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

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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.

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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.

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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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