2

I have yet to ascend to the heights of university education, and before I do, I would like to clear something up:

As I was revisiting a book on complex analysis, I see questions like the following:

Show that if $f(z)$ is holomorphic on $\mathbb{C}$ (entire) and $f(z)\not \in \mathbb{R^+}\cup \{0\} $ for all $z\in \mathbb{C}$, then $f(z)$ itself is constant.

The usual method is to observe that $g(z)=\ln(f(z))$ is holomorphic, and that the imaginary part of $g(z)$ is bounded, but suppose that in a college exam I were to write: "Picard's Theorem: QED" (and perhaps a line or two to show that I know what it means, although I have no idea how to prove it). Would I lose points and be disciplined? Are professors annoyed about such things?

I am thinking about such questions because I did not see the elementary solution immediately, and I suppose that one does not enjoy the privilege of time in an exam, with the air conditioning freezing one's hands and grades to fret about.

Chris Sanders
  • 7,137
  • 10
  • 23
  • A related and amusing story: I believe that a Brazilian prodigy who represented his country in some Ibero-American Mathematical Olympiad found that the last question was a straightforward application of advanced elliptic curve theory. Much to the fury of virtually everyone involved, the authorities disqualified him because they had not expected graduate-level material. – Chris Sanders Jul 19 '16 at 13:46
  • 2
    Solving a question with material not covered in the course makes it hard to grade someone. In principle you should prove everything you use not covered in the course itself. – Mathematician 42 Jul 19 '16 at 13:55
  • 1
    Something else worth noting is that it is often times easy to appeal to high-powered weaponry to dispense with problems on exams. The issue is that the statement of the theorem you want to use is likely substantially easier than the proof. The function of the exam question is to test your knowledge of the material, not test your ability to recall the largest weapons in your mathematical arsenal. – A. Thomas Yerger Jul 23 '16 at 08:37

0 Answers0