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              <text>This project report explores the base sizes of group actions. We begin with some preliminary definitions and results. Next, we investigate a combinatorial approach to proving the bound $|G| \geq 2^{b(G)}$; we give a conjecture for a stronger statement concerning a system of distinct representatives for sets $\left\{ \bigcap\limits_{\alpha \in \Omega}\mathrm{Stab}_G(\alpha) : \emptyset \neq \Omega \subseteq B \right\}$, where $B$ is a minimal base for a permutation group $G$.  Subsequently, we follow a paper of Burness, O'Brien and Wilson in explaining various computational and character-theoretic techniques that can be used to compute base sizes. Finally, we apply these methods to a selection of almost simple sporadic groups and their subgroups.</text>
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              <text>&lt;p&gt;I finished my 2nd year of mathematics knowing a lot of maths but feeling unconfident in how to do “real world” problems that involved data, numerical methods and statistical tests. Therefore, I was so excited to work with Siri Chongchitnan in a Cosmology research project. &lt;br /&gt;&lt;br /&gt; I learnt practical Bayesian statistics which is something that passes by a lot of maths students unless they take a more academic module. Then, I learnt some Cosmology and the programming language R, to infer things like the curvature of the universe from real telescope data! &lt;br /&gt;&lt;br /&gt; The actual project took the form of me and my supervisor discussing what I would spend the next week researching/investigating, and then me trying to do that. So, whilst I wasn’t going in blind, I was doing the researching and problem solving myself which was fun (but tough in places).&lt;br /&gt;&lt;br /&gt; Furthermore, me and my supervisor got on really well. Therefore, an unseen bonus of the URSS was having someone to chat to about my future who had studied the things I wanted to study. Now in fact, he is supervising my 3rd year essay.&lt;/p&gt;</text>
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