Geometricians often say that a geometric mode of cognition is more effective than algebra in many tasks. This dissertation investi- gates geometrisation as a mathematical approach: its main epistemic constituents and benefits. The aim is to explain why geometrisation can be effective and how this effectiveness may be achieved. The use of the term 'geometric' in mathematical practice seems to be applied not only for mathematical concepts and methods. Of- ten it simply indicates the use of diagrams. The analysis of various examples draws the distinction between these two meanings. It also clarifies the impact of the two aspects into mathematical advance. The central argument of this thesis is that visual 'geometry' can ease the application of geometric concepts and methods. The argument is based on a case study drawn from a promising contemporary mathematical area - geometric group theory. This ap- proach involves the diagrammatic representations of groups by Cayley graphs. They are not only attractive objects in themselves but also useful constructions which can allow the endorsement of an interesting and sophisticated geometry of groups.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:557275 |
| Date | January 2012 |
| Creators | Starikova, Irina |
| Publisher | University of Bristol |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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