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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?

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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: 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
up vote 15 down vote accepted

This is not usual. Most undergraduate classes, especially real analysis, are proof-based.

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What should i do? Is there any facility i can complain this? – John. p Mar 8 '14 at 16:01
@John. p You should be able to complain to the relevant faculty of wherever you are taking the class at. – Andrew D Mar 8 '14 at 16:02
If there's nothing that the faculty wants to do/can do, you have to make a decision about whether or not to stay in the class. If the credits aren't necessary/useful for you, I would advise studying it on your own if you can. – William Chang Mar 8 '14 at 16:04

I totally agree with what other participants say: QUIT this course. It is a serious matter: your future. Then nobody has the right of joking or playing with it as an incompetent lecturer can do.

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Real analysis classes are all about proofs. The definition of limit point given is also not the usual one. I highly doubt the competency of your lecturer. Complain immediately to the head of department.

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I'm not sure the definition of limit point is wrong, but it is unusually phrased. I suppose the distinction is whether by neighborhood he means punctured neighborhood. But the presentation is awkward, for sure. – Emily Mar 8 '14 at 16:09

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