I am starting an MSc in Computer Science in the autumn and I am concerned that I don't have any research experience. My interest is in Theoretical Computer Science and I am finding it hard to find any internships, as there is very little funding for undergraduates available at my university and no advertised positions in this area. I have seen an industrial position that matched my interests, but it was only advertised for Msc/PhD students.
I asked around last year and was unsuccessful but it was suggested that I self study a topic, so I don't know if I should do this again, or try to pursue an actual internship.
I think the reason I was unsuccessful was that I was too general and not specific enough about my interests. However, as an undergrad I am finding it hard to identify something that is achievable at my level and to narrow down to one area.
Therefore, would it be better to find a paper and a topic and directly approach an academic, or would I be better off using the summer to study more broadly and find a specific topic to pursue? Is there anything else I should do to increase my chances of getting an internship?