November, 2016

Ask Uncle Colin: A Rational Mess

Dear Uncle Colin, I've got a ratios question, and I don't understand the solution. The question is: Three numbers, $x$, $y$, and $z$, have a sum of 871. The ratio $x:y$ is 4:5 and the ratio $y:z$ is 3:8. What is the value of $y$? Their solution is to say

How The Mathematical Pirate Integrates By Parts

The student sighed. "$\int x^3 e^{-2x} \dx$", he said. "That's going to be integration by parts. And it's going to take three steps. What a pain." "Aharr!" swashbuckled the Mathematical Pirate. "That's what you think!" "It is what I think," said the student, slightly bemused. "Would you like to know..."

Ask Uncle Colin: Should I Interrupt?

Dear Uncle Colin, Sometimes, my professors write wrong things on the board, and I'm never sure whether to correct them. On one hand, I feel like I should respect them and their work; on the other, if I say nothing, I worry that my classmates are getting bad information. What

Wrong, But Useful: Episode 38

It’s your annual Wrong But Useful Big MathsJam Special! Recorded live, so the audio is a bit shaky in parts. @icecolbeveridge, @reflectivemaths and @peterrowlett discuss Tantrix with some excited background chatter Colin interviews @teakayb (Tom Briggs in real life), who’s at MathsJam with an Enigma machine @pecnut and @mscroggs (Adam

Ask Uncle Colin: Dividing by decimals

Dear Uncle Colin, A question came up asking me to work out $4.5 + 1.5k = 18-3k$. Obviously, I can rearrange that to get $4.5k = 13.5$ - but how can I divide by 4.5 without a calculator? - Calculating A Number Turning On Ratio Hi CANTOR, and thank for

This is a guest post from Mark Ritchings, a maths tutor in Bury. A quadratic sequence is a sequence for which the $n$th term is $an^2+bn+c$. The constants $b$ and/or $c$ might be zero but $a$ definitely isn't. The first term is $a\times 1^2 +b \times 1 + c = Read More Ask Uncle Colin: is there a link? Dear Uncle Colin, I noticed the sum of an arithmetic series and the formula for the area of a trapezium were very similar. How are they related? - Watching Every Interesting Equation, Recognised Something Trapeziumesque Regarding Arithmetic Sequence Sums Hi, WEIERSTRASS, Indeed, they are related, as you can see from Read More How do you estimate the normal distribution for large$z$? In working out a recent blog post, I had cause to find the probability, in a standard normal distribution, of$z < -23$. Beyond "that's a REALLY SMALL NUMBER"1, I was stumped. Could I get anywhere close mentally? A good question. Starting from the definition of the normal distribution,$p(z)

Dear Uncle Colin, Is there a reason you don’t use "Dr" in your author name? - Presumably Has Doctorate Hi, PHD! Thanks for your question. Yes, there are several reasons. The one I usually give is that my bank calls me Dr Beveridge and it makes me uneasy. It's also