The Nearest Neighbor algorithm is one of the simplest and oldest classification techniques. A given collection of historic data (Training Data) of known classification is stored in memory. Then based on the stored knowledge the classification of an unknown data (Test Data) is predicted by finding the classification of the nearest neighbor. For example, if an instance from the test set is presented to the nearest neighbor classifier, its nearest neighbor, in terms of some distance metric, in the training set is found. Then its classification is predicted to be the classification of the nearest neighbor. This classifier is known as the 1-NN (one-nearest-neighbor). An extension to this classifier is the k-NN classifier. It follows the same principle as the 1-NN classifier with the addition of finding k (k > l) neighbors and taking the classification represented by the highest number of its neighbors. It is easy to see that the implementation of the nearest neighbor classifier is effortless, simply store the training data and their classifications. The drawback of this classifier is found when a test instance is presented to be classified. The distance from the test pattern. to every point in the training set must be found. The required computations to find these distances are proportional to the number of training points (N), which is computationally complex, especially with N large. The purpose of this thesis is to reduce the computational complexity of the testing phase of the nearest neighbor by using the Hilbert Space Filling Curve (HSFC). The HSFC NN classifier was implemented and its accuracy and computational complexity is compared to the original NN classifier to test the validity of using the HSFC in classification.

Mathematics is perceived as a difficult subject to many students internationally and Sweden ranks among EU/OECD countries that perform poorly, cited in the TIMSS 2007 assessments. The aim of this essay is to investigate the causes of the poor performance in Mathematics in many of Swedish Secondary schools and it will contribute to the solutions of this problem. The framework of this essay takes into consideration issues on; school curriculum, instruction of knowledge by teachers, construction of knowledge by students, their interactions and experiences in the situation of learning. Teaching methods have been seen as the starting point upon which students can be invited to carry out communications, reasoning and arguments in mathematics. This can be useful in developing capabilities of solving mathematical problems as recommended in Secondary School regulations book. The interviewed teachers’ experiences and approaches in selecting teaching methods have been interpreted to correspond with students’ involvement in learning mathematics. The essay has found out that there is a positive effect on understanding mathematics if teachers can select teaching methods that suits a specific object of learning. This however, has left one disturbing question for further researchers to answer; to whether it is enough for highly motivated and hard working students to study mathematics based on memorized wisdom (ideas) as it does not promote mathematical awareness.

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The following thesis is at once a somewhat rudimentary attempt to relate the history of the classroom while describing the potential impact on the space of learning by the introduction of a new type of computer program into a school setting. It asks the question: how is the space of learning affected by the use of this specific type of computer program as an educational tool? In order to begin to formulate an answer to this question I have drawn upon the theorizing of Foucault and Deleuze in particular. Establishing the modern classroom as a relative of sorts to the disciplinary spaces of the past, I conclude that the means and practices by which pupils are being controlled within the space of learning have shifted from discipline being extorted exclusively by the teacher – who in turn is aided by the physical and temporal constraints of the classroom – to control being applied by each individual pupil through technologies of the self. This, in turn, led me to the conclusion that although there are certainly quite tangible effects on the space of learning itself, the actual mode of learning may very well be kept intact through techniques designed to control the behavior of the individual pupil beyond the disciplinary spaces of the past.

Originating from a disenfranchisement with the contemporary definition and realisation of Westernised architecture as a commodity and product, this thesis seeks to explore alternative examples of positive socio-spatial practice and agency. These alternative spatial practices and methodologies are drawn from participatory and grass-roots development agency in informal settlements and contexts of economic absence, most notably in the global South. This thesis explores whether such examples can be interpreted as practical realisations of key theoretical advocacies for positive social space that have emerged in the context of post-Second World-War capitalism. The principal methodological framework utilises two differing trajectories of spatial discourse. Firstly, Henri Lefebvre and Doreen Massey as formative protagonists of Western spatial critique, and secondly, John F. C. Turner and Nabeel Hamdi as key advocates of participatory development practice in informal settlements. These two research trajectories are notably separated by geographical, economic and political differentiations, as well as conventional disciplinary boundaries. However by undertaking a close textual reading of these discourses this thesis critically re-contextualises the socio-spatial methodologies of participatory development practice, observing multiple theoretical convergences and provocative commonalities. This research proposes that by critically comparing these previously unconnected disciplinary trajectories certain similarities, resonances and equivalences become apparent. These resonances reveal comparable critiques of choice, value, and identity which transcend the gap between such differing theoretical and practical engagements with space. Subsequently, these thematic resonances allow this research to critically engage with further appropriate surrounding discourses, including Marxist theory, orientalism, post- structural pluralism, development anthropology, post-colonial theory and subaltern theory. 5 In summary, this thesis explores aspects of Henri Lefebvre's and Doreen Massey's urban and spatial theory through a close textual reading of key texts from their respective discourses. This methodology provides a layered analysis of post-Marxist urban space, and an exploration of an explicit connection between Lefebvre and Massey in terms of the social production and multiplicity of space. Subsequently, this examination provides a theoretical framework from which to reinterpret and revalue the approaches to participatory development practice found in the writings and projects of John Turner and Nabeel Hamdi. The resulting comparative framework generates interconnected thematic trajectories of enquiry that facilitate the re-reading and critical reflection of Turner and Hamdi's development practices. Thus, selected Western spatial discourse acts as a critical lens through which to re-value the social, political and economical achievements of participatory development. Reciprocally, development practice methodologies are recognised as invaluable and provocative realisations of the socio-spatial qualities that Western spatial discourse has long advocated for, and yet have remained predominantly unrealised in the global North.