BURA Collection:http://bura.brunel.ac.uk/handle/2438/2352016-10-22T08:56:14Z2016-10-22T08:56:14ZOnline assessment of graph theoryHatt, Justin Dalehttp://bura.brunel.ac.uk/handle/2438/133892016-10-21T02:00:27Z2016-01-01T00:00:00ZTitle: Online assessment of graph theory
Authors: Hatt, Justin Dale
Abstract: The objective of this thesis is to establish whether or not online, objective questions in elementary graph theory can be written in a way that exploits the medium of computer-aided assessment. This required the identification and resolution of question design and programming issues. The resulting questions were trialled to give an extensive set of answer files which were analysed to identify whether computer delivery affected the questions in any adverse ways and, if so, to identify practical ways round these issues. A library of questions spanning commonly-taught topics in elementary graph theory has been designed, programmed and added to the graph theory topic within an online assessment and learning tool used at Brunel University called Mathletics. Distracters coded into the questions are based on errors students are likely to make, partially evidenced by final examination scripts. Questions were provided to students in Discrete Mathematics modules with an extensive collection of results compiled for analysis. Questions designed for use in practice environments were trialled on students from 2007 – 2008 and then from 2008 to 2014 inclusive under separate testing conditions. Particular focus is made on the relationship of facility and discrimination between comparable questions during this period. Data is grouped between topic and also year group for the 2008 – 2014 tests, namely 2008 to 2011 and 2011 to 2014, so that it may then be determined what factors, if any, had an effect on the overall results for these questions. Based on the analyses performed, it may be concluded that although CAA questions provide students with a means for improving their learning in this field of mathematics, what makes a question more challenging is not solely based on the number of ways a student can work out his/her solution but also on several other factors that depend on the topic itself.
Description: This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University London.2016-01-01T00:00:00ZDevelopment and evaluation of computer-aided assessment in discrete and decision mathematicsZaczek, Kingahttp://bura.brunel.ac.uk/handle/2438/109732015-06-09T02:00:29Z2015-01-01T00:00:00ZTitle: Development and evaluation of computer-aided assessment in discrete and decision mathematics
Authors: Zaczek, Kinga
Abstract: This thesis describes the development of Computer-Aided Assessment questions for elementary discrete and decision mathematics at the school/university interface, stressing the pedagogy behind the questions’ design and the development of methodology for assessing their efficacy in improving students’ engagement and perceptions, as well as on their exams results. The questions give instant and detailed feedback and hence are valuable as diagnostic, formative or summative tools. A total of 275 questions were designed and coded for five topics, numbers, sets, logic, linear programming and graph theory, commonly taught to students of mathematics, computer science, engineering and management. Pedagogy and programming problems with authoring questions were resolved and are discussed in specific topic contexts and beyond. The delivery of robust and valid objective questions, even within the constraints of CAA, is therefore feasible. Different question types and rich feedback comprising text, equations and diagrams that allow random parameters to produce millions of realisations at run time, can give CAA an important role in teaching mathematics at this level. Questionnaires identified that CAA was generally popular with students, with the vast majority seeing CAA not only as assessment but also as a learning resource. To test the impact of CAA on students’ learning, an analysis of the exam scripts quantified its effect on class means and standard deviations. This also identified common student errors, which fed into the question design and editing processes by providing evidence-based mal-rules. Four easily-identified indicators (correctly-written remainders, conversion of binary/octal/hexadecimal numbers, use of correct set notation {…} and consistent layout of truth tables) were examined in student exam scripts to find out if the CAA helps students to improve examination answers. The CAA answer files also provided the questions’ facilities and discriminations, potentially giving teachers specific information on which to base and develop their teaching and assessment strategies. We conclude that CAA is a successful tool for the formative/summative assessment of mathematics at this level and has a positive effect on students’ learning.
Description: This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University London.2015-01-01T00:00:00ZSolving cardinality constrained portfolio optimisation problem using genetic algorithms and ant colony optimisationLi, Yibohttp://bura.brunel.ac.uk/handle/2438/108672015-05-19T08:25:43Z2015-01-01T00:00:00ZTitle: Solving cardinality constrained portfolio optimisation problem using genetic algorithms and ant colony optimisation
Authors: Li, Yibo
Abstract: In this thesis we consider solution approaches for the index tacking problem, in which we aim to reproduces the performance of a market index without purchasing all of the stocks that constitute the index. We solve the problem using three different solution approaches: Mixed Integer Programming (MIP), Genetic Algorithms (GAs), and Ant-colony Optimization (ACO) Algorithm by limiting the number of stocks that can be held. Each index is also assigned with different cardinalities to examine the change to the solution values. All of the solution approaches are tested by considering eight market indices. The smallest data set only consists of 31 stocks whereas the largest data set includes over 2000 stocks. The computational results from the MIP are used as the benchmark to measure the performance of the other solution approaches. The Computational results are presented for different solution approaches and conclusions are given. Finally, we implement post analysis and investigate the best tracking portfolios achieved from the three solution approaches. We summarise the findings of the investigation, and in turn, we further improve some of the algorithms. As the formulations of these problems are mixed-integer linear programs, we use the solver ‘Cplex’ to solve the problems. All of the programming is coded in AMPL.
Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London2015-01-01T00:00:00ZComplex networks with node intrinsic fitness: on structural properties and contagious phenomenaHoppe, Konradhttp://bura.brunel.ac.uk/handle/2438/103452015-03-06T03:00:22Z2014-01-01T00:00:00ZTitle: Complex networks with node intrinsic fitness: on structural properties and contagious phenomena
Authors: Hoppe, Konrad
Abstract: Complex networks is a vibrant research field and has received much attention over the last decade. Central to this area is the question of how networks around us are constructed. The essential notion of network research is that these systems are assembled in a decentralised way, thus no central agent is planning the network beforehand. Despite this lack of central coordination, many networks present intriguing universalities, such as broad degree distributions, in the form of power-laws. The subject of study in this thesis is a class of networks that are constructed by a node intrinsic variable, called fitness. The way these networks grow could be called a rich-get-richer mechanism. The fitter a node is, the more likely it is to acquire new connections inside the network. Several aspects that are directly connected to these networks are explored in this thesis. In the first part, the properties of growing networks that are driven by fitness are investigated and it is shown that the introduction of growth leads to a topological structure that is different from its static counterpart. In the subsequent chapter, percolation on fitness driven networks is studied. The results give insights into possible mechanisms that can stabilise systems. Furthermore, the theory can be used to identify vulnerable structures around us. In the following chapter, the world trade network is discussed. This numerical investigation highlights possible improvements to the methodology to make statistical analysis more robust. That chapter is followed by an analysis of time-varying networks.Time-varying networks represent an interesting construct that allows a formulation of stochastic processes on the same time-scale as the evolution of the network itself. This possibility is highly relevant to the investigation of epidemics, for instance. In the last chapter, a study of a system of clusters and their self-organised formation is presented.
Description: This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University London.2014-01-01T00:00:00Z