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I am about to go in to my honours year in computer science.

If I intend to apply for a PhD at another university when I finish, how much does it matter who my honours supervisor is? Will this make any difference when being assessed for entry at another university?

And as a general rule am I better choosing a pure (mathematical) or applied (programming/engineering) topic?

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All things being equal, a well-known and respected individual in your field who can write an excellent letter of recommendation for you is better than a person who is not nearly so well known who can write a similar letter.

However, you should not choose a famous name just to have that person write you a letter of recommendation if you are not actively interested in that person's research. The obvious reason for this is that hunting for a letter of a recommendation is likely not to work as well as doing a project you're truly interested in, because the motivation to work on it won't be nearly as strong.

As for topic, if possible, I would recommend picking a topic in the general area you wish to pursue as a PhD student. Note that it doesn't need to be the same topic—but if you want to do, for instance, theoretical CS, it's probably better to do a theoretical CS project than something more applied.

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