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.

Puzzles at YorkThe 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.

University of York Department of Mathematics
York Careers Fair poster

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:

Advert for my talk at Newcastle
Sheffield:
Advert for my talk at Sheffield