# Is it usual that a professor never proves a theorem in a class?

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?

• What do you study? What academic undergraduate is that class for? – DonAntonio Mar 8 '14 at 15:59
• I agree with fish: if possible drop the course and also complain to the head master. – DonAntonio Mar 8 '14 at 16:08
• You meet such people every once in a while. I agree, that doing proofs is essential, still, don't be so harsh, my experience is that such people usually have great intuitions and it is a big opportunity to learn, to gain a deeper understanding (even at the cost of proofs, which I recommend you to do by yourself). However, I must admit, this only applies to mathematicians of world class (i.e. if it made him/her a world-class mathematician, then it's worth listening to, whatever it is); if someone is skipping proofs because he lacks the knowledge or understanding, get away as fast as you can. – dtldarek Mar 8 '14 at 16:52
• The definition of limit point you gave is the one I'm familiar with. It's also the definition given on Wikipedia: en.wikipedia.org/wiki/Limit_point. What is the "usual" definition? – Cocopuffs Mar 9 '14 at 1:25
• @John.p Assuming that by neighborhood, your lecturer means neighborhood excluding $p$, then I don't see the difference. Of course, if your lecturer means neighborhood containing $p$, then every point will always be a limit point. I guess the issue was with the definition of neighborhood and not of limit point. – Cocopuffs Mar 9 '14 at 4:03