Posts about Math

Math Education Results Show China, Singapore, Korea and Japan Leading

The most comprehenvise comparison of student achievement in math and science around the globe undertaken by the Organisation for Economic Co-operation and Development (OECD). The 2012 Program for International Student Assessment (PISA) focuses on math understanding of 15 year olds (the 2014 report will focus on science). The 2009 report focused on the results of science education student achievement around the globe.

2012 results for the math portion (rank – country – mean score)(I am not listing all countries):

  • 1 – Singapore – 573
  • 2 – Korea – 554
  • 3 – Japan – 536
  • 5 – Switzerland – 531
  • 6 – Netherlands – 523
  • 7 – Estonia – 521
  • 8 – Finland – 519
  • 9 – Canada – 518
  • 12 – Germany – 514
  • 24 – UK – 494 (this is also the OECD average)
  • 34 – USA – 481
  • 49 – Malaysia – 421
  • 50 – Mexico – 413

All 34 OECD member countries and 31 partner countries and economies participated in PISA 2012, representing more than 80% of the world economy. Portions of China participated and did very well including Shanghai-China (highest mean score of 613 points – if you ranked that as a country, I ignored these “regional results” in the ranks I shown here), Hong Kong-China (561, 3rd if including countries and regions together), Chinese Taipei [Taiwan] (560, 4th), Macao-China (538, 6th).

Boys perform better than girls in mathematics in 38 out of the 65 countries and economies that participated in PISA 2012, and girls outperform boys in 5 countries.

Related: Playing Dice and Children’s NumeracyNumeracy: The Educational Gift That Keeps on GivingMathematicians Top List of Best OccupationsThe Economic Consequences of Investing in Science EducationCountry H-index Ranking for Science PublicationsEconomic Strength Through Technology Leadership

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Many Great, Free, Online Courses in Science, Engineering and More

The video, above, provides an overview of an online course, Calculus: Single Variable, via coursera from the University of Pennsylvania. This course provides a brisk, entertaining treatment of differential and integral calculus, with an emphasis on conceptual understanding and applications to the engineering, physical, and social sciences.

Robert Ghrist is the Andrea Mitchell University Professor of Mathematics and Electrical & Systems Engineering at the University of Pennsylvania. Coursera offers many courses in all sorts of disciplines including: Introduction to Genetics and Evolution (Duke), Scientific Computing (University of Washington), Principles of Economics for Scientists (California Institute of Technology), Game Theory (Stanford University and The University of British Columbia), A Beginner’s Guide to Irrational Behavior (Dan Ariely, Duke University), The Modern World: Global History since 1760 (University of Virginia), Microeconomics for Managers (University of California, Irvine), Data Analysis (Johns Hopkins University), Fundamentals of Human Nutrition (University of Florida), Algorithms, Part I (Princeton University), The Ancient Greeks (Wesleyan University), Astrobiology and the Search for Extraterrestrial Life (University of Edinburgh) and Epigenetic Control of Gene Expression, (University of Melbourne).

All the classes are free. These courses, and many more, are extremely appealing. I signed up for 2. I would be interested in signing up for much more but I worry about having the time to commit to keeping up with the coursework. I hope the first two go well and I can sign up for more in the future.

Related: Top Online Graduate Engineering Programs in the USAOpen Source Education CurriculaScience and Engineering Education ResourcesExploring Eukaryotic Cells

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Teen Solves Puzzle That Has Stumped Mathematicians for 300 Years

Teen solves Newton’s 300-year-old riddle

An Indian-born teenager has won a research award for solving a mathematical problem first posed by Sir Isaac Newton more than 300 years ago that has baffled mathematicians ever since.

The solution devised by Shouryya Ray, 16, makes it possible to calculate exactly the path of a projectile under gravity and subject to air resistance. Shouryya, who lives in Dresden, eastern Germany, came up with the solutions to this and a second mathematical riddle while working on a school project.

Only partial solutions had been discovered up to now, requiring simplified assumptions or calculations by computer. Shouryya’s elegant solutions could contribute to greater precision in fields such as ballistics.

Related: Teen Tackles Centuries-old Numbers challenge (this time it was an Iraqi immigrant in Sweden)Numeracy: The Educational Gift That Keeps on GivingOur Brains Reorganize As We Learn Math

Numeracy: The Educational Gift That Keeps on Giving

I like numbers. I always have. This is just luck, I think. I see, how helpful it is to have a good understanding of numbers. Failing to develop a facility with numbers results in many bad decisions, it seems to me.

A new article published in closed anti-science way, sadly (so no link), examines how people who are numerate (like literate but for number—understand) process information differently so that they ultimately make more informed decisions. Cancer risks. Investment alternatives. Calories. Numbers are everywhere in daily life, and they figure into all sorts of decisions.

People who are numerate are more comfortable thinking about numbers and are less influenced by other information, says Ellen Peters of Ohio State University (sadly Ohio State allows research by staff paid by them to be unavailable to the public – sad), the author of the new paper. For example, in one of Peters’s studies, students were asked to rate undergraduates who received what looked like different test scores. Numerate people were more likely to see a person who got 74% correct and a person who got 26% incorrect as equivalent, while people who were less numerate thought people were doing better if their score was given in terms of a percent correct.

People make decisions based on this sort of information all the time. For example, “A lot of people take medications,” Peters says. Every drug has benefits and potential risks, and those can be presented in different ways. “You can talk about the 10 percent of the population that gets the side effect or the 90 percent that does not.” How you talk about it will influence how dangerous the drug seems to be, particularly among people who are less numerate.

Other research has shown that only less numerate people respond differently to something that has a 1 in 100 chance of happening than something that has a 1 percent chance of happening. The less numerate see more risk in the 1 in 100 chance—even though these numbers are exactly the same.

“In general, people who are numerate are better able to bring consistent meaning to numbers and to make better decisions,” Peters says. “It suggests that courses in math and statistics may be the educational gift that keeps on giving.”

Related: full press releaseBigger Impact: 15 to 18 mpg or 50 to 100 mpg?Data Doesn’t Lie, But People Can be FooledUnderstanding Data: Simpson’s Paradoxapplied statistics is not about proving a theorem, it’s about being curious about thingsEncouraging Curiosity in KidsDangers of Forgetting the Proxy Nature of DataCompounding is the Most Powerful Force in the Universe

Fields Medalist Tim Gowers Takes Action To Stop Cooperating with Anti-Open Science Cartel

The Fields medal is know as the Nobel of mathematics. Tim Gowers was awarded the Fields medal in 1998 for contributions to functional analysis, making extensive use of methods from combinatorial theory. Tim Gowers is currently the Rouse Ball Professor of Mathematics at Cambridge University. He posted recently on his decision to stop supporting (with his actions, such as submitting paper and reviewing papers) the anti-open-science behavior of Elsevier (a particularly aggressive anti-open-science publisher that also has very bad pricing practices).

Elsevier — my part in its downfall

One method that they have for getting away with it is a practice known as “bundling”, where instead of giving libraries the choice of which journals they want to subscribe to, they offer them the choice between a large collection of journals (chosen by them) or nothing at all. So if some Elsevier journals in the “bundle” are indispensable to a library, that library is forced to subscribe at very high subscription rates to a large number of journals, across all the sciences, many of which they do not want. (The journal Chaos, Solitons and Fractals is a notorious example of a journal that is regarded as a joke by many mathematicians, but which libraries all round the world must nevertheless subscribe to.) Of course, given that libraries have limited budgets, this often means that they cannot subscribe to journals that they would much rather subscribe to, so it is not just libraries that are harmed, but other publishers, which is of course part of the motivation for the scheme.

Elsevier supports many of the measures, such as the Research Works Act, that attempt to stop the move to open access. They also supported SOPA and PIPA and lobbied strongly for them.

I also don’t see any argument at all against refusing to submit papers to Elsevier journals.

So I am not only going to refuse to have anything to do with Elsevier journals from now on, but I am saying so publicly. I am by no means the first person to do this, but the more of us there are, the more socially acceptable it becomes

Good for him. All we need is for more and more scientists, mathematicians and engineers to support open science with thier actions and open science will be the way things are. It is as simple as that. The outdated business practices of the old journals will die. Either the existing publishers will finally give up on their extremely outdated practices or they will be replaced.

Related: The Architecture of Access to Scientific KnowledgeMerck and Elsevier Publish Phony Peer-Review JournalThe Future of Scholarly Publication (2005)Science Journal Publishers Stay Stupid (2007) “It is time for the scientific community to give up on these journals and start looking to move to work with new organizations that will encourage scientific communication and advancement”

How Algorithms Shape our World

Our modern world is influenced greatly by algorithms. As computing power allowed incredibly complex calculation we have taken advantage of that and used algorithms to find solutions to our desires. Great things are done but we also find ourselves getting into trouble occasionally as we develop these algorithm.

Related: Algorithmic Self-AssemblyComputer Science RevolutionGoogle’s Answer to Filling Jobs Is an AlgorithmWhat are Genetic Algorithms?Google Prediction API

The Value of Displaying Data Well


Anscombe’s quartet: all four sets are identical when examined statistically, but vary considerably when graphed. Image via Wikipedia.

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Anscombe’s quartet comprises four datasets that have identical simple statistical properties, yet are revealed to be very different when inspected graphically. Each dataset consists of eleven (x,y) points. They were constructed in 1973 by the statistician F.J. Anscombe to demonstrate the importance of graphing data before analyzing it, and of the effect of outliers on the statistical properties of a dataset.

Of course we also have to be careful of drawing incorrect conclusions from visual displays.

For all four datasets:

Property Value
Mean of each x variable 9.0
Variance of each x variable 10.0
Mean of each y variable 7.5
Variance of each y variable 3.75
Correlation between each x and y variable 0.816
Linear regression line y = 3 + 0.5x

Edward Tufte uses the quartet to emphasize the importance of looking at one’s data before analyzing it in the first page of the first chapter of his book, The Visual Display of Quantitative Information.

Related: Edward Tufte’s: Beautiful EvidenceSimpson’s ParadoxCorrelation is Not CausationSeeing Patterns Where None ExistsGreat ChartsPlaying Dice and Children’s NumeracyTheory of Knowledge

Dangerous Infinity

In this BBC documentary, Dangerous Knowledge, David Malone looks at four brilliant mathematicians – Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing – whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide.

The film begins with Georg Cantor, the great mathematician whose work proved to be the foundation for much of the 20th-century mathematics. He believed he was God’s messenger and was eventually driven insane trying to prove his theories of infinity.

They explore, among other things, varying levels of infinity. With Ludwig Boltzmann they explore challenges to the understanding of physics.

Related: BBC Dangerous Knowledge web sitePoincaré ConjectureProblems Programming MathCompounding is the Most Powerful Force in the UniverseInnovation with Math

Teen Tackles Centuries-old Numbers challenge

teen tackles centuries-old numbers challenge

A 16-year-old Iraqi immigrant in central Sweden has single-handedly figured out a formula with Bernoulli numbers that is normally reserved for much more seasoned mathematicians, earning him praise from professors at prestigious Uppsala University.

While it’s not the first time that someone has shown such Bernoulli number relationships, it’s highly unusual for a first year high school student to make his way through the complicated calculations, according to Uppsala University senior maths lecturer Lars-Åke Lindahl. “He’s a very clever guy,” Lindahl told The Local.

“What he did isn’t necessarily new, but it is quite remarkable for a first year high school student to take on these types of problems all on his own. It’s certainly an achievement.”

Altoumaimi plans to continue studying advanced math and physics over the summer. “I wanted to be a researcher in physics or mathematics; I really like those subjects. But I have to get better at English and social science,” he told Falu-Kuriren.

Related: Making Magnificent Mirrors with MathPlaying Dice and Children’s Numeracy1=2: A Proof

Mathematicians Top List of Best Occupations

These lists are basically silly but here is one sites opinion on the best occupations. I don’t really accept the methodology used as providing anything very meaningful about the “best jobs” but at least the spell it out. Best jobs

  1. Mathematician
  2. Actuary
  3. Statistician
  4. Biologist
  5. Software Engineer
  6. Computer Systems Analyst

Their criteria really value being able to sit at a desk and not having to do physical work. High salary and limited stress are also significant factors.

Related: The Economic Benefits of MathWho Killed the Software Engineer?Knowledge Is Power – Teaching MathThe IT Job Market in the UK

Making Magnificent Mirrors with Math

At Drexel, he designs amazing mirrors

Could math provide the path to better reflection? Perline asked.

Indeed it could. Eight years and numerous calculations later, Hicks is now testing a prototype mirror – for a car, not a bike – and he is in talks with a foreign manufacturer. As with the bike mirror, the rounded surface provides a wide field of view – so wide that it eliminates the dreaded, driver-side “blind spot” – yet the subtle mathematics of his design result in little or no distortion.

He didn’t stop there. The 42-year-old mathematician went on to design half a dozen other reflective surfaces for various applications – a few of them in collaboration with Perline – and they are like nothing you’d ever see on the bathroom wall.

Panoramic mirrors. Mirrors for use with high-tech surveillance cameras. Mirrors with odd, undulating surfaces that are fashioned with a computer-guided milling machine. And one wacky mirror that doesn’t yield a mirror image at all. If you raise one hand while looking into the curved surface, your reflection appears to be raising the opposite hand.

It’s not clear what use that one will have, beyond entertainment – Perline calls it “the vampire mirror” – but with his driver-side prototype, Hicks may be onto something.

Related: Innovation with MathThe Emperor of MathTimemath related posts

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