Podcast: Episode 14 – Paul Shepherd – Parametric Geometry Generation

These are the show notes for episode 14 of the Travels in a Mathematical World podcast. 14 is the the largest number for which there are as many composite numbers less than it as there are primes.

This week on the podcast we hear from Dr. Paul Shepherd of the University of Bath. Paul is a mathematician working in the Department of Architecture and Civil Engineering and speaks about his work designing buildings using parametric models. There is more information on Paul’s work including some interesting pictures of Parametric Models on his website. Paul was interviewed about his work on Arsenal football stadium in the Plus podcast in December 2007.

I mentioned I was excited this week to discover a blog called “Dunc’s Shed” in which the author had posted a link to the podcast.

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

Careers advice for mathematicians

In response to the poor state of generally available careers advice for mathematicians, Vanessa Thorogood, Education Officer at the IMA has produced an IMA Maths Careers Advice leaflet. I would recommend this to anyone who is interested in careers advice for mathematics undergraduates or mathematics graduates or who offers such advice through a graduate careers advisory service, careers library or otherwise.

Obscure number facts

I noticed today a link to the Travels in a Mathematical World podcast from the blog of Duncan Margetts, “Dunc’s Shed”. It’s great to see someone liking and pointing others to the podcast :)

Duncan was sufficiently impressed by the peculiar episode number facts that he was moved to write about palindromic numbers on his blog following episode 11. Someone asked me a while ago why I was doing a fact about the episode number at the start of each episode. I told them it was my inner geek trying to express himself. It’s interesting to see one person out there at least likes this, anyway. The big question is: for how many episodes can I keep finding the facts…?

iSquared Magazine

As you may know, Sarah Shepherd helps me out with the podcast by meeting with me once a month to talk over some maths news. Sarah edits iSquared Magazine, which I’m sure some of you will be familiar with. Sarah sent through some information about iSquared which I thought I would share in case you aren’t familiar with it. Sarah says:

iSquared is a quarterly magazine which sheds light on the growing number of real-world applications of mathematics. In iSquared magazine you can read a wide variety of articles about how maths is used in the modern world and keep updated on the latest developments at the forefront of mathematical research. You can also read reviews of recently released books on mathematical topics, biographies of celebrated mathematicians and interviews with people for whom mathematics is a crucial element of their work.

You can subscribe to iSquared magazine for just £11.20 or buy a single issue for £3.15. For further information please visit www.isquaredmagazine.co.uk, where you can either purchase the magazine online or download a subscription form. Alternatively, to have a subscription form posted to you, please email your name and address to subscriptions@isquaredmagazine.co.uk.

I would be grateful if you could pass this information on to any friends or colleagues who might be interested in iSquared magazine.

I have designed adverts to go on the back cover of iSquared Magazine over 4 issues. Each highlights an aspect of IMA membership and will provide a regular income to support iSquared, something the IMA are keen to do. The first was in the autumn and you can view it on this blog. The second advert concentrates on mathematics careers. I originally had an advert drafted with a nice picture of Canary Wharf from across the Thames at Greenwich but in the current climate I wasn’t sure that was an attractive picture to use. Every time I see Canary Wharf on the telly it is being played over a bad news story! So just before the advert was due I was passing through St. Pancras Station in London. I stood on the upper level for a few minutes until I had to leave for my meeting and took a few photos. I tried to choose one with a mix of people looking like they’re off to work. The advert is below, click on it to see a larger version.

IMA advert for iSquared Winter 2008

London University Events

Noel-Ann Bradshaw of the University of Greenwich has been trying to get a group of London Universities together to cross promote events. In London there is such a concentration of universities and such a lot going on that it makes sense to cross-promote events between students at different universities. Anyway, this group is going well and Noel-Ann has posted 3 new events on the Facebook group “London University Maths Societies – IMA”, namely:

“The man who invented the concept of pi: William Jones and his circle”
by Patricia Rothman
William Jones was important in his lifetime primarily for three things: he was the first person to use the Greek letter π in its modern sense; he had acquired such a significant archive of manuscripts that he was appointed to the Royal Society committee, to investigate the invention of calculus; and he was influential as communicator in a network of mathematicians, astronomers and natural philosophers in the early eighteenth century.
This lecture will also touch on the lives of some of the notable characters of the seventeenth and eighteenth centuries who contributed to his story.
22 January 2009 13:15 – 13:55
Darwin Lecture Theatre, UCL
Facebook event; UCL page.

Finding Moonshine: A Mathematician’s Journey Through Symmetry”
by Marcus du Sautoy
Symmetry is all around us. Our eyes and minds are drawn to symmetrical objects, from the sphere to the swastika, from the pyramid to the pentagon. Of fundamental significance to the way we interpret the world around us, this unique, all-pervasive phenomenon indicates a dynamic relationship between objects. In chemistry and physics, the concept of symmetry explains the structure of crystals or the theory of fundamental particles. In evolutionary biology, the natural world exploits symmetry in the fight for survival. What’s more, symmetry – and the breaking of it – are central to ideas in art, architecture and music. This talk takes a unique look into the mathematical mind as Marcus explores deep conjectures about symmetry. These conjectures have culminated in the most exciting discovery to date – the summit of mathematicians’ mastery in the field – the Monster, a huge snowflake that lives in 196,883-dimensional space with more symmetries than there are atoms in the sun.
3 February 2009 18:00 – 20:00
Oliver Thompson lecture theatre, City University
Facebook event; City University page; The book; Marcus’ blog.

“Bertrand Russell: Man of Dissent”
by Ivor Grattan-Guinness
16 February 2009 6.30-8pm
New Theatre, East Building, LSE
Russell argued against the Great War, but he also wanted to drop atomic bombs on the Soviet Union after WWII, and later advocated nuclear disarmament. How could a great logician accommodate such inconsistencies? How, as a private citizen, did he make such a world-wide impact?
Ivor Grattan-Guinness is Emeritus Professor of the History of Mathematics and Logic at Middlesex University, and an associate member of CPNSS. He has written widely on Russell’s logic and philosophy, and has been an Advisory Editor on the Russell ‘Collected papers’ edition since its inception in 1979.
Facebook event; LSE page.

If you are in London or can get there sometimes I would recommend joining the London Maths Facebook group for event notifications.

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.