I am an amateur mathematician with an interest in the subjects named in the title. I have recently come to understand that my B.A. in math gives me absolutely no qualification at all in the Swedish job market. Hence I will try to compliment it with something else. I'd like to remain as close as I can to the pure world so now I'm wondering if anybody has any idea of related yet practical fields.
Edit: I am thinking (very vaguely) that there might be something along the lines of organizing database into functional and searchable structures.