For the thesis component, a student will undertake independent study in the appropriate area of applied mathematics, pure mathematics, physical oceanography, quantitative risk or statistics according to their honours stream. The student will be supervised by at least one member of the academic staff of the School of Mathematics and Statistics, possibly jointly with an academic external to the School, or, with the permission of the Head of School, a suitable other person in a non-university research position. The student will write a thesis and give an oral presentation on the thesis to the appropriate department. 


数学和统计学论文|MATH4001 Mathematics and Statistics Honours Thesis

In essence, fun can be conceptualized by a combination of utilitarian and hedonic aspects. The former is directly related to performance, being about interesting physical or cognitive challenges and the ways to overcome them, as well as the recognition of interesting but yet unknown patterns in the world. The latter is related to affect, thus about the emergency of empathy with objects and characters and, specially, the experimentation of emotions. B oth of them are related to the gradual focus of attention, either to focus on tasks at hand or awe from sensory and imaginative information. The utilitarian aspect of fun does not exist without the hedonic aspect. First of all, performance requires involvement, so the needed skills c an be experienced and learnt. But also because emotion is necessary for actions (Lazzaro, 2010 ). Consequently, fun can be defined by two essential dimensions, as it is summarized by figure $2.10$ : immersion, as the increasing level of involvement with the task, that subsumes all the sensory, cognitive and emotional systems, and the emotions experienced by performing the task, which can be considered pleasurable despite their general likeness in other contexts.

Among the emotions that are important for the experience of fun there are the six prototypic emotions and also the pleasurable emotions named Fiero $^{7}, N a$ ches $/$ Kvell $^{8}$ and Schadenfreude ${ }^{9}$. But even though these pleasur able emotions can be distinctly recognized by players experiencing them, they seem to have roots on the prototypic emotions. For instance, the bodily changes produced by Fiero are very similar to the ones that accompany extreme Anger, while Schadenfreude’s bodily changes have been shown to not differ from Joy’s (Boecker et al., 2015 ). Therefore, the prototypic emotions are arguably the most relevant emotions to the experience of fun.


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