# Maths Faculty Podcasts

Back in the summer I, along with a number of other colleagues, recorded some video podcasts for themathsfaculty.org. These videos are designed for A-Level students and I gave two lectures: one on induction and one on trigonometric identities. (I was supposed to give a third on the Millenium Prizes but didn’t due to a back injury. The material I created for this will appear elsewhere – stay tuned!). The recorded videos can now be seen on the Maths Faculty website:

Here’s induction and here’s trig identities.

Look out for the great domino toppling sequence at about 1:56 in the induction video.

We did have problems recording as we did not have any tele-prompters and so I was always glancing at my notes rather than looking at the camera. If there is a next time I might just give the lecture without referring to notes. Makes it more natural.

Any feedback would be appreciated. Thanks!

I seem to be having problems with the links to both the video and to The Maths Faculty itself – when I click on either I get the Microsoft ‘waiting’ symbol for ever and ever! That is, the link ‘hangs’ as IT folk would say. I’ve done a ‘refresh’ by way of testing the connection to the server (i.e. Internet connection) and that wass fine. So it does look as if there’s a problem at The Maths Faculty end. If this can be sorted I’ll pass the link about induction on to people I know as I’ve recently been extolling the value of proof!

Well, I now have to say that I did get through to the site eventually – it didn’t hang indefinitely – but it did take a very long time, much longer than usual for opening broadband connections. I opened a new tab and put the site address directly into the browser which may have helped. I’ve passed the link to the video about induction to people I know via email and Facebook so we’ll see who comes back and what happens.

Well, responses not without interest. I’ve had a couple of replies to date – one from a friend in the teaching profession: her school only goes to GCSE and the video was reckoned over the head of pupils (although on another occasion a cast-off poster about the Solar System was popular). The other was an acquaintance at work to whom I’ve shown some maths topics: he liked it and appreciated being shown (even if he didn’t understand all of it) how real mathematics is done!

I shall be going to a Liberal Democrat Party meeting in WSM discussing education on 16/2/2012 and will take with me one or two of the easier exercises from ‘How To Think Like A Mathematician’ to show to speakers/politicos if I get the chance. I think you said elsewhere on this blog that you were going to have some research carried out on the value of emphasising proof in University level mathematics – any progress? I understand (surprise, surprise!) that there may be funding issues.

I still think that some of the exercises in HTTLaM could be managed by bright children quite a long way down the age range – to year 7 if not younger – sky’s the limit perhaps! More seriously perhaps you could get out a version or versions for the various stages of secondary education at least, starting with year 7’s. Less sure about primaries. I was doing proofs based on Euclid at a little private school from about age 11 or 12.

Talking of education I’ve found one way of making the ‘constant of integration’ actually mean something, rather than something you have to tack on in a rote, ritualistic and possiblhy meaningless way. Taking the 3 standard equations of motion we have:

1: a=9.81

2: v=u + 9.81t

3: s=p + ut + (9.81t^2)/2.

In other words, integrating twice with respect to t.

Now, in equation 2 I reckon the constant of integration translates as the ‘u’ term or initial velocity which could be zero, could be 100m/s etc.

In equation 3 (not seen it quoted quite like this) the constant of integration translates as the ‘p’ term or the initial position.

Just a thought on how the constant of integration could be made to make sense.

I’m aware we should really be expressing a, u and p as vectors, and also be including the ‘MLT’ units. Even so, I think the main point – actual real-life use of the constant of integration – is not changed. I’m afraid the character set on here’s a bit limited so I think the simplification’s justified to make the point. If you disagree – i.e. that I’ve missed something important to my argument re constant of integration – do let me know.

I’ve sent a telegraphese version of this to the Maths Faculty website (500 characters max. allowed).

Sorry – ‘WSM’ means ‘Weston-super-Mare’ in North Somerset which is where I live.