The Flying Colours Maths Blog: Latest posts

The Mathematical Ninja and the Poisson Distribution

"What are the ch…" "About 11.7%," said the Mathematical Ninja. "Assuming $X$ is drawn from a Poisson distribution with a mean of 9 and we want the probability that $X=7$." "That's a fair assumption, sensei," pointed out the student, "given that that's what the sodding question says." A wiser student

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Ask Uncle Colin: Parametric Second Derivatives

Dear Uncle Colin, I have a pair of parametric equations giving $x$ and $y$ each as a function of $t$. I'm happy with the first derivative being $\diff{y}{t} \div \diff{x}{t}$, but I struggle to find the second derivative. How would I do that? – Can't Handle An Infinitesimal Nuance Hi,

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Sweet and Sour Limits

Eagle-eyed friend of the blog @robjlow spotted an error in Uncle Colin’s last answer. As I’m forever telling my students, making errors is how you learn; Rob has graciously delivered a lesson for us all. Thanks for keeping me honest! Recently, Uncle Colin gave a couple of ways to see

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Ask Uncle Colin: A Short, Sweet Limit

Dear Uncle Colin, What is $\lim_{x \to \infty} \left\{ \sqrt{x^2 + 3x} – x\right\}$? – Raging Over Obnoxious Terseness Hi, ROOT, and thanks for your very brief question. My approach would be to split up the square root and use either a binomial expansion or completing the square, as follows:

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Wrong, But Useful: Episode 43

In this month's installment of Wrong, But Useful, our special guest co-host is @mathsjem (Jo Morgan in real life) from the indispensable We start by talking about and how Jo manages to fit such a punishing blog schedule around being a nearly-full-time maths teacher. Colin wonders how writing

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The Mathematical Pirate and The Quotient Rule

"Arr, that be a scurvy-lookin' expression!" said the Mathematical Pirate. "A quartic on the top and a quadratic on the bottom. That Ninja would probably try to factorise and do it all elegant-like." "Is that not the point?" "When you got something as 'orrible as that, it's like puttin' lipstick

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Ask Uncle Colin: Approximating an embedded exponential

Dear Uncle Colin, Help! My calculator is broken and I need to solve – or at least approximate – $0.1 = \frac{x}{e^x – 1}$! How would you do it? — Every $x$ Produces Outrageous Numbers, Exploring New Techniques Hi, ExPONENT, and thanks for your message! That’s a bit of a

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The Mathematical Ninja lets the student investigate… cube roots

"Sensei! I have a problem!" The Mathematical Ninja nodded. "Bring it on." "There's a challenge! Someone has picked a five-digit integer and cubed it to get 6,996,364,932,376. I know it ends with a six, and I could probably get the penultimate digit with a bit of work… I just wondered

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Announcing: Ninja|Alpha

After several months of high-intensity development, we’re very happy to announce the launch of Ninja|Alpha. Go ahead! Ask it anything you like.

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Ask Uncle Colin: Why does the constant term vanish?

Dear Uncle Colin, When I differentiate $y=2x^2 + 7x + 2$ and apply the $nx^{n-1}$ rule, why do I only apply it to the $2x^2$ and the $7x$ but not the 2? — Nervous Over Rules, Mathematically A Liability Hi, NORMAL, and thanks for your message! There are several ways

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