This looks like it has an 8-semester prerequisite sequence, unless the student can start in a more advanced math course with AP credit:
MATH 1151 → MATH 1172 → MATH 2173 → MATH 2174 + MECHENG 2850.01 → MECHENG 3670 → MECHENG 3671 → MECHENG 4900 + MECHENG 490X.01 → MECHENG 490X.02