Preliminaries

Victor Bryant and Hazel Perfect
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Victor Bryant: University of Sheffield, Department of Pure Mathematics
Hazel Perfect: University of Sheffield, Department of Pure Mathematics

Chapter Chapter One in Independence Theory in Combinatorics, 1980, pp 1-11 from Springer

Abstract: Abstract Plato is reputed to have said ‘God ever geometrizes’. Since geometrical terminology is widely used throughout mathematics, and ‘spaces’ of all kinds are studied nowadays, mathematicians have evidently followed the divine example. We find it natural to think in visual terms even in branches of mathematics which are not themselves basically geometrical. For example, in elementary mathematics we draw graphs of functions and Venn diagrams of sets; on a higher level, linear equations and linear algebra are clarified when studied within the framework of general ‘vector spaces’, and calculus and analysis have been transformed by the study of ‘metric spaces’ and ‘topologi- cal spaces’. In the last forty years or so ‘independence spaces’ (called by many authors ‘matroids’ or ‘pre-geometries’) have found a place in the mathematical literature, and the insight which they have increasingly brought, notably to parts of algebra, to graph theory and more general combinatorics, make us confident of their continuing importance in the future.

Date: 1980
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DOI: 10.1007/978-94-009-5900-2_1

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