This thesis focusses on the notion of analysis (&vàXuatç) in Stoiclogic, that is to say on the procedure which the Stoic logiciansfollowed in order to reduce all valid arguments to five basicpatterns. By reconsidering the uses of its Aristotelian homonym and byexamining the evid…
This thesis is principally concerned with Arthur Cayley's work on Invariant Theory, but also considers his contribution to matrix algebra and other algebraic systems, drawing on sources including unpublished letters between Cayley and his contemporary, J. J. Sylvester. The histo…
Using the method of dimensional reduction of N=l supersymmetric Yang-Mills theories from higher dimensions down to four dimensions, all possible supersymmetric Yang-Mills theories in four dimensions are obtained. The conserved currents associated with the symmetries of these mod…
The rank one symmetric spaces of non-compact type are the real, complex, quaternionic and octonionic hyperbolic spaces. Real hyperbolic geometry is widely studied complex hyperbolic geometry less so, whilst quaternionic hyperbolic geometry is still in its infancy. The purpose of…
The contents of this thesis are a detailed study of the implementation of Finite Element method for solving linear and non-linear elliptic partial differential equations. It commences with a description and classification of partial differential equations, the related matrix and…
The commutative theory of Unique Factorisation Domains (UFDs) is well-developed (see, for example, Zariski-Samuel[75], Chapter 1, and Cohn[2l], Chapter 11). This thesis is concerned with classes of non-commutative Noetherian rings which are generalisations of the commutative ide…
This thesis starts by constructing a complex line bundle for a simple 3-parameter family of 2 x 2 Hermitian matrices and explicitly computing its first Chern number. This example illustrates in the simplest possible context the connection between topology and degenerate eigenval…
