The Flying Colours Maths blog has been running posts twice weekly since 2012, covering maths from the basics to… well, the most advanced stuff I have a clue about.
Here they all are, sorted by date. Some day, other ways to filter them will be possible.
OK, so you’ve got to grips with the SUVAT equations, you’re on top of resolving forces, you understand that $F=ma$ and you have M1 under control… only for them to start throwing $\bi$s and $\bj$s around. Who ordered those? Maybe you have a vague recollection of vectors from GCSE - …
This month, @reflectivemaths (Dave Gale in real life) and I discuss: The birth of baby Bill (d’aww) Dave’s loyalty to More or Less, and nappies WBU ultra-loyalist [twit handle = “srcav”]’s comments on Episode 9 and a plea for reviews Whether to up our podcasting output …
A big hello to 2014! Last year was a fantastic year for me: I spoke at the Edinburgh festival, I ran the Berlin marathon, I had crosswords published in 1 Across… oh, and I became a dad for the first time. Cracking year. 2014 is going to struggle to top that. I have a few goals for 2014 that I …
I am - I confess - a professional purveyor of tricks. A mnemonic here, a shortcut there - whatever it takes to get my students the skills they need to get the grade they want. As such, I wasn’t expecting to enjoy Nix The Tricks, a free e-book offering alternatives to some common rules of …
In which @reflectivemaths and I find out which graphs have been naughty and nice. Hint: none of them are nice. Constable Gale blew a party streamer and I shot him a steely glare. “Are you hanging up your stockings on the waaaalll?” he crooned. “No, Gale. I am decidedly not hanging …
A few episodes of Wrong But Useful ago, Dave posed the problem: A regular unit heptagon1 has two different diagonal lengths, $a$ and $b$. Show that $a+b = ab$ Unusually, I didn’t blog a solution. Sorry about that. A hat-rack trick I’ve come up with two approaches, but wanted to showcase …
Integration by parts is one of the two important integration methods to learn in C4 (the other is substitution1 ). In this article, I want to run through when you do it, how you do it, and why it works, just in case you’re interested. When you use integration by parts Integration by parts is …
Doing long division is like going to watch Raith Rovers play: you can force yourself do it, but why would you? I’m not going to show you the long division way. It’s too much fuss to set out, and frankly I can’t be bothered with it. There’s a way I find much easier. …
Fittingly, I’m sitting down to write this review while Google celebrates the 107th birthday of Grace Hopper - one of the first computer programmers, and - reputedly - the first person to debug a computer (by removing a moth from a vacuum tube). She wasn’t the first computer programmer, …
A student asks: I’m currently getting a G in maths and I need to get a C within 6 months - what am I going to do? Help! I wish I had a magic bullet for you, but I’m afraid the bad news is you’ll need to work quite hard over the next six months to get your grade up. You can totally …
In Episode 9 of Wrong, But Useful, @reflectivemaths (Dave Gale in real life) and I (sounding a bit like a Dalek) discuss: MathsJam conference @johndavidread’s ideas on minches and mounds @srcav’s post on multiplication, Colin’s forthcoming post on division, and @robeastaway’s …
The 2012 PISA results came out yesterday, showing that the UK’s place in the world rankings has remained almost unchanged over the last three years. It struck me, listening to the Today programme in a half-asleep stupor (as is my cliched, lefty-academic morning routine) that I didn’t …
If you subscribe to the Sum Comfort newsletter, you might have picked up that I’m going to be a dad soon. I understand this will be pretty all-consuming for at least the next few months - which means I’m more than usually open to guest posts. Here are some guidelines you might want to …
Depending on your AS-level maths exam board, you might encounter the equation of a circle in C1 (OCR) or C2 (everyone else). It’s really just a restatement of Pythagoras’ Theorem: saying $(x-a)^2 + (y-b)^2 = r^2$ is the same as saying “the square of the horizontal distance between …
The gravitational slingshot is something I’d heard about but had never bothered to look up - until now. It sounded like magic: you fire a spaceship towards a planet and (then a miracle occurs before) it comes out moving faster. It’s how the Voyager spacecraft picked up enough speed to …
It’s nearly two years since I last tackled quadratics with a number in front. Recently, though, I stumbled on a slightly different method that’s a bit less involved. I won’t say it’s easier or better - different methods suit different people, after all - but I like it. …
I’m struggling with the simplex algorithm. How do I read the tableau at the end? And how do I pick the right pivot? The simplex algorithm - which is D2 for most students, but D1 if you’re doing OCR - is frequently listed as one of the top ten algorithms of the 20th century. It’s a …
One of the OTHER things I love about MathsJam is that I always come away with a notebook full of new ideas for posts. Most of them are indecipherable, but some stick in the mind. This one is based on a real-life dilemma posed by a friend of Elizabeth, which I’ve depoliticised slightly: …
In complaining that astrophysics was hard because of all the maths, a student recently told me: “The way it’s presented is: ‘OK, you get that $A+B=C$? Excellent. Now derive $DQH$, use a matrix to get $Y$, find $M$ by mysterious means. What? Why can’t you do that?” …
The Mathematical Ninja surreptitiously pressed a button under the table. There was a flash, a sizzle and a slight smell of burning. The student prodded the on-button of his calculator increasingly frantically. “Oh dear,” said the Mathematical Ninja. “It must have been a passing …
Because, well, what’s not to love? About 100 mathematicians gathered together to play with maths for a whole weekend. What, in all seriousness, could be better? There’s something fantastic about there being, in one room, probably about as much mathematical brainpower as the Manhattan …
In a recent Maths Challenge, students were told the area of a triangle ($7$cm$^2$) and the length of two of its sides ($6$cm and $8$cm), and asked how many possible lengths there were for the third side. It’s easy enough to show there are two: let the base of the triangle $AB$ be the $8$cm …
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 …
“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,” …
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 …
“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 work out $17 \times 24$. …
“… 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… …
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 …
This is an odd, out-of-sequence post, but I just saw this and thought it needed sharing. [twit handle=‘crypticpaul’] - 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 …
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 the …