Co-requisite: MATH 791. Approval of the dissertation advisor is required for registration. Experimental and/or theoretical investigation of a relevant topic in mathematical sciences. For PhD students who have successfully defended their dissertation proposal. The student must register in MATH 790A every semester until successful dissertation defense. A written dissertation must be defended and approved by a committee of at least five members. Students enrolled in the PhD program before 2015 Fall must accumulate a minimum number of credits in Doctoral Dissertation Research and Pre-Doctoral Research (see graduate catalog for program-specific details; the same requirement may apply to joint PhD programs with other universities).