Below is the advice my mentor gave me for Personal Statements. I'm submitting mine pretty soon and It's much better than it was because of this. Take it or leave it though, it's your statement
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Oxbridge basically don't care about extra-curricular activities, and most other top unis (which I hope you'd be applying to also) won't care much either. Now I'm not saying you're whole personal statement should be about computer science (mine wasn't), but you shouldn't be using a significant proportion of your statement on it either. Try and link it to your subject if you can, but don't force it, not everything has to be about Computer science, just make sure it demonstrates something about you.
Show that've gone above and beyond what you're taught in school. I guess it actually kind of works well for you because you don't do Computing A-Level, so anything to do with Computer Science is your own decision. This is my idea, so take it or leave it: Show a progression, an example:
- I learnt about Bayes Theorem in school, I heard about Bayes Classifiers
- Attended a lecture/taster day
- Built my own Naive Bayes Classifier
If you haven't done much, build something. Computer Science is one of the only courses (a reason why I love it) is where you can, in your free time, create something without much experience. Then on your PS, talk about a field you're interested in, and you can demonstrate it, by talking about what you learnt when you built a web app/phone app or even a simple script.
Don't boast, don't list
Don't get too attached to what you've written, I went through about 13 drafts and there wasn't a single sentence that didn't get changed/removed/added from the original draft.
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I also got a personal statement hints sheet with examples attached if you want to take a look. I used this too but I wouldn't follow it to the letter. Talk more about academics and super-curricular stuff (programming, work experience at a relevant company, building things) and less of everything else.
- Emmanuel