Hi Elia and welcome to the community.

You might find some of the articles here of interest especially the one called "So you want to be a Business Analyst".

In terms of qualifications, you don't need any - and employers in my experience just look for (in this order) experience of doing analysis in the employers' industry, followed by a good degree (which you have big time!) and lastly and always optional but an advantage a BA qualification like the ISEB Diploma in Business Analysis or the IIBA CBAP.

Given your lack of commerical experience you are probably looking at junior BA roles but getting those can be challenging and here's why...

In my experience Junior BAs usually aren't born - they mutate! The scenario I am thinking of is how I came to be a BA and one I have seen in my capacity as trainer many times: people from IT or the Business get a reputation for problem solving and get dumped in to the role when circumstances in their company change. Sometimes they jump in to the role but most often they seem to be dumped.

The question is - how did they get a reputation for problem solving? Answer: they were working alongside or even in change projects in some capacity and as a problem arose, they analysed it, solved it and got the reputation. So there may be a strategy for you here: instead of looking for junior BA roles look for roles that involve working alongside projects (e.g. project management office) - here in the UK for example there are always loads of temp agencies trying to fill these positions. Once in a project, make sure you have researched the role of a BA and know the outline of the theory at the very least. Then do your day job, watch and wait for your opportunity and start volunteering to help BAs, sort out requirements issues and so on. Get a few months of that under your belt and then you can update your CV to reflect that you have actually been doing analysis, and you might even be able to transfer in the organisation you have been gaining experience in.

You can then start applying for BA roles with the justification of having done the job even though you haven't been called a BA.

Oh - the other things are

1. get testimonials (preferably from Project Managers and BAs)

2. keep copies of the analytical work you do: suitable anonymised.

Nothing impresses interviewers like examples of your own analysis and testimonials if you can get get them (I haven't been refused one yet!).

I hope this is useful!

Google Chrome just stole my detailed post... back to IE for me for now

Based on what you've posted, I would think you would be well suited to a field that focuses on the development of complex algorithms to solve hard problems.  Quantitative finance, operations management and video game development (graphics and/or game AI) come to mind off of the top of my head.  In these areas you would not be a day to day coder necessarily, but instead focusing on developing provably optimal solutions. 

I'm not trying to dissuade you to get into BA positions if that's what you really want to do - it just sounds like from what you described that you would be more into a job that worked on solving interesting and challenging problems.  I worked in the before optimal nonlinear filtering, which we applied to areas such as defense, quant finance, performing arts and many others.

I would suggest that you start to look into some of the above fields and see what types of companies are hiring.  Typically large companies such as Lockheed Martin, Electronic Arts, etc. are your best bet.  I don't know what part of the world you're from, but a good place to start would be your school's career office.  If you don't have one, start chatting up your profs and see if they can help.  Look for applied science academics who have research projects sponsored by these types of companies.

One place to start that can show you the possiblities is the MITACS site.  This was an organization I was affiliated with in the past and focused on bringing advanced mathematics into industry.  I co-spun off a couple of companies from here, and have friends who did as well.  Look through their Partners and Commercialization pages to see what's out there and what can be done. 

Hope this helps!