html?showComment=1413889358852#c7893872002833512194 THE PROBLEM Mdm Shanti bought 1/3 as many chocolates as sweets. She gave each of her neighbours' children 4 chocolates and 3 sweets, after which she had 6 chocolates and 180 sweets left. (a) How many children received the chocolates and sweets? (b) how many sweets did she buy? ans: 18 children; 234 sweets. FROM THE COMMENTER ON THE BLOG ABOVE This is the questions our 12…
• ### Round your answer to nearest cent: $1.29 or$1.30?

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

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

• ## mathrecreation

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

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

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

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

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

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

• ### Bee-Bot Floor Robot – Teaching Basic Programming

25 Oct 2014 | 7:11 am
A friend gave me a Bee-Bot floor robot on “permanent loan.” She wanted me to figure out some good ways to teach the basics of programming as well as some algebra. I was happy to take on the challenge. What is the bee-bot? I handed the bee-bot to the kids with the prompt, “What do you think?” When they asked about it, I answered: “Figure it out.” They mashed some buttons. Some students figured it out. But some needed my prompts: Press clear. Now press two arrow buttons. Put it down and press “Go.” With this they got enough of what it is, a…
• ### Using the Hundreds Chart to Teach Beginning Multiplication

21 Oct 2014 | 5:50 am
We typically think of beginning multiplication as memorizing your math facts for 2’s, 3’s, 4’s and 5’s. But in my new job, things aren’t so typical. So I’m trying something new. Sieve of Eratosthenes It started with a brilliant idea to teaching the Sieve of Eratosthenes. I began by asking the students to color in (or cross out) each of the multiples of 2, 3, 5 and 7. Alas, the plan went awry quickly. Students got confused when they needed to cross out a number that was previously crossed out (like 6). So they moved to the next number and crossed it out:…
• ### Really Big Numbers: The 100 Dots Project

13 Oct 2014 | 10:26 am
Note: this post has affiliate links. If you use these, you support my work in giving you free content. The AMS sent me a copy (for free, yay me!) of their first publication ever – Really Big Numbers by Evan Schwartz. I loved reading the first few pages with K8, and it gave me an idea. What if I used this in class to introduce numbers? I started teaching at a private, special education school recently. I quickly figured out that everything I know about math education is wrong. I thought this book (and the activity that spawned from it) might work well. And for once, with these kids, I…

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

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

• ### Diminishing Differences Puzzle

18 Oct 2014 | 3:05 am
Source: Australian Mathematical Society Gazette Puzzle Corner 34 Problem: Begin with n integers x1, . . . , xn around a circle. At each turn, simultaneously replace all of them by the absolute differences Repeat this process until every number is 0, then stop. Prove that this process always terminates if and only if n is a power of 2. Shameless plug: Follow CSE Blog on CSE Blog - Twitter and CSE Blog on Quora. :-)
• ### Balancing Act Puzzle

19 Sep 2014 | 1:21 am
Source: Australian Mathematical Society Gazette Puzzle Corner 35 Problem:There are some weights on the two sides of a balance scale. The mass of each weight is an integer number of grams, but no two weights on the same side of the scale share the same mass. At the moment, the scale is perfectly balanced, with each side weighing a totalof W grams. Suppose W is less than the number of weights on the left multiplied by the number of weights on the right.Is it always true that we can remove some, but not all, of the weights from each side and still keep the two sides balanced?
• ### "Flawless Harmony" Puzzle

26 Aug 2014 | 2:40 am
Source: AUSTMS Puzzle Corner 35 Problem: Call a nine-digit number flawless if it has all the digits from 1 to 9 in some order. An unordered pair of flawless numbers is called harmonious if they sum to 987654321. Note that (a, b) and (b, a) are considered to be the same unordered pair. Without resorting to an exhaustive search, prove that the number of harmonious pairs is odd. Update (23 Oct 2014): Solution: Posted by me (Pratik Poddar) in comments!
• ### Minimum sum of numbers in an array

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

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

• ## Math for all Grade blog

• ### Oct 26, Surface area of a cube

26 Oct 2014 | 1:03 am
Total Surface area of a cube is 6 times side squared, lateral surface area is 4 times side squared.
• ### Oct 26, Geometry-help

26 Oct 2014 | 1:03 am
math for all grades covers in depth all math subjects :algebra, arithmetic, calculus with essential concepts and unlimited solved problems.
• ### Oct 26, Surface-area-of-a-cylinder

26 Oct 2014 | 1:03 am
Surface area of a cylinder (closed right circular) is curved surface area plus areas of the two circular ends.
• ### Oct 26, Alligations

26 Oct 2014 | 12:30 am
Alligations is the ratio of the difference of dearer and mean to the difference of mean and cheaper
• ### Oct 26, Arithmetic

26 Oct 2014 | 12:30 am
Arithmetic
• ## Marauders of the Lost Sciences

• ### Thorp on avoiding gambler’s ruin

31 Oct 2014 | 3:10 am
The famous mathematician turned speculator describes the importance of the Kelly Criteria for sizing bets in games of chance where you have an edge (i.e. a positive expectation of winning). The Kelly Criteria is widely used in the stock market today. The fundamental problem in gambling is to find positive expectation betting opportunities. The analogous problem in investing is to find investments with excess risk-adjusted expected rates of return. Once these favorable opportunities have been identified, the gambler or investor must decide how much of his capital to bet. This is the problem…
• ### Schrödinger modifies the Hamilton-Jacobi equation

30 Oct 2014 | 3:10 am
Quantization as an eigenvalue problem, or alternatively, the origin of Schrödinger’s Equation. In this paper I wish to consider, first the simple case of the hydrogen atom (non-relativistic and unperturbed), and show that the customary quantum conditions can be replaced by another postulate, in which the notion of “whole numbers”, merely as such, is not introduced. Rather when integralness does appear, it arises in the same natural way as it does int he case of the node-numbers of a vibrating string. The new conception is capable of generalization, and strikes, I believe,…
• ### R. Fisher on the devilish nature of acceptance procedures

29 Oct 2014 | 5:40 am
Late in Fisher’s career he wrote a critique of Neyman-Pearson statisical testing. The operative properties of an acceptance procedure, single or sequential, are ascertained practically or conceptually by applying it to a series of successive similar samples from the same source of supply, and determining the frequencies of the various possible results. It is doubtless in consequence of this that it has been thought, and frequently asserted, that the validity of a test of significance is to be judged in the same way. However, a rather large number of examples are now known in which this…
• ### Turing mathematically models morphogenesis in biology

27 Oct 2014 | 11:10 pm
Alan Turing decided to make a mark in mathematical biology a few years before taking his own life. LEFT-HANDED AND RIGHT-HANDED ORGANISMS The object of this section is to discuss a certain difficulty which might be thought to show that the morphogen theory of morphogenesis cannot be right. The difficulty is mainly concerned with organisms which have not got bilateral symmetry. The argument, although carried through here without the use of mathematical formulae, may be found difficult by non—mathematicians, and these are therefore recommended to ignore it unless they are already troubled by…
• ### Shannon used Bayes Theorem to define perfect secrecy

26 Oct 2014 | 11:10 pm
Shannon is famous for his paper on communication and information theory. This work on cryptography may not be as well known since it was originally classified. 10. PERFECT SECRECY Let us suppose the possible messages are finite in number and have a priori probabilities , and that these are enciphered into the possible cryptograms by     The cryptanalyst intercepts a particular and can then calculate, in principle at least, the a posteriori probabilities for the various messages, . It is natural to define perfect secrecy by the condition that, for all the a posteriori probabilities…