Is Diplom-Mathematiker equivalent to M.Sc?
(Note: The answer is primarily referring to the question in the title, which is not quite the same as the one in the text.)
No. Why would you think so?
Diplom-XXX is a title which is, mostly, not awarded any more. The "Diplom" system has been replaced with the BSc/MSc-system. But this does not mean they are equivalent (it is a rather different system), and you certainly cannot call yourself Dipl.-Math..
From a more pragmatic point of view, I would consider it a more or less equivalent degree. But again, this does not mean you can call yourself "Diplom-Mathematiker" if you got an MSc in Maths.