In a certain STEM graduate course, my professor made a claim and provided an solution without showing any derivations. After doing this, he mentioned that the students should derive the solution at home. I was able to derive the solution, but I was uncertain about some parts of my derivation. Basically, I wasn't sure if I was "right for the wrong reasons." As a result, I typed up my work and emailed it to my professor and mentioned my uncertainty. A part of his response was the following:
"Your work is so thorough!"
Is it appropriate to respond with the following:
Dear Dr. _______, Thank you very much. Sincerely, _______
Does this response seem like I am proud of the compliment? Does it make me seem arrogant? Or is this short response appropriate?
Note: My professor is in my grandparents' generation. He is from Eastern Europe.
Note: I always say "Thank you very much" to any professor's email, but all such emails were NEVER responses to compliments. This is not the first time I have taken a class taught by this professor.