I'm taking "real analysis" this year and the lecturer's major is PDE.
What he does is literally reading texts except proofs. This drives me crazy, so I asked the professor why he is not giving any proofs, and then he told me, "I'm not interested in proofs. I just understand big stories. If you are interested in the foundation of mathematics, go find a such professor".
I absolutely don't agree with him and don't understand him. I even got offended. Is it usual that a professor never proves a theorem in a class?
Moreover, he's giving definitions nobody uses. For example, he defines a limit point $p$ of $A$ as a point where every neighborhood $N$ of $p$ and $A$ are not disjoint. This is not the usual definition of a limit point.
I'm hesitating to drop the course and study it by myself. Have you ever experienced a similar case before? What was your choice?