Historical and Cultural Perspectives on Mathematics

The aims for this module are set into the context of the QAA Framework for Higher Education Qualifications and they relate to the SEEC level descriptors for level 6 study.

All societies have developed some mathematics in order to help them understand the world in which they live.  The mathematics we study today is a culmination of what has gone before and reflects the age and society in which it was developed. Mathematics continues to change due to the curiosity of its practitioners, advances in technology and the changing needs of business and industry.

The influence of different ages and cultures can be seen in all aspects of the subject.  This module provides opportunities for students to study these influences and, through examining them to deepen their own understanding within the subject.

In relation to the QAA Framework for Higher Education Qualifications and the SEEC level descriptors for level 6 study, by the end of the module students should be able to:

1. recognise mathematical activity in possibly unfamiliar contexts;
2. interpret original writings of mathematicians of the past and appreciate their efforts to communicate new ideas;
3. appreciate and understand the ways mathematics has developed in response to a changing social environment;
4. explore links between areas of mathematics.

Tracing a mathematical problem through time. (Fermat’s last Theorem took over 300 years from statement to proof; The Four Colour Problem took 100 years to resolve and is still questioned; Methods of solving polynomial equations changed through the centuries).

Some specific topics will be covered such as the development of number systems and views on infinity.

Students will consider the development of mathematical ideas not only across time but also across differing areas of the globe.  Students will be encouraged to compare educational texts from different countries of the world.

Contact Time:

Each session will include a mixture of lecture and mathematical activity undertaken by students through small group work and discussion and reflection on the processes involved in mathematics. Reflection on the nature of the activities whilst working at them will be a key aspect of the course.

Non-contact Time:

Students will be expected to read extracts from original writings, to work on mathematical problems and techniques from other cultures and to bring their ideas to sessions.

Books:

Ascher, M.   Mathematics Elsewhere: an exploration of ideas across cultures; (2002)  Princeton NJ: Princeton University Press

Berggren, J. L.  (2003)  Episodes in the mathematics of medieval Islam; New York: Springer

Davis P.J. & Hersh, R.  (1981)  The Mathematical Experience  Boston MA: Birkhauser

Dunham, W.  (1990)  Journey Through Genius  New York: Wiley

Dunham, W.  (1997)  The mathematical universe: an alphabetical journey through the great proofs, problems, and personalities  New York: Wiley

Eves, H.  (1981)  Great Moments in Mathematics before 1650  New York: MAA

Eves H.  (1981)  Great Moments in Mathematics after 1650  New York: MAA

Fauvel, J. & Gray J.  (1987)  The History of Mathematics  London: Macmillan

Hersh R.  (1997)  What is Mathematics, Really?  London: Penguin

Hofstadter, D.  (1984)   Godel, Escher & Bach  London: Penguin

Joseph, G.G.  (2010)  The Crest Of The Peacock: non-European roots of mathematics  Princeton NJ: Princeton University Press

Kline, M. (1972)  Mathematical Thought From Ancient to Modern Times  London: OUP

Kline, M. (1953)  Mathematics in Western Culture  London: OUP

Selin, H. & D’Ambrosio, U.  (2001)  Mathematics across cultures: the history of non-western mathematics  New York: Springer

Stewart, I.  (1987)  The Problems of Mathematics  Oxford: OUP

Smith D.E.  (1959)  A Source Book in Mathematics Vols 1 & 2  New York: Dover

Struik, D.J.  (1969)  A Source Book in Mathematics 1200 – 1800 (1969)  Harvard: Harvard University Press; London: Oxford University Press

Journals:

Mathematics in Schools; a Journal of the Mathematical Association.

MT: Mathematics Teaching; The Journal of the Assoc of Teachers of Mathematics

Electronic Sources: (accessed June 2011)

African Mathematical Union: http://archives.math.utk.edu/topics/history.html

History of Mathematics archive: www-history.mcs.st-and.ac.uk/

The MacTutor British Society for the History of Mathematics: www.dcs.warwick.ac.uk/bshm/index.html

University of Tennessee:  http://archives.math.utk.edu/topics/history.html

Other:

BBC Podcasts (Du Sautoy): www.bbc.co.uk/podcasts/series/maths

School home:

School of Education