Team work at Masters level Ok so first off a bit of background. I've been working professionally three years in a software engineer position after my BSc. in Mathematics and Physics. At some point I realized I missed doing true research so I enrolled in Masters in Financial Mathematics, which seemed to me the ideal trade off between maths, programming and well finance which is quite interesting.

So now, here I am, first year, with full time lectures. My first reaction was to be disappointed by the amount of team work, since in my BSc days all homeworks were individually graded. For some mathematics courses it's fine, since there's a single good answer. However, there are some instances where it's definitely more research-like, almost like a lab report actually. 

What however is unnerving is that I'm stuck with teammates with whom I don't exactly share the same work ethic. For instance, I had to insist on writing formal proofs. Anyway, I just feel that if it wasn't for me we'd keep to the bare minimum. AFAIK this is quite different from the industry where, if a team screws up, then either someone is going to get fired or at least the team is going to be split by the management. Here, the prof just won't care and will assign a global grade and go on to the next team. 

So I'm not sure what's the right path. On one side, I really want to make sure our team performs well, this is quite a big move I made here, but on the other side, I just don't want be bossy with them, yet here I am writing emails where I detail clearly what I'm awaiting from each of us. Also, well, I haven't talked openly with them about this issue, I'm not certain how I can bring it.
As scaaahu commented: This happens ALL the time in industry (one could say it is the rule, not the exception). We do not always get to pick our teams and it is common for high-performers to be stuck with those who do not really care about the quality of their work. Will someone get fired in industry? Maybe...maybe not (complex issue).

The thing you must understand is the difference between management, where someone has formal authority based on their position in the organization, and leadership, where someone's authority basically comes from the followers.

If your team is fill with under-performers you need to figure out if you can use some leadership skills to motivate them to do better. This is the same when studying and when working. If you cannot motivate them then you must decide if someone else can (perhaps you need to encourage someone else to act as the leader). If it seems the team simply cannot be motivated, then you should do your best to find another team.

A team can only be successful if the team feels like a team and that means, in part, that everyone believes in the same goal and are willing to sacrifice to achieve that goal.

The solution is to develop some leadership skills and have a direct talk with the team about what they hope to achieve.