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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?

John. p
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    What do you study? What academic undergraduate is that class for? – DonAntonio Mar 08 '14 at 15:59
  • Proofs are useful because -among others- they use a lot of computational techniques (tricks) that one can use in exercises or latter in research. So, I would suggest, be patient, it will be just a course, but never choose one of his courses in the future again. – Jimmy R. Mar 08 '14 at 16:00
  • @DonAntonio Senior of mathematics.. – John. p Mar 08 '14 at 16:04
  • Personally, I would drop the course and take a different one (if possible) only because of your first paragraph. I'm not sure whether choice of definitions is actually detrimental, but I'm only a beginner. – user7610 Mar 08 '14 at 16:05
  • @John.p , then more than unusual I'd say it is seriously flawed ad I wonder how come that university's mathematics Dept. allows such a thing in such a basic course. Besides the already said reasons, proving stuff enhances logical reasoning and develops calculating and proving skills. – DonAntonio Mar 08 '14 at 16:06
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    I agree with fish: if possible drop the course and also complain to the head master. – DonAntonio Mar 08 '14 at 16:08
  • What text is the lecturer using? Is this text/syllabus his design or is he just assigned to the course? What is his background and rank, e.g. is he grad student, a mathematical physics person, an adjunct professor, or...? – Emily Mar 08 '14 at 16:12
  • @Akramis Real Analysis by E.Stein. I don't know about his backgrounds but he even told me that this year is the first time he's reading this text. When i asked a question in real analysis, he said he learned real analysis about 20years ago so he needs to study again to answer that question.. – John. p Mar 08 '14 at 16:15
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    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 08 '14 at 16:52
  • He should have been a physicist. Maybe got in the wrong line. – evil999man Mar 08 '14 at 17:17
  • I was lucky to have had Analysis/Topology lectures by Prof. Manfred Lehn (Mainz, Germany) who is lecturing always exclusively by heart including all proofs. That is very impressive. – Raffael Mar 08 '14 at 19:28
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    The definition of limit point you gave is the one I'm familiar with. It's also the definition given on Wikipedia: http://en.wikipedia.org/wiki/Limit_point. What is the "usual" definition? – Cocopuffs Mar 09 '14 at 01:25
  • @Cocopuffs No, it is not.. Following wikipedia definition, an isolated point is not a limit point. However, following my lecturer's definition, every isolated point is limit point! Do you see the difference? – John. p Mar 09 '14 at 02:35
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    @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 09 '14 at 04:03
  • @Cocopuffs I remember correctly that he restricted everything to Euclidean and he defined a neighborhood as an open ball, which is again not the general definition of neighborhood. – John. p Mar 09 '14 at 06:44
  • If the definitions in class don't agree with the text, run away as fast as you can. – vonbrand Apr 13 '14 at 05:37

3 Answers3

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

William Chang
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  • What should i do? Is there any facility i can complain this? – John. p Mar 08 '14 at 16:01
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    @John. p You should be able to complain to the relevant faculty of wherever you are taking the class at. – Andrew D Mar 08 '14 at 16:02
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    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 08 '14 at 16:04
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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.

Community
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Claude Leibovici
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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 08 '14 at 16:09