Search

The main objective of my research is to explore how secondary school children used the concept of Boredom to make sense of, and construct, their daily lived experiences in school. My interest is the pragmatic rather than semantic, and the emic rather than etic. This is an examination of the everyday use of Boredom in secondary school classrooms. My main research method was a researcher-absent focus group. Overall, fourteen researcher-absent focus group interviews were carried out in two waves, with a total of 50 secondary school pupils between the ages of 14-18 taking part over three separate secondary school sites. In addition, three secondary school teachers kept diaries reflecting on their daily teaching experiences during the autumn term of 2018. Transcripts and diaries were analysed using Grounded theory. This research takes the position that modern Boredom is a sociohistorically situated subjectivity which has its roots in the rational, technological and industrial developments of the last 200 hundred years. Moreover, modern Boredom can act as a sanctuary of self-care into which the individual can retreat and be insulated from a toxic environment. Contemporary classroom Boredom is a response to neoliberal performance-based education which fosters a toxic 'ontological insecurity' amongst pupils. Boredom is articulated in four stories, endemic, predominant, contingent and non-bored. Furthermore, these stories fracture at the intersection of social class and gender. With historical biographies of low educational achievement and experiencing structural inequalities, working-class pupils describe greater levels of Boredom and use a bored, nonchalant and blasé demeanour to insulate themselves against the toxicity of ontological insecurity. With working-class girls, this process is often invisible. Girls can be just as bored as boys, but gendered narratives disassociate classroom Boredom from femininity and allow working-class girls to invisibly disengage from education. Accordingly, classroom Boredom is a situated subjectivity that can be seen as a form of, albeit self-defeating, resistance to neoliberal performance-based education.

This thesis presents a study of some topics and problems of graph theory that are related to partial orders. It is an attempt to develop and utilise the links between score sequences of oriented graphs, different types of partial orders, and combinatorial aspects of finite topologies. In the first chapter Landau's concept of the score structure of a tournament is extended to that of the score sequence of an oriented graph, and the condition is given for an arbitrary integer sequence to be the score sequence of some oriented graph. The proof involves the construction of a specific oriented graph D(S) with the given score sequence S. Landau's condition for the score structure of a tournament is deduced as a simple consequence by constructing a tournament T(L) with given score structure L. It is shown that D(S) is a partial order for every S, and an enumeration of score sequences /labelled score sequences provides a lower bound for the number of partial orders /T* topologies. The partial order D(S) has the minimum number of arcs among the oriented graphs with score sequence S, and T(L) has the maximum number of upsets among the tournaments with score structure L. We also establish that given two oriented graphs with the same score sequence, one can be transformed to the other by successively transforming appropriate intransitive triples to transitive triples or vice versa. The proof of an analogous earlier result of Ryser for tournaments reduces to a particular case of the proof of this result. The second chapter begins with an introduction to some of the ideas of paired comparison experiments. If indifference is not permitted then the preference pattern induced by such an experiment is a tournament, and a consistent preference pattern is a linear order. If indifference is permitted then the Induced preference pattern is an oriented graph, and one interpretation of consistency is that indifference as well as preference should be transitive, in which case consistent preference patterns are weak orders. We show that those oriented graphs which are specified up to isomorphism by their score sequences are weak orders, and establish some further results relating weak orders and score sequences. In a similar vein, the condition is given for a tournament to be specified up to isomorphism by its score structure. The third chapter is about semiorders, which, like weak orders, are special types of partial orders. Luce and others have suggested that preferences in paired comparison experiments become recognisable only when of sufficient magnitude. Under this assumption, consistent preference patterns are characterised as semiorders. The proof relies upon reformulating the definition of a semiorder in terms of its score sequence. There is an interesting application of this result to significance testing in statistics. The number of semiorders with n vertices is shown to be the nth Catalan number and labelled semiorders are counted. Harary's reconstruction conjecture is proved for semi-orders. Then we consider extensions of the Kendall and Babington Smith definition of the coefficient of consistency of a paired comparison experiment to those experiments in which indifference is permitted. In the final chapter, the links between finite topologies and transitive digraphs are studied. It is well Known that there is a natural one- to-one correspondence between the finite topologies and transitive digraphs with the same point (vertex) set. This correspondence is exploited to derive the graphical analogues of topological properties such as connectivity, maximal connectivity, fineness, the TQ separation axiom and closure. Certain binary operations between topologies which produce other topologies, such as union. Intersection and the cartesian product, are also shown to have simple analogues in graph theory. The number of n-point maximal connected topologies is counted and related to the counting series for rooted trees. Then the following problem is investigated: given n, for which values of r is there an n-point topology with r open sets? The cardinalities of topologies are studied by considering their associated digraphs, and it transpires that it is necessary to consider only those transitive digraphs which are partial orders. Various results are proved, including existence and non-existence criteria, enabling a complete solution to be given for n ^ 9. In conclusion, three conjectures about cardinalities are put forward.

This thesis investigates the circuits of edge-coloured complete graphs. There are various kinds of edge-coloured circuits. Amongst the most interesting are polychromatic circuits (each edge is differently coloured), alternating circuits (adjacent edges are differently coloured) and monochromatic circuits (every edge is the same colour). In the case of triangles, there are monochromatic, bichromatic (2-edge-coloured) and polychromatic triangles. This thesis is an investigation into edge-coloured complete graphs which do not contain one of the above kinds of circuits. Special emphasis is given to those edge-coloured complete graphs which do not contain one type of triangle, and those in which two types of triangle are forbidden. Where possible, the structure of these graphs is determined and a method of construction given; various types of extremal results are obtained.