WordPress MU

I have wpmu installed on a domain, set-up to use sub-directories. I would like to have multiple sites on different sub-domains each using sub-directories for the different blogs.

Basically I would have a series of sub-domains for the subjects I teach e.g. economics.mydomain.com and business.mydomain.com and each one of these would represent a wpmu site using sub-directories. This would then allow me to have blogs for students in each class, e.g. economics.mydomain.com/jim/, economics.mydomain.com/andrea/ and business.mydomain.com/jane/, business.mydomain.com/alex/

I have tried to use the multi-site manager plugin and it will allow me to set up a site economics.mydomain.com, but when setting up a new blog on this site it is set up as a sub-directory of mydomain.com e.g. mydomain.com/john/ rather than economics.mydomain.com/john/

Does anyone know if it possible to do what I want without setting up a separate install of wpmu on each sub-domain?

Then you've got the wrong multi-site plugin, because I know there's at least one out there that works exactly how you want.

modesty prevents andrea_r from mentioning it directly, but i can :-)
http://wpmututorials.com/simple-multi-site-plugin-e-book/

If one were to use this plugin with this type of installation how would they go about changing the cookies to enable site wide login and logouts across sub domains?
Please, please, tell me that's doable.