What kind of experience do I need to get into an AI master's programme? I'm about to go into my third and final year of my mathematics degree and I recently discovered some master's programmes in AI that really interest me. I have very little experience in programming. I've done some very basic programming in Python when I was doing my A-levels and some of my Uni modules so far included the use of MATLAB, Maple and R. I'm also going to be doing a module called Formal Languages and Theory of Computation this year, but I feel like this is not going to be enough to show my interest in the subject when I apply.

Can anyone advise on what sort of things I should be doing over next year in order to prepare myself for a course in AI and how do I go about doing them? 

Thanks!
Well, mathematics is a very strong field in AI as that is what most AI algorithms revolve around. You only need to learn how to write code (Mostly python or c++, python is easier to learn in my opinion) and how to write mathematical equations in code. Once you have that down it should be enough but I don't how courses work at yours as I know our University require a degree in computer science.

If you want to impress somebody then I can pass you an old University assignment I had about backpropagation in neural networks. It does not involve any code but to determine the partial derivative of an equation that is used to update weights in a neural network. If you do the assignment correctly you should know the basics of how a fully connected neural network works, which is the cornerstone of most neural networks, and also how to train it through backpropagation using only maths. Not only would you know how neural networks work but you would have something to show for it. Witch hopefully could contribute to applying for your Masters. 

Lastly, I know of people that wrote scientific papers in the realm of computer science, to prove they would survive in masters, and then applied for a Master's degree in Computer Science. If you are really serious about it you can do this but just double-check with someone as you might do all the work for naught.