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The answers in the comments are probably the best (in particular @James S. Cook's advice to talk to a professor at a local university if you have such a connection) but here's at least a list to get you started: Given that you've got quite a range of interested there I would suggest going through the MAA's list of Math programs: https://www.maa.org/...


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Since you are in the UK, I have a few specific suggestions below. I agree with existing answers and comments that there is little benefit in rapid acceleration. The Royal Institution hosts mathematics masterclasses in some areas. See https://www.rigb.org/education/masterclasses for more information. Sometimes the sessions are for students in specific age ...


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