October, 2013

A reader asks… about matrices

A reader asks: I know that a square matrix $\mathbf{M}$ maps point $\mathbf{x}$ to point $\mathbf{y}$. Do I have enough information to work out $\mathbf{M}$? In a word: no, unless you’re working in one dimension! In general, to work out a square transformation matrix in $n$ dimensions, you need to

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Normal distribution – but fast! Secrets of the Mathematical Ninja

“A $z$-score of 1.4,” said the student, reaching for his tables. “0.92,” said the Mathematical Ninja, without skipping a beat. “0.9192,” said the student, with a hint of annoyance. “How on earth…” “Oh, it’s terribly simple,” said the Mathematical Ninja. “It turns out, for smallish values of $z$, the normal

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Wrong, But Useful: Episode 8

In this month’s Wrong, But Useful, @icecolbeveridge (Colin Beveridge in real life) and @reflectivemaths (Dave Gale when he’s at home)… … completely forget about the Maths Book Club, which was going on during the recording; … get all excited about the MathsJam conference on the weekend of November 2nd-3rd …

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Why $17 \times 24$ isn’t 568

“You would not be certain that $17 \times 24$ is not 568.” – Daniel Kahneman, Thinking Fast And Slow Thanks to Alice for pointing out that yes, she bloody well would. Most people under 50 in the UK would reach for a calculator, or possibly a pen and paper to

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Why you don’t add across probability trees – Secrets of the Mathematical Ninja

“… Evidently not,” said the student, with a look of sheer terror that was music to the Mathematical Ninja’s eyes. He smiled a nasty smile. “No,” he said, “you categorically do not add probabilities as you go through the tree.” “You… multiply?” The student was cautious. The Mathematical Ninja hadn’t

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The geometry of $sec$

Ask virtually any maths teacher what $\sec(\alpha)$ means, the chances are they’ll say “it’s $\frac{1}{\cos(\alpha)}$,” without missing a beat. Ask them what it means geometrically… well, I don’t want to speak for the teaching profession as a whole, but I’d have been stumped until the other day. As with the

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John Halpern’s TEDx talk on crosswords

This is an odd, out-of-sequence post, but I just saw this and thought it needed sharing. – John Halpern in real life – is one of my heroes. I’d rate him comfortably among the top five crossword compilers in the UK (possibly the world), and not just because he has

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The Mathematical Ninja gets mean

Chair: If ‘good’ requires pupil performance to exceed the national average, and if all schools must be good, how is this, how is this mathematically possible? Michael Gove: By getting better all the time. Chair: So it is possible, is it? Michael Gove: It is possible to get better all

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Dividing by 42 – Secrets of the Mathematical Ninja

In honour of ‘s birthday this week, here’s a post with a vaguely Douglas-Adams-related theme. The student looked at the Mathematical Ninja and decided this was a moment where reaching for the calculator would be appropriate. “$\frac{29}{42}$…” she said aloud. “0.69,” said the Mathematical Ninja. She threw the calculator down

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The Bayesian umbrella

At a recent MathsJam, there was a puzzle. This is nothing out of the ordinary. It went something like: If an absent-minded professor takes his umbrella into a classroom, there’s a probability of $\frac{1}{4}$ that he’ll absent-mindedly leave it there. One day, he sets off with his umbrella, teaches in

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