Generally speaking the average guy marginally acquainted with quantum field theory or advanced combinatorics describes Wick's theorem as some sort of correspondence between higher order differential calculus and combinatorics. In fact more words can be added to drive the point. I want to understand something here. Can someone tell me what Wicks theorem is in the following fashion:
- Meaning of differentiation in ordinary language.
- New and suitable language for differentiation (say as used in QFT).
- Higher order derivatives in this language and why it is better than traditional language.
- Define a few basics of combinatorics as relevant to the problem.
- Make the connection with combinatorics.
- Make connection with quantum field theory.
If you are really sure this is not the right way to teach this stuff propose an alternative way, but start the description with X* so I am sure you are talking about something else. As usual correct me where necessary.