Podcast: Episode 13 – History with Noel-Ann Bradshaw – Florence Nightingale

These are the show notes for episode 13 of the Travels in a Mathematical World podcast. 13 is prime and is the number of Archimedian solids, which includes the Truncated Icosahedron, the shape used in the construction of common footballs and is a model of the structure of the fullerene allotrope of carbon, which is carbon-60. More about the number 13 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 the life of Florence Nightingale. You can read a comprehensive biography of Florence Nightingale at MacTutor and a wealth of information at the Florence Nightingale museum. There are some links to further information on her statistics at “Florence Nightingale – Statistical Links“.

I said in the episode I would post a link to the Theorem of the Day website by Robin Whitty, who sent a kind email and put a link to the podcast on that website.

You can find out more about my work with the IMA by reading this blog and visiting www.ima.org.uk/student.

N.B. The widely quoted story of Sylvester being Nightingale’s tutor has been questioned but dates to a contemporary obituary of Sylvester. For details please see: James Joseph Sylvester: Jewish Mathematician in a Victorian World by Karen Hunger Parshall. Johns Hopkins University Press 2006.

Mathematics graduates’ employability skills

Yesterday the BBC highlighted the issue of graduate employability with a story about a Government plan to offer graduate internships at top companies.

One of the things I do when I’m not University Liaison Officer for the IMA is some lecturing at Nottingham Trent University. As part of this, I am currently enrolled on the Postgraduate Certificate in Higher Education (PGCHE) course, a 60 credit Masters level module for new lecturers. The most recent assignment involves the evaluation of a module on which I am teaching. I chose a module I will be teaching in the second half of the 2008/9 academic year which is a group projects, problem solving module focused on skills development rather than knowledge acquisition. As such, I have recently done a little reading from mathematical educational literature on employability and transferable skills and share some snippets below.

The Quality Assurance Agency for Higher Education (QAA) publish Subject Benchmark Statements which describe what a subject offers its graduates. The QAA Benchmark Statement for Mathematics, Statistics and Operational Research (MSOR) [1] suggests skills MSOR graduates possess include:

“general study skills, particularly including the ability to learn independently using a variety of media which might include books, learned journals, the internet and so on. They will also be able to work independently with patience and persistence, pursuing the solution of a problem to its conclusion. They will have good general skills of time-management and organisation. They will be adaptable, in particular displaying readiness to address new problems from new areas. They will be able to transfer knowledge from one context to another, to assess problems logically and to approach them analytically. They will have highly developed skills of numeracy, including being thoroughly comfortable with numerate concepts and arguments in all stages of work. They will have general IT skills, such as word processing, use of the internet and the ability to obtain information (there may be very rare exceptions to this, such as distance learning students studying abroad in countries where IT facilities are very restricted). They will also have general communication skills, such as the ability to write coherently and communicate results clearly” (p. 11).

The Statement suggests it is because of these skills that MSOR graduates “find employment in a great variety of careers and professions” (p. 11). Hibberd [2] agrees that mathematics graduates “play an important role in meeting the demands of employers for skilled personnel to ensure the UK can maintain its competitive edge in a global market” (p. 6). While Kahn [3] regards it as “essential” that modules are “built around mathematical considerations,” he suggests module designers also need to take account of “wider considerations” such as “preparing students for employment” (p. 92).

Beevers and Paterson [4] describe “key skills” as “what is left after the facts have been forgotten” (p. 51). Challis, et al [5] define a subset of key skills as “transferable” (p. 80) and say as well as academic knowledge,

“professional mathematicians require good transferable skills, such as reading, writing, speaking and working with others. They may be applied mathematicians, in one or more of a variety of guises such as scientists, engineers, economists or actuaries, and will be working with others, using mathematics and mathematical modelling to solve problems and answer questions that may arise in industry, commerce or a social context. If they are pure mathematicians, they will almost certainly be employed by a university with some requirement to conduct research and to teach. Those mathematics graduates who become schoolteachers will certainly need good interpersonal and leadership skills … Some mathematics graduates will go into general employment, and they, like their peers will need all of the aforementioned transferable skills.” (p. 79).

The findings of MacBean, Graham and Sangwin [6] indicate some students may need convincing that they need to develop employability skills at all. Challis, et al say mathematics students “are often surprised to see the emphasis placed on the acquisition of transferable skills” (p. 89).

Challis et al report the findings of an employer survey (MathSkills project). This,

“suggested that a mathematics graduate is advantaged by being logical, systematic and rigorous, being able to take an abstract and broad approach, and being analytical, clear thinking and fast to understand. On the negative side, mathematics graduates tended to lack presentation and communication skills (including report writing and presentation to a non-technical audience), pragmatism in real problem solving, social skills and commercial awareness” (p. 81).

Communication is important; they say,

“professional mathematicians in industry will probably be working on problems that require their specialized knowledge and skills, and they will be working with others who have different specialities, or who are managing the project, or have commissioned it. They must converse lucidly with others, who are ignorant of mathematics, and they must know what can, and what cannot, be solved mathematically. They must simplify problems through modelling, and find or create suitable methods of solution. They must then convey their findings persuasively to a wide range of others, in discussion, in writing and through a presentation: with many audiences, a persuasive argument is more convincing than a rigorous proof!” (p. 81).

They also note that “most mathematics graduates do not go on to call themselves professional mathematicians, although they still bring their special qualities to their job” (p. 82). Finally, Challis, et al warn: “The effort involved in teaching, embedding and assessing [transferable skills] is considerable but cannot be avoided if the modern graduate is to be properly prepared for the workplace” (p. 90).

  1. QUALITY ASSURANCE AGENCY FOR HIGHER EDUCATION, THE, 2002. Subject benchmark statements: Academic standards – Mathematics, statistics and operational research. Gloucester: The Quality Assurance Agency for Higher Education.
  2. HIBBERD, S., 2005. Use of Projects in Mathematics. MSOR Connections, 5(4), pp. 5-12.
  3. KAHN, P., 2002. Designing courses with a sense of purpose. In: P. KAHN, ed. and J. KYLE, ed., Effective Teaching and Learning in Mathematics & its Applications. London: Kogan Page, 2002, pp. 92-105.
  4. BEEVERS, C., and PATERSON, J., 2002. Assessment in mathematics. In: P. KAHN, ed. and J. KYLE, ed., Effective Teaching and Learning in Mathematics & its Applications. London: Kogan Page, 2002, pp. 49-61.
  5. CHALLIS, N., GRETTON, H., HOUSTON, K., and NEILL, N., 2002. Developing transferable skills: preparation for employment. In: P. KAHN, ed. and J. KYLE, ed., Effective Teaching and Learning in Mathematics & its Applications. London: Kogan Page, 2002, pp. 79-91.
  6. MACBEAN, J., GRAHAM, T. and SANGWIN, C., 2001. Guidelines for Introducing Groupwork in Undergraduate Mathematics. Birmingham: HEA Maths, Stats and OR Network.

Podcast: Episode 12 – Terry Lyons – Stochastic Calculus

These are the show notes for episode 12 of the Travels in a Mathematical World podcast. 12, the number of edges of a cube, is the first number that can be written as a product of its proper divisors in more than one way. These are, of course, 2×6 and 3×4. More about the number 12 from thesaurus.maths.org.

This week on the podcast we hear from Professor Terry Lyons of the University of Oxford, who talked to me about Stochastic Analysis. You can find out more about his work on Terry Lyon’s homepage and the page of the Stochastic Analysis Group at Oxford.

If you’re interest is piqued by this topic, there is a set of introductory notes on Stochastic Calculus at King’s College, London. During the course of the episode, Terry mentions work by Andrey Kolmogorov, Joseph Doob and Kiyosi Ito.

You can find out more about my work with the IMA by reading this blog and visiting www.ima.org.uk/student.

Podcast: Episode 11 – History with Noel-Ann Bradshaw – Euler

These are the show notes for episode 11 of the Travels in a Mathematical World podcast. All palindromic numbers (that is, numbers that remain the same when their digits are reversed) with an even number of digits are divisible by 11. More about the number 11 from Prime Curios. There is a wealth of information on palindromic numbers at worldofnumbers.com.

Always carry an emergency Maths Careers postcard

On the way home from my 6 monthly review of the University Liaison Project (sorry? Oh, really well, thanks for asking) I was on the train listening to music through my headphones & tapping away on my laptop. At Leicester or Loughborough two lads got on and sat opposite me. A girl across the aisle had got on too and was talking to them in a defensive way about how much maths there was in her course: “yeah there’s quite a bit of physics and some maths too”. One of the lads remarked “Is there any solid state physics?” and they laughed. In my experience, peer pressure doesn’t work this way round!

After a while, one of them nudged the other and said “look, we’ve sat at the right table.” They were looking at the IMA sticker on the top of my laptop. I didn’t acknowledge that I’d heard – I had a report to work on. As we were pulling into the station I heard one of them say to the other, “I might contact them, you know, to ask what careers you can do with maths.” I quietly reached into my bag and pulled out my emergency Maths Careers postcard and slid it across the table to him. He laughed and said he would check out the website. Turns out he’s a physics undergrad interested in the mathematics side of things. He is looking at defence jobs at the moment. I told him I know a lot of mathematicians who work in this area, and that the Maths Careers website carries some good careers advice. He was still clutching the postcard when he left the station onto the streets of Nottingham, on the way to the outdoor skating rink in the market square.

Of course, this is the very opposite of the leverage I wrote about in Mathematics Today December.

Podcast: Episode 10 – Adrian Bowyer (part 2)

These are the show notes for episode 10 of the Travels in a Mathematical World Podcast. 10 is both a Triangular number and a Tetrahedral number. More about the number 10 from thesaurus.maths.org.

Following on from last week, this week on the podcast is the second of two installments from Dr Adrian Bowyer, who talks through some of the areas his career has taken him into. You can find out more about Adrian from his homepage at the University of Bath, and Adrian has a Wikipedia page.

This week, Adrian talks about his work mimicking biological adaptions in engineering. He talks about his work on the self-replicating machine, RepRap and there is a wealth of information on that website.

While Adrian is speaking I am fascinated by a pile of objects made through a commerical rapid prototyping machine which are sitting on a table in Adrian’s office. These are pictured below along with a picture of a RepRap machine and Adrian.

I would very much recommend watching the video on YouTube of “Building RepRap 1.0 ‘Darwin'”, which shows in fast forward Adrian assembling a RepRap machine. This is at times both fascinating and hilarious, particularly the tea break in the middle and the guy who completely grasps the possibility for humour in the different frames of reference of the situation.

For the latest from the RepRap project, read the blog.

rapid prototyping objects
a RepRap machine
Adrian Bowyer and a RepRap machine