Archive for the ‘maths’ Category

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If you believe you can get better at math through hard work, you’re more likely to do so

30 October 2013

scaryM

Quartz is a digital news channel on economics and business. Two academics have written an interesting story in it about ability and achievement at mathematics.

People’s belief that math ability can’t change becomes a self-fulfilling prophecy.

For almost everyone, believing that you were born dumb—and are doomed to stay that way—is believing a lie. IQ itself can improve with hard work.

They found that students who agreed that “You can always greatly change how intelligent you are” got higher grades.

Math education, we believe, is just the most glaring area of a slow and worrying shift. We see [the USA] moving away from a culture of hard work toward a culture of belief in genetic determinism.

This problem happens outside the US too. I know a lot of people who believe they’re just naturally bad at maths. They seem resigned to it. The research – and professor anecdotes – presented in the article suggests that’s not the case.

It’s a shame then that people believe they’re just innately, genetically, unsuited to mathematics. In today’s high-tech world not being able to speak the language of science, technology, finance, and engineering means you’ll never understand what’s under the hood. And you’re probably limiting your well-paying career choices, if that’s important to you.

I’ve always been prejudiced towards mathematics but I’ve been reminded of its importance in the last couple of weeks during my Interactive Python course. People in the discussion forums for that course are complaining because while they expected to learn a new programming language they didn’t expect to have to understand and apply modulo operations and logarithms. But you need to use these concepts to create on-screen graphics and interactive elements in event-driven programming.

Maths is important. If you think you can’t do it you’re probably wrong.

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Another Coursera course completed: Introduction to Mathematical Philosophy

2 October 2013

I finished my second free online Coursera course last week: Introduction to Mathematical Philosophy.

It was a pretty intense and esoteric 8 weeks. Taught by two professors from Ludwig-Maximilians-Universität München it was not about the philosophy of mathematics. Instead it showed how some areas of philosophy can be made more precise by using mathematical language and techniques.

It’s hard to give simple examples but we identified axioms that indicate whether people are being consistent and logical in their judgment of probabilities, wrote formulae for indicative and subjunctive statements, expressed Bayes theorem and confirmation theory, defined sample metalanguages, used set theory to define possible worlds, and used different voting methods to determine group preferences.

lmu

I found it interesting and fun. Brain challenges are enjoyable. And the two professors obviously love the topic in an adorably nerdish way.

I passed, with a 79% grade on my first attempt at the final exam (worked up to 95% in later attempts; we had five). But the course creators admitted the exam is a bit of a formality; the course was to get people interested in the topic.

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Coursera: Data Analysis final grade

24 March 2013

The grades are in for the Data Analysis course I completed recently on Coursera: I passed quite easily with a score of 88.8%. Yay me!

completion grade

However, the minimum score for a pass with distinction was 90%. AAARRGGGHHH!

Never mind. I had a lot of fun, and learned an immense amount. It’s not like this certificate is actually recognised as a formal qualification by anyone, nor do I need it for my job.

But I was so close.

The professor released a few course stats, and they are impressive numbers:

  • There were approximately 102,000 students from around the world enrolled in the course at the start.
  • About 51,000 watched the lecture videos.
  • About 20,000 did weekly online quizzes.
  • About 5,500 did the two data analysis assignments.

There’s no word yet if Coursera is going to offer this course again. If you want to torture yourself with data analysis you can already do so, though:

  • All the lecture videos are on YouTube.
  • All the lecture notes are on Github.

You can also watch a podcast to hear Jeff, our professor, share his thoughts on the first-time experience of teaching a massive open online course (MOOC). The key points for me:

  • He purposely made the course difficult.
  • The biggest challenge was the immense heterogeneity of students (i.e., how different we all were).
  • The message boards were really helpful and interesting, as they give students more time to explore ideas.
  • The message boards were like any other on the internet in that some people are great and some people are jerks and most are in between.
  • He knew there would be problems with peer grading but there was really no other way to grade assignments.
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Coursera: Data Analysis complete

14 March 2013

I just finished an 8-week online data analysis course that challenged my brain more than has been done in a very long while. I wrote about this course on my personal blog some weeks ago. Now that I’ve completed it I’ve realised that discussing it definitely belongs here in my science blog.

I took it via Coursera, a relatively new online source of free, compressed, university-level training. The quality of educators involved is very high. My course in data analysis was taught by Jeff Leek, a Ph.D. and associate professor in biostatistics at Johns Hopkins University.

coursera

The course was much harder than I expected. I mentioned that after my first week, but it got really difficult later on. I had to learn a whole new statistical programming language (R), build on a lot of stats I took at uni many years ago, and learn many advanced numerical concepts besides. Moreover we learned how to know when to use different techniques; it becomes an art as much as a science.

We had to do an online multiple-choice quiz each of the eight weeks, and two lengthy written peer-graded assignments. The assignments were quite practical: for example, use Samsung phone accelerometer data to predict, from phone sensor readings, whether the person holding it is sitting, walking, standing, etc.

It will be a few more days before I get the score for the final assignment but I did well enough to know that I’ve passed already regardless of that grade. I’m hoping (though not expecting) to get a pass with distinction.

One of the best parts of the Coursera platform is that there is an extensive discussion forum for each course. It was like having a virtual study group of thousands of people around the world to bounce ideas off of, discuss the lectures, brainstorm how to tackle the assignments, and chat and bitch about the difficulty. There were plenty of people who felt entitled and complained about errors or things that were unclear. I was of the opinion that those people needed to think about how they were taking a detailed course of great complexity from a globally-recognised expert over the internet for free.

I’m planning to take another Coursera course later in the year; topic is to be determined. I recommend it highly, but caution those who think it will be a simple pastime.

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The Monty Hall Problem

5 June 2012

Someone tried to trick me the other day with the Monty Hall Problem. Luckily I’d come across this counter-intuitive puzzle before, nyah nyah.

It is one of my favourite illustrations of probability.

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Google Adds Graphical Math Calculator To Search Results

6 December 2011

This is awesome! Enter a function in Google’s search bar and it’ll display that function plotted on a graph.

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Google goes maths crazy

17 August 2011

Google seem to be cementing their “mad genius” status. Not content with seizing control (i.e., buying Motorola mobile and therefore obtaining 30% of the North American Android market they kicked off) they seem fixated on mathematics.

Last month they bid the digits of pi in the auction for Nortel’s patents.

Now today the Google search page doodle image is an homage to Fermat’s Last Theorem (it’s the anniversary of Fermat’s birthday).

I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain.

I can hear cackling behind those castle walls, I tell you.

 

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Why I Love Science: Arithmetic at the maple house

12 July 2011

As a kid I worked the retail counter at my parents’ maple syrup business (very Canadian, I know). We’d total up people’s sweet purchases, take their money, and make change for them.

Customer after customer, and I eventually got accustomed to doing this arithmetic in my head. I came to recognise how those numeric gymnastics represented stuff that happened in the real world; that they were a language that described things (like a litre of maple syrup) and processes (like summing amounts for a total purchase). Math became visual in my head.

That visualisation only increased when I started playing around with the calculators we used for those retail transactions. I found the squaring function especially  mesmerising. Square 2 and you get 4. Square 4 and you get 16. Small potatoes. But square 16 and suddenly you’re off: 256. Square 256 and you’ve got a number that’s suddenly out of the range of a kid’s conception: 65,536. From there the numbers got so big so fast it made my head spin.

Those transactions at the maple counter were how I came to love numbers and mathematics.

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Bees easily solve the Travelling Salesman maths problem

26 October 2010

There’s a mathematical optimisation problem called the Travelling Salesman problem. The problem is: if a salesman has to visit several cities, what’s the shortest route he can take to visit them all? There are numerical methods to solve these sorts of problems, and they can take a long time, even with computers.

Researchers at the University of London have found that bees learn to solve these problems pretty quickly, though. They do so as they visit flowers, figuring out the optimum routes between them, despite having only tiny little brains. Maybe those brains have evolved this one really useful (for them) capability.

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Maths problems

19 September 2010

Someone posed me a maths problem the other day, one that their sixth-grade son had had difficulty with. Turns out he’d had difficulty, too. It struck me that simple arithmetic and unit conversion are handy skills to have.

The question was along these lines:

You’re in a large 70 metre squared room. You drop a big bag of tiny marbles on the floor. You see that 3 marbles fit in 1 square centimetre. If you assume that the marbles cover the rest of the room in the same proportion, how many marbles are in the room?

Okay, so it’s a ludicrous setup. But they’re looking for understanding. And you need to understand two main things here:

  1. That the term “squared” means the room is square and 70m on each side.
  2. That there are 100cm in 1m.

So if the room is 70m by 70m, then it’s also 7000cm by 7000cm. That means its area is 49,000,000cm². If each of those square centimetres has 3 marbles in it, then there are 147,000,000 marbles in the room.

The question the young man was posed had three multiple choice answers. None of the answers was close to what I just calculated. I’d like to see the teacher show her work.

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NYC transport on a spreadsheet

6 June 2010

Many who know me – especially those who know me professionally – know that I love a spreadsheet. It’s perhaps unsurprising that an engineer who loves maths is tickled by all those figures and calculations and charts. But I really do love ‘em. I put everything work-related into spreadsheets. The orderliness appeals to me, and because it’s easy to manipulate and chart the data (even if that’s only a possibility later). I’m one of those guys people in the office go to when they have a spreadsheet question.

I put my personal life into spreadsheets, too: lists of the CDs I own (when I bought them) and flags and calculations for how many of the artists I’d seen live. Inventories for insurance purposes. Task lists for moving. Christmas gift lists. I wrote a program to calculate beam deflections in grad school with spreadsheet macros.

I love spreadsheets.

Yesterday I read a Wired article about Charles Komanoff, a traffic expert, who has modelled “the economic and environmental impact of every single car, bus, truck, taxi, train, subway, bicycle, and pedestrian moving around New York City” in an effort to create the optimum set of tolls and flows. And he’s done it all in an Excel spreadsheet. If you read that article there’s even a link where you can download the spreadsheet itself.

That’s so hot. I’m serious, it’s so amazing.

It’s got 50 tabs. Everything’s well-documented (a key element if you want to share your spreadsheet with others). It may be a bit pie-in-the-sky to expect Americans to accept Komanoff’s vision, which would implement several public road tolls around the city. But I am in awe of his dedication, organisation, and capacity to numerically model what is an inherently chaotic system.

Fragment of the NYC traffic spreadsheet. Click to enlarge.

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The difference between science and art

2 June 2010

From SMBC comics:

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First Maths Museum opens in the US

17 May 2010

Mathematician Glenn Whitney has opened America’s first math museum in New York. With interactive exhibits, too.

Read about it on ScienceBlogs.

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Aussie Insider: Pi calculated to new length

8 January 2010

I’ve received several blogworthy tips from my good pal The Aussie (who – ironically, now that I’m living in Sydney – lives in London). This is the first of four daily posts thanks to him.

From the BBC:

A computer scientist claims to have computed the mathematical constant pi to nearly 2.7 trillion digits, some 123 billion more than the previous record.

Fabrice Bellard used a desktop computer to perform the calculation, taking a total of 131 days to complete and check the result.

Pi has served as more than just a simple but lengthy constant, however.

“People have used it as a vehicle for testing algorithms and for testing computers; pi has a precise sequence of digits, it’s exactly that, and if your computer isn’t operating flawlessly some of those digits will be wrong,” he explained.

Click to enlarge.

Image from Flash Cafe

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The Royal Society’s 2009 Summer Science Exhibition

30 June 2009
Penrose tiling: how nature and art fill spaces

Penrose tiling: how nature and art fill spaces

If you’re in central London tonight, or during the day this week, you should find a few moments to stop by The Royal Society. The national academy of science of the UK and the Commonwealth is staging their Summer Science Exhibition. Not only are they putting on a week of exhibits from the cutting edge of science but also featuring involved scientists themselves for you to ask questions of.

What a cool opportunity. This is a direct public-engagement event. You can look at items and exhibits and models lots of places, but how often do you get a chance to ask questions of a real, live scientist? There’s a list of exhibits here, along with writeups that indicate which ones might be good for kids.

From their site:

We’ve got over 20 fascinating, diverse and interactive exhibits. Fields of study range from how fluorescent fish could provide better understanding of human diseases, to a chewing robot that can help us develop dental technology, to how new space missions could help to unlock the history of the universe.

There’s also a good writeup at Nature Network’s London blog about the exhibition.

You can find info on how to get there and what their hours are here.

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Cannes film festival falls in love with maths

18 May 2009

Hypatia of Alexandria was an ancient Greek mathematician, most notable for being the first famous female maths scholar. In addition to writing commentaries on and editing some of the most famous early works of maths, like Arithmetica and Euclid’s Elements, she’s said to have done work in astronomy, measuring the relative density of liquids, and possibly independently developing an astrolabe.

A new film – named Agora – based on the life of Hypatia, who’s played in the movie by Rachel Weisz, has received big cheers at Cannes. That’s pretty cool: Greek mathematicians aren’t your typical silver-screen subjects.

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Advances in maths strengthen IT security

16 May 2009

Another interesting ScienceDaily article, this one about mathematics and IT security methods.

Cryptography – the science of hiding information – is used to secure internet communications and commerce. Most internet cryptography uses a technique called RSA which relies on the difficulty inherent in determining factors for very large integers.

In recent decades mathematicians have developed techniques using elliptical functions to more easily do large-number factorisation. While this implies RSA encryption is easier to break using these methods, salvation has come from those same elliptical functions. They can themselves be used as a form of encryption.

In recent years this elliptic curve cryptography has gained attention. Since it’s newer it’s not prone to the majority of crypto-attacks, which have been developed to attack RSA. But it’s also been shown that you can get the same level of protection with elliptical encryption by using a much smaller encryption key than is needed for RSA. This makes it more computationally efficient, and helps keeps ahead of those who would attack and break those systems of protection.

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Math is funny

6 March 2009

From xkcd:

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More math fun

4 March 2009

From Boing Boing:

  • Yesterday (03/03/09) was Square Root Day (that is, the day when both the day and month number are square roots of the two year digits).
  • A week from Saturday (03/14) is Pi Day, but only in stupid North American mm/dd format.
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World Maths Day

4 March 2009

March 4th is World Maths Day.

Celebrate with some real-life math problems!

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