Suggested topics for undergraduate projects
Many mathematics students undertake a final year project, where the student works independently with guidance from a tutor. It can be difficult to find suitable projects in mathematics, since few undergraduates are in a position to produce original work, but a successful individual project develops, and is evidence of, skills in time management, independent learning, and communication which are highly valued by employers. The topics with which “Being a Professional Mathematician” is concerned provide a rich area for final year projects, involving research, critical thinking, and understanding of the mathematical community.
This list provides a variety of possible project ideas with, in many cases, suggested starting points.
Professional Mathematicians
The Professional Mathematician: how has the idea of a mathematican developed over the last four hundred years?
Start with the historical case studies here. When did the word "mathematician" start defining a profession?
How do mathematicians think of the profession?
Start with Amir Alexander's book "Duel at Dawn" (see booklist) which argues that the way mathematicians think of themselves changed after the time of Galois and Abel.
How do today's university mathematicians balance the demands of teaching and research?
Start with the case studies of today's academics Dyson, Porter and Stallard and the historical case studies, especially Sylvester.
Is mathematics a solitary or collaborative activity? Has this changed over time?
Start with the case studies
Professional Bodies
Why is the proliferation of professional bodies in mathematics so different from that in Physics, where the Institute of Physics speaks for the profession?
Starting point  the resources here on professional bodies and the worksheet on that topic. This project could look at the origins of the various societies and the subsequent relationships between them.
Obstacles
How have historical mathematicians overcome obstacles they faced because of their race, gender or religion? How was their mathematics influenced by these factors?
Start with the case studies of Sylvester or du Chatelet, or research other mathematicians such as Emmy Noether or David Blackwell. Hersh and JohnSteiner's book Loving + Hating Mathematics (see book list) might be helpful.
Branches of Mathematics
When did statistics emerge as a discipline in its own right?
Start from the Wikipedia article "History of Statistics"
You could also study the emergence of operational research, financial mathematics, actuarial mathematics, or subjects like topology, analysis, etc.
The Impact of Mathematics
How does mathematics developed for its own sake come to find applications?
Start from this Plus magazine article, which links to Peter Rowlett's article in Nature, and find further examples of planned or unplanned impact of mathematics.
The Undergraduate Curriculum
Where is the mathematics you have studied during your degree actually used? You might focus on one module and find examples where its ideas and methods are used in industry or do an overall study of the whole curriculum.
Mathematics Education
Have initiatives like the Undergraduate Ambassadors Scheme helped address problems in maths education in the UK?
There is valuable background material in the report of Adrian Smith's 2004 inquiry, "Making Mathematics Count", and in Carol Vorderman's recent report on maths education.
How does maths education in the UK compare with that elsewhere?
Compare curriculum, numbers, outcomes
Representations of Mathematics
How are mathematicians depicted in fiction? OR How is mathematics used by fiction writers?
Alex Kasman maintains a list of mathematical fiction at http://kasmana.people.cofc.edu/MATHFICT/ and Tony Mann's list of mathematical fiction is at http://staffweb.cms.gre.ac.uk/~A.Mann/Fiction/. See also Tony Mann, 'From Sylvia Plath's The bell jar to the Bad Sex Award: a partial account of the uses of mathematics in fiction', BSHM Bulletin: Journal of the British Society for the History of Mathematics, 25 (2010): 2, 58  66. See also Wikipedia on The Oulipo.
How are mathematicians depicted on screen?
See Oliver Knill's web page "Mathematics in Movies" at http://www.math.harvard.edu/~knill/mathmovies/
Visual images of mathematicians
Start from the worksheet on this topic
Mathematics in the Press
How accurately is mathematics or statistics) represented in the press?
Start by finding recent reports.
How could mathematicans improve public awareness of their subject
What attempts do mathematicians currently make to put their subject before the public? Think about popular books, newspaper articles, British Science Festival, StandUp Maths and so on.
