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.

Serverfail

Earlier this week my server underwent what might be politely termed an "unscheduled outage". This has messed up a lot of stuff, including the Travels in a Mathematical World podcast. This is now back from another server and all is well again. All episodes are linked from www.travelsinamathematicalworld.co.uk.

My personal website and ELMS remain offline at present. If I close my eyes and wish hard enough, maybe I'll find some spare time to sort them out too.

Puzzling over careers in York

Last week I spent two days in York giving talks. Firstly I gave an evening lecture to the York University Maths Society (YUMS) on Puzzles. I found this highly enjoyable. I think was the first talk I have written that I was looking forward to giving rather than being preoccupied with anxiety on its first outing. I gave a number of puzzles for the audience to work through, talked through a little of the history of puzzles and then we had a session at the end with my collection of puzzles for the audience to play with (pictured below). Following this, YUMS and I retired to the bar for some beer and darts.

The following morning I went to the maths department (pictured below) for the careers fair. One of the students told me that when I offered to give my careers talk to the department the staff asked the students if they wanted a maths careers talk. The students said they did, and a maths-specific careers fair as well. It is nice to know that I inadvertently started the event! The day was organised jointly by the Careers Service and the Department of Mathematics, and advertised by YUMS as well. I think this combination really helped because the turnout was excellent. I was to give my careers talk to open the day. All the seats were gone and there were people sitting and standing at the back and in the aisles, and they were turning people away! I gave my talk and I think it went well, then we arranged I would give it again for the people who had been turned away. In total my helper for the day, York undergraduate Yi Ding, counted 80 students in the two sittings. As well my stall was hard at work without me; the organisers told me it was one of the most popular stalls even without me attending to it!

The best part of the day for me was when I was speaking to the lady from the TeachFirst stall. She said that usually when she comes to university careers fairs she finds the students naïve about the nature of the jobs market. She told me the students coming out of my talks were clued in and motivated to explore possible careers options. She said they kept telling her about the talk they'd just been in and what I had said about skills and employment prospects. This is brilliant to hear, a huge ego boost.

Wii ball games in Newcastle and Sheffield

At the end of April I made a trip to Newcastle and back via Sheffield to give my talk on Spin in Ball Games and play on the Wii. Both of these events were fun and I think provided some welcome revision relief for the students. At this time of year a lot of universities have ceased all but revision lectures and the appetite I found for careers talks in February is much reduced by now. Both of these talks were organised by the student societies and I think it is useful for me to have in my repertoire more fun events to engage with students in these situations.

Below are the posters used to advertise my presence in the two universities (click to enlarge). Apart from the completely made up title and abstract at Sheffield (my fault for not sending the real one), I think it is interesting to note the differences in approach taken. At Sheffield, an attempt is made to make the talk appear like a serious mathematical lecture on the physics of spin in ball games and how these are modelled in video games, using 'examples' on the Wii. On the other hand Newcastle make no bones about it, using a large photo of a Wii on the poster! In reality, the Newcastle interpretation is closer to reality; this is intended to be a fun night out of tenuous mathematical relevance in which the students have a laugh and go home a little more aware of the existence of the IMA. The 'serious' talk at Sheffield had to pause at one point when one of the players had a call from his girlfriend who, with the noise of the Wii in the background, would simply not believe he was at a maths event. "No really, it's a serious maths lecture from the IMA" he said, with Mario Power Tennis sound effects in the background.

Newcastle:


Sheffield:

Conferences on Mathematics in London

At the end of the Easter conference season I spent two days in London for conferences.

The first was the IMA's flagship general mathematical interest conference, Mathematics 2009. At this I was very excited to hear Sir Roger Penrose speak. Read an outline of Sir Roger's work at Plus. I was also pleased for the second time to hear David Spiegelhalter speak on public understanding of uncertainty (I also attended his keynote at Young Researchers in Mathematics 2009). I also heard the following speakers at the conference: Ben Heydecker on transport modelling, John McWhirter on his research, Makhan Singh and Zia Rahman on the more maths grads project's use of video, Helen Byrne on mathematical biology and Fred Piper on cryptography.

The second was the Women in Mathematics Day 2009. This event is designed for women who are active in mathematics to get together, including plenty of talks and posters by PhD students.

On my way home to Nottingham I stopped by the University of Leicester for an IMA East Midlands Branch talk on The Physics of Finance by Iain Clark.

Young Researchers in Mathematics 2009

Back in conference season, I attended the Young Researchers in Mathematics conference at Cambridge (AKA Beyond Part III). This was my first time in Cambridge and it was good to see the maths building, of which I have heard a lot during my travels. Unfortunately, when I got there it appeared someone had parked a spaceship on top of it (picture below).


This conference was the product of an exciting new initiative to bring together young mathematics researchers and was a vibrant inaugural conference. The organisers are to be congratulated. The Young Researchers in Mathematics is an ongoing initiative. From the website:

We exist to promote links between graduate mathematician communities at universities across the UK, and facilitate the organisation of conferences, workshops and social events for young mathematicians.

The conference was part-sponsored by the IMA and so I ran a stall at the event (pictured below) and spent a good amount of time mingling.


Below you will find a link to the conference photo on the Young Researchers in Mathematics website. Click to enlarge. I am almost in the middle towards the back, in a brown jumper and just behind the guy in green who stands out.

Podcast: Episode 28 - Maths news with Sarah Shepherd

These are the show notes for episode 28 of the Travels in a Mathematical World Podcast. 28 is the number of dominoes in a standard dominoes set. More about 28 from NumberADay.

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.

"'Maths' to crack climate change," an article on the BBC News website about the Numerical Algorithms and Intelligent Software (NAIS) team, a group of Scottish scientists attempting to tackle some of the numerical challenges presented by modern science.

Article in the Guardian, "Go figure ... why mathematicians rule the internet," on algorithms, covering supermarket loyalty cards, shelf stacking, special offers and stock control, traffic lights, the price of low cost flights, air traffic control, Amazon recommendations, Google search results, weather forecasts and radio station playlists.

Piece in the Oxford Mail highlighting the importance of mathematics in fire fighting. Read "Flaming good way to teach maths."

Piece in the Guardian, "Newly hatched chicks pass maths test," on basic mathematical skills in newly hatched chicks.

"Scientists reveal how eating chocolate can help improve your maths," a piece in the Telegraph which reports on a study on the effects of flavanols (found in cocoa) on mathematical ability.

"Could quantum mathematics shake up Google?", a piece from the New Scientist which discusses the use of random matrix theory to identify salient words in documents and its potential use in search engine results.

"Maths teachers 'taught to teach'" from the BBC News website reports on a booklet containing advice on teaching mathematics which are being sent to maths teachers in England and some reaction to the booklet.

The report of the suggestion of a government advisory committee that suggests national SATS tests should be phased out. Read "Testing of 11-year-olds should be phased out, advisers tell government" from the Guardian.

"Puzzling behaviour: Maths professor finds the formula that will solve ANY Sudoku" from the Daily Mail reports on an article by James Crook, "A Pencil-and-Paper Algorithm for Solving Sudoku Puzzles."

The story "Salmond stumped by a mother's maths question" is an interesting one. Since we recorded, there has been an apology from the BBC journalist involved, Brian Davies, in a blog post "To infinity and beyond" where he offers "to one and all, 3.14159265 apologies". The original story is gone from the Scotsman website at the time of writing these notes, replaced with the seemingly technical error, "The article has been unable to display." At the time of writing, Google still has a cache of the original story "Salmond stumped by a mother's maths question - Google Cache". I have not been able to find any reference to it, or its deletion, on the Scotsman website, apart from in deleted user contributed comments (view Google cache version). Minitrue at work.

The 14th of March was Pi Day. You can read the text of the US Government Bill which officially recognises Pi Day on The Library of Congress THOMAS website by searching for Bill Number "H.RES.224" or for the text "Pi Day".

The 24th March 2009 was Ada Lovelace Day, in recognition of women in technology. The BBC have a good roundup of what took place.

The International Centre for Mathematical Sciences (ICMS) in Edinburgh held a maths film festival – watching Hollywood films The Oxford Murders, 21 and N Is A Number, a documentary about Paul Erdös. This was reported in The Scotsman as "Lights, camera, action – maths and the movies adds up to a winning formula".

I recommended Marcus du Sautoy's column Sexy Maths in the Times, the latest I had seen was "Sexy maths: the Fibonacci sequence's prime rate."

I also recommended the work of David Spiegelhalter through the Understanding Uncertainty website and a piece in Plus, "Understanding uncertainty: 2845 ways of spinning risk."

I mentioned the Independant guide on Maths at university in which Noel-Ann Bradshaw and I feature. I mentioned Neil Goldwasser, who featured on Episode 7 of the Travels in a Mathematical World podcast, is now featured on the Maths Careers website.

You can find out about IMA membership grades on the Membership section of the IMA website.

I also mentioned the error I made in episode 9 of the Travels in a Mathematical World podcast, in which I claim 9 is prime.

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.