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Physics with hidden calculus

Crossing campus this afternoon, a student whose exam is later this week asked me “when you ask a real-world question on the exam and you want us to solve an ODE, can we just do it using formula we memorised from A-level physics?” Like what? “Like with one of the distance questions we might just use $v^2 = u^2 + 2as$.” I said that if they were relying on a result we didn’t use in the module and that they hadn’t proven, this would be a problem.

In the latest Taking Maths Further podcast (Episode 19: Computer games and mechanics), we had a puzzle that we say could be answered roughly, but the precise answer 23.53 (2 d.p.) required a little calculus. On Twitter, @NickJTaylor said

π approximation: Machin’s formula

In the excellent $\pi$ approximation video, Katie Steckles asked for $\pi$ approximations. I teach a first year techniques module (mostly calculus and a little complex numbers and linear algebra). This year I have changed a few bits in my module; in particular I gave some of my more numerical topics to the numerical methods module and took in return some of the more analytic bits from that module. This gives both modules greater coherence, but it means I have lost one of my favourite examples, from the Taylor series topic, which uses a Maclaurin series to approximate $\pi$.

Ivor Grattan-Guinness 1941-2014

An obituary has been published in The Guardian for Ivor Grattan-Guinness, historian of mathematics and logic, who died of heart failure on 12th December 2014. This begins by explaining that when Ivor became interested in the history of mathematics in the 1960s,

it was an area of study widely considered to be irrelevant to mathematics proper, or something that older mathematicians did on retirement. As an undergraduate at Oxford, he found that mathematics was presented drily, with no inkling of the original motivations behind its development. So Ivor set himself the task of asking “What happened in the past?” — as opposed, he said, to taking the heritage viewpoint of asking “How did we get here?”

Read more: Ivor Grattan-Guinness obituary (The Guardian).

Via Dave Richeson on Twitter.

More to be done between universities and industry

I saw the video below, which is Rachel Riley being asked questions about her maths education at a Your Life event, in a tweet by Rob Loe, who quoted a section of one answer around 4:50 where Rachel says: “stop saying proudly that ‘I’m really bad at maths’ because you wouldn’t say ‘I can’t read’, you wouldn’t say ‘I can’t write’ as a proud thing.”

What particularly caught my ear was this section (around 5:30):