The Flying Colours Maths Blog: Latest posts

Ten great books to give an interested mathematician

Oh no! Your favourite mathematician has a birthday/Christmas/other present-giving occasion coming up and you don’t know what book to get them! They’ve already got Cracking Mathematics and The Maths Behind, obviously… so what can you give them this year? Fear not, dear reader. I am at hand to list some

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Ask Uncle Colin: Some Rigour Required

Integration by substitution, rigorously Dear Uncle Colin, Can you explain why integration by substitution works? I get that you’re not allowed to ‘cancel’ the $dx$s, but can’t see how it works otherwise. – Reasonable Interpretation Got Our Understanding Ridiculed Hi, RIGOUR, and thanks for your message. First up, confession time:

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The Mathematical Ninja and the Cube Root of 4

The student swam away, thinking almost as hard as he was swimming. The cube root of four? The square root was easy enough, he could do that in his sleep. But the cube root? OK. Breathe. It’s between 1 and 2, obviously. What’s 1.5 cubed? The Mathematical Ninja isn’t going

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Ask Uncle Colin: A Ridiculous Restriction

Dear Uncle Colin, In a recent test, I was asked to differentiate $\frac{x^2+4}{\sqrt{x^2+4}}$. Obviously, my first thought was to simplify it to $\br{x^2+4}^{-\frac{1}{2}}$, but I’m not allowed to do that: only to use the quotient rule and the fact that $\diff {\sqrt{f(x)}}{x} = \frac{f'(x)}{2f(x)}$. When Evaluating, Inappropriate Rules Demanded Hi,

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Factorising a large number, part II: Gaussian integers

You know how things escalate on Twitter sometimes? Somebody makes an off-hand comment wondering whether a number is prime and suddenly you’re neck deep in number theory? This is the story of how you might factorise 842,909 on paper. In fact, it’s the second part of the story; we join

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Ask Uncle Colin: a nasty integral

Dear Uncle Colin, How would you integrate $e^x \sin(x)$ (with respect to $x$, obviously)? – Difficult Integral, Just Kan’t See The Right Answer Hi, DIJKSTRA, and thanks for your message! As seems to be the way recently, there are several ways to approach this. My favourite way One of the

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Wrong, But Useful: Episode 60

In this month’s episode of Wrong, But Useful, we’re joined by Special Guest Cohost @macaronique, who is Angela Brett in real life. Angela recites her poem They Might Not Be Giants We discuss joy in teaching and learning, and crosswords Number of the podcast: 44, the number of derangements of

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Factorising a large number, part I: Sums of squares in different ways

There is a theorem that states: if a number can be written as the sum of two squares in two different ways, it is composite. Because of Twitter, I became interested in factorising $n=842,909$. Can this be written as the sum of two squares1? How – without cheating and using

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Ask Uncle Colin: A Differential Equation

Dear Uncle Colin, What’s the correct method to find the general solution of $y”+4y’+4y=(3+x)e^{-2x}$? I’ve got the complementary function just fine (it’s $y=Ae^{-2x}+Bxe^{-2x}$), but I’m going in circles with the particular integral. – Differential Equation’s Solutions Are Really Gruesome; Ugly Exponential Scariness Hi, DESARGUES, and thanks for your message! I

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Review: Hello World, by Hannah Fry

The best science writers (as far as I’m concerned, at least) are the ones who make you feel like you’re sitting down for a coffee with a smart friend, excited about a thing they know about, a thing they’ve found out, or a thing they’ve just put together. I have

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