Your residence permit for studying is bound on a certain purpos. Therfore your residence permit is issued for a concret subject. Take a look on your green paper „Zusatzblatt zur Aufenthaltserlaubnis“ it says exactely for what purpos you are allowed to stay in Germany. 

Please note that it is very important to get the permission from the foreign authorty bevore you change your subject. Only with the allowence of the foreign authority you can exmatriculate and enrole for a new subject. Please come in good time to „Hochschulbetreuungsstelle“ and talk with us about your plans if you think about changing your subject.