  An important goal of graduate physics core courses is to help students
develop expertise in problem solving and improve their reasoning and
meta-cognitive skills. We explore the conceptual difficulties of physics
graduate students by administering conceptual problems on topics covered in
undergraduate physics courses before and after instruction in related first
year core graduate courses. Here, we focus on physics graduate students'
difficulties manifested by their performance on two qualitative problems
involving diagrammatic representation of vector fields. Some graduate students
had great difficulty in recognizing whether the diagrams of the vector fields
had divergence and/or curl but they had no difficulty computing the divergence
and curl of the vector fields mathematically. We also conducted individual
discussions with various faculty members who regularly teach first year
graduate physics core courses about the goals of these courses and the
performance of graduate students on the conceptual problems after related
instruction in core courses.
