Podcast: Episode 32 – Maths news with Sarah Shepherd

These are the show notes for episode 32 of the Travels in a Mathematical World Podcast. 32 is the number of panels in the spherical polyhedron corresponding to the Archimedean solid the truncated icosahedron which is the most popular design of a modern football. More about the truncated icosahedron from Wolfram Mathworld. More about 32 from Number Gossip.

This week on the podcast I met Sarah Shepherd, PhD student at the University of Nottingham and Editor of iSquared Magazine and we discussed some maths news. Links to all the articles we mentioned are below.

May saw the general release of Wolfram|Alpha, a computational knowledge engine. For a general overview read “Wolfram ‘search engine’ goes live” from the BBC or a little more detail from “Ask Alpha: Quizzing the world’s first answer engine” from New Scientist or “Where does Wolfram Alpha get its information?” from The Guardian. You can read the BBC’s Rory Cellan-Jones investigation “Does Wolfram work?” Read about the first week of operation on Stephen Wolfram’s blog post “The First Week of Wolfram|Alpha: Thank You!”. You can read my blog post when I was playing around with Wolfram|Alpha.

A mobile phone comparison site powered by statistical analysis has become the first of its kind to be accredited by Ofcom, the communications regulator. You can read about this in “Academics tot up costs of mobiles” from the BBC or “BillMonitor comparison site rings Ofcom’s bell” from the Guardian.

The Guardian talks to Paul Wilmott, a financial mathematician who claims to have seen the credit crunch coming and has fairly strong views on who is to blame. Read “Number cruncher who foresaw financial crash.”

The inaugural Christopher Zeeman medal, jointly awarded by the Institute of Mathematics and its Applications and the London Mathematical Society and named in honour of Sir Christopher Zeeman, is to be awared to Professor Ian Stewart FRS. Read “It all adds up to connecting with people about numbers” from Times Higher Education.

On 15 May 2009, the Royal Society elected 44 new Fellows and 8 Foreign Members. I spotted 3 in maths – Professor Jonathan Peter Keating FRS, Professor Burt James Totaro FRS, Professor Yakov Sinai ForMemRS – plus 3 other using maths – Professor (John) Michael Batty CBE FBA FRS, Professor (Oscar) Peter Buneman FRS, Professor Angela McLean FRS. You can read profiles of all new Fellows and Foreign Members on the Royal Society website.

On six degrees of seperation, following the BBC programme, you can read “How Kevin Bacon sparked a new branch of science” from the BBC. You can read a general overview of the mathematical topic and its links to popular culture from Wikipedia. The BBC experiment sending packages to Boston is based on a study from the 1960s; you can read more about this and a later attempt to recreate this via email at “E-mail Study Corroborates Six Degrees of Separation” in Scientific American. There is a piece covering the small world phenomenon in Plus “Rap: rivalry and chivalry

You can read the article from the New Scientist which covers quantum computing and game theory, “Quantum poker: Are the chips down or not?

On films, Sarah mentions “Fermat’s Room” and I talk about “Agora“. You can read about the impact of the latter at Cannes in “Cannes film festival falls in love with maths” from the Guardian.

On improved weather forecasting, you can read “Met Office unveils supercomputer” from the BBC.

I mentioned Marcus du Sautoy’s Sexy Maths column in the Times. Recent editions at the time of recording were “A game of 12 pentagons: Why a football match is actually geometry in motion” and “In search of the poetry of Muslim symmetry.”

You can find out more about iSquared Magazine on the iSquared website.

You can find out more about my work with the IMA by following me on Twitter, reading this blog and visiting http://www.ima.org.uk/student/. Join the Facebook page.

Podcast: Episode 31 – Matt Parker, Maths communication

These are the show notes for episode 31 of the Travels in a Mathematical World Podcast. 31 is the earliest and the only known case such that the sum of the divisors of two distinct numbers (16 & 25) is the same prime quantity (31), that is to say: 1+2+4+8+16 = 31 and 1+5+25 = 31. More about 31 from Number Gossip.

Not too long ago I spoke to the Maths Promotors Network about New Technologies, including podcasting. As part of this I made a live podcast recording with Matt Parker. Matt talked and gave examples of how he communicates maths to enthuse school students. After the ‘show’, Matt gave another example of an exercise he does with students and gave some advice on getting into maths communication and teaching.

During this recording Matt swallows helium and sulfur hexafluoride, which both affect the voice in comedic ways. For more fun with sulfur hexafluoride, check out “Ship floating on nothing!” You can find out more about maths humour (probably more correctly, math humor) in the Simpsons at SimpsonsMath.com. You can read an introduction to the UK National Lottery and its odds at Plus.

A good starting point if you are interested in teaching or the Student Associates Scheme is the TDA website. You can find out about more maths grads on the project website and see some of their output on the Maths Careers website.

You can find out more about my work with the IMA by following me on Twitter, reading this blog and visiting http://www.ima.org.uk/student/. Join the Facebook page.

Maths Promotion and new technologies

Last week I went to a meeting of the Maths Promotors Network in London which had a focus on use of new technologies in mathematics promotion. I spoke at this, giving an introduction and contributing to panels on social networking (with Noel-Ann Bradshaw of the University of Greenwich and Meetings Co-ordinator of the British Society for the History of Mathematics) and podcasting (with Marianne Freiberger of Plus). The third panel was on social networking and featured Zia Rahman of more maths grads and Richard Browne of MEI.

I found the day very enjoyable with some interesting discussions about the use of these technologies. I spoke about the Maths Prom Network and how it can work to promote interesting activities. In the social networking panel Noel-Ann Bradshaw talked about use of Facebook for maths at Greenwich and the Who invented Mathematics? group, while I spoke about my use of Twitter and the IMA’s use of social networking sites Facebook, MySpace and LinkedIn. In the podcasting session I gave the amateur point of view and made a live podcast recording with maths communicator Matt Parker which will appear, all being well, as episode 31 at the weekend and Marianne Freiberger spoke about the more professional version of podcasting you get with the Plus podcast.

The meeting was well attended and I am listing below a few links I collected to interesting people and their work. I encourage you to explore these links to find interesting content.

Zia Rahman works for more maths grads and contributes to the Maths Careers website, which I hope readers of this blog will know is an encyclopedic resource relating to careers information in mathematics.

Sarah Shepherd edits iSquared Magazine, a popular maths magazine that is well worth a read. Sarah contributes to the regular maths news features on the Travels in a Mathematical World podcast.

Richard Browne works for Mathematics in Education and Industry who are a body committed to mathematics education and publish newsletters, reports and interesting maths resources including the “item of the month feature“. Sue de Pomerai works for MEI’s Further Maths Network, whose website has information about further maths, CPD and other items.

Charles Goldie is Emeritus Professor in the Department of Mathematics at the University of Sussex and General Secretary of the London Mathematical Society.

Marianne Freiberger edits Plus, an online maths magazine including a podcast.

John Sharp is co-organiser of the Maths-Art Seminars at London Knowledge Lab, whose website includes seminar announcements and video streaming of many previous talks. John is also involved with Bridges, an initative which includes an international maths art conference whose website has pages on exhibitions. John’s work in this area is the subject of episode 24 of the Travels in a Mathematical World podcast.

Sara Santos works for the Royal Institution of Great Britain. The website is search based and visitors are encouraged to search for “mathematics”, “magic of mathematics” and “calculating colours”.

The meeting was hosted by Caroline Davis of the Maths Promotion Unit.

Podcast: Episode 30 -Noel-Ann Bradshaw, Ramanujan

These are the show notes for episode 30 of the Travels in a Mathematical World Podcast. 30 is the largest number with the property that all smaller numberscoprime to it are prime. More about 30 from Number Gossip.

In the regular Maths History series, Noel-Ann Bradshaw of the University of Greenwich and also Meetings Co-ordinator of the British Society for the History of Mathematics talks about Ramanujan. You can read a biography of Ramanujan at the MacTutor History of Maths Archive.

You can find out more about my work with the IMA by following me on Twitter, reading this blog and visiting http://www.ima.org.uk/student/. Join the Facebook page.

N.B. Correction (26/05/09): In this episode Noel-Ann makes a slip of the tongue, saying “G.K. Hardy” which should be “G.H. Hardy”. We’re sorry!

Wolfram|Alpha: Sometimes answering the question misses the point

Wolfram|Alpha was released today. This is a fascinating piece of technology and I am trying to work out how I feel about it. If you don’t know what it is, for a general overview you could read “Wolfram ‘search engine’ goes live” from the BBC or a little more detail from “Ask Alpha: Quizzing the world’s first answer engine” from New Scientist. The technology enthusiast inside me is giddy with excitement but there is a little voice inside me crying caution.

It doesn’t do everything very well yet. For example, it knows “number of people in Nottingham” but not “number of bars in Nottingham” (it doesn’t know how to relate the unit “bars” to a city). But that’s not really the point, we should be interested in potential here. I am interested in how it handles maths particularly and in whether when it fails to answer a question this is because it never can or just can’t yet.

I have been typing in some questions from a ‘fun’ maths quiz used at the University of Nottingham on open days. I shouldn’t list too many here (as they should remain useful!) but an interesting situation has occurred.

One question asks “What is the difference between six dozen dozens and half a dozen dozens?”

It’s a slightly silly question and I’m sure there are more mathematical examples, but I immediately wonder if it could be answered with no knowledge (or, importantly, without acquiring the knowledge) of what a “dozen” is.

I tweaked the question and got a correct response from “difference between half a dozen dozens and six dozen dozens.” I now know the answer is 792 and at no point have I either found out (or been told) what a dozen is.

[An aside: On the subject of an unfinished product: Strangely, “difference between six dozen dozens and half a dozen dozens” (the other way around) doesn’t work. Interestingly, “six dozen dozens minus half a dozen dozens” produces an erroneous result, by implying a bracket in the wrong place. It interprets it as “six dozen times (one dozen minus half a dozen dozens)”. Seems it needs to learn BIDMAS/BODMAS]

This example is merely illustrative. However, I wonder if there are situations where an answer (with “working”) can be received via Wolfram|Alpha by typing key phrases from a coursework question and that answer is completely satisfactory to the assessment method (and marker) but the student has at no point understood what is being asked or what is to be learned. Mind you, as Adam Partridge (AdamJTP) points out to me on Twitter, this is not too different from the many many university students up and down the land who are currently cramming ‘knowledge’ into their heads which will only remain for a few hours while they get through their exam.

The other caveat is that the same answer can be obtained through a Google search for “difference between half a dozen dozens and six dozen dozens” and the student is only slightly more likely to find out what the term means.

So perhaps it doesn’t matter. Google does stuff like this, we’ve had computer algebra for years and Wolfram|Alpha doesn’t work all that well anyway. But, remembering this is a first look at a new type of technology, it makes me uneasy.

Another question gives me another example: “The diameter of a circle of circumference 1 is…?” Wolfram|Alpha makes light work of “the diameter of a circle of circumference 1” (even gives a nice little diagram), a question Google doesn’t cope well with. It is very easy to plug the text of this question into Wolfram|Alpha and get an answer, without the student having to muck out developing an instinct for the properties of a circle. Another example you might give a student to tease out an understanding of the relationship between circumference and diameter is “the diameter of a circle of circumference 12 pi“.

I am glad it doesn’t seem to know how to “list pairs of prime numbers which sum to 999“, a neat little trick I picked up from Math_Bits on Twitter and used successfully with students in York. I am using questions here that are quite basic because Wolfram|Alpha isn’t doing so well with more involved questions – but in many cases there’s no reason it shouldn’t be able to in time. But I think the point I am trying to make here is that sometimes we ask questions so that the student will learn something while thinking about the answer (and the actual answer is immaterial).

In the same way that skill at mental arithmetic shortcuts (and corresponding easy familiarity with numbers) is largely lost in my generation by use of calculators, I worry what this means about more advanced maths. Still, perhaps my unease is just a sign I am getting old and all this means is that questions which explore mathematical concepts need to be better crafted, which we (should) know anyway.

Of course this technology isn’t going to go away. It is a fascinating device for the betterment of humanity and such is progress. But it might force a change in the way certain concepts are taught/learned.

How many of your questions are answerable by Wolfram|Alpha with no need for understanding? Rather, give Wolfram|Alpha your assessment – how well does it score?

Podcast: Episode 29 – Noel-Ann Bradshaw, Evolutionary algorithms for financial applications

These are the show notes for episode 29 of the Travels in a Mathematical World Podcast. 29 is prime, the 29th power of two is the largest power of two to have all different digits. More about 29 from Prime Curios.

Regular listeners will know Noel-Ann Bradshaw as the regular contributor of the maths history features on the podcast. Noel-Ann is a PhD student at the University of Greenwich and this time we hear from Noel-Ann about her research.

You can read a reasonable overview of evolutionary algorithms at Wikipedia. There is an introduction to the portfolio selection problem, portfolio optimisation demo and example of a mathematical formulation at Northwestern University. You can find out more about working in the areas touched on by this episode by looking at the finance career profiles, IT and computers career profiles and postgraduate study sections of the Maths Careers website.

You can find out more about my work with the IMA by following me on Twitter, reading this blog and visiting http://www.ima.org.uk/student/. Join the Facebook page.

The use of Careers Advisory Services

My response to “Careers Advisory Service any use?“, which is in response to “Is careers advice up to the job?“.

a) Students don’t realise the value of the Careers Advisory Service while they’re at uni. I spoke to one University Careers Advisor who said he has friends who do exactly what he does but charge huge consultancy fees for it whereas his students get it for free and don’t value it.

b) For a long time I was cross with the careers advice given to mathematicians – in a lot of places students are just shown the “Finance” boxfile. But then I realised: if you’re going to give maths students the full range of options open to them you will end up throwing half the careers library at them and they will drown in information overload. Now I tell students to check out some careers profiles on the Maths Careers website (www.mathscareers.org.uk), Plus Careers Library (http://plus.maths.org/interview.html) and my podcast Travels in a Mathematical World (www.travelsinamathematicalworld.co.uk) to find out which areas interest them so they can work with the Careers Service to develop their ideas.