Putting complex variables into a separate forum

[brmath]

Right now all the material about complex functions is in the general math section. Complex analysis comes up a lot and probably deserves a section of its own, or at least to be put in the analysis section.

 

[strangerep]

Complex analysis comes up a lot and probably deserves a section of its own, or at least to be put in the analysis section.

The description of the "Topology & Analysis" forum says:

Point-set topology. Real, complex, harmonic and functional analysis. Measure and integration theory

I.e., complex analysis is already there.

 

[jackmell]

The description of the "Topology & Analysis" forum says:

I.e., complex analysis is already there.

And in my opinion, we're doing a dis-service both to the field and to students wishing to learn about it by placing it there.

 

[brmath]

complex analysis

I understand that I didn't properly read the description. But now that you've pointed it out to me, it seems awfully broad. Also, the inclusion of the term "harmonic analysis" may introduce some confusion, as the real and imaginary parts of an analytic function are harmonic functions, a different topic. The study of harmonic functions probably belongs in with complex variables (although you may, quite justifiably, have it under differential equations?).

So I now know where to look re complex analysis, but still wonder if the forum would consider carving it out into a separate place.

Of course, trying to categorize mathematical topics is very difficult because math is very intertwined and no matter what category you choose, something from some other category will pop up there.

 

[strangerep]

Micromass did a fantastic job of reorganizing the math forums some time ago. Imho, the new organization is a considerable improvement over the old, although there was inevitably some nitpicking. You can't please everybody.

A couple of remarks:

"Complex analysis" is a much larger (and more advanced) subject than mere calculus of complex variables.

"Harmonic analysis" is likewise a much larger and advanced subject than you seem to realize.

For "complex variables" to justify its own forum there would have to be a sufficient number of threads on that subject such that it dominated the existing forum(s). What is the current creation rate of new threads on that subject in the existing forum(s)?

OTOH, I think a case could be made for augmenting the description of the "Calculus" forum to say
"Real & complex elementary functions"...

 

[Nugatory]

Of course, trying to categorize mathematical topics is very difficult because math is very intertwined and no matter what category you choose, something from some other category will pop up there.

I don't have a dog in this fight...

But having tried to organize other online discussions in the past, I will say that in my experience splitting only works if the lines between categories are crystal-clear obvious to the majority of people who will be starting threads.

 

[WannabeNewton]

And in my opinion, we're doing a dis-service both to the field and to students wishing to learn about it by placing it there.

Surely you jest? You do realize that there is a limit to pointless pedanticism don't you? If you're being serious then boy...just boy.

 

[brmath]

Micromass did a fantastic job of reorganizing the math forums some time ago. Imho, the new organization is a considerable improvement over the old, although there was inevitably some nitpicking. You can't please everybody.

A couple of remarks:

"Complex analysis" is a much larger (and more advanced) subject than mere calculus of complex variables.

"Harmonic analysis" is likewise a much larger and advanced subject than you seem to realize.

For "complex variables" to justify its own forum there would have to be a sufficient number of threads on that subject such that it dominated the existing forum(s). What is the current creation rate of new threads on that subject in the existing forum(s)?

OTOH, I think a case could be made for augmenting the description of the "Calculus" forum to say
"Real & complex elementary functions"...

Actually, I'm well aware of the extent and difficulty of complex analysis -- could be that's why I thought it should be separate. However, I think the question of how many threads could be a very sensible determining factor. Re harmonic analysis, of course it's a very big subject -- one which has nothing to do with harmonic functions -- I mentioned it because I thought there could be some confusion.

I can well imagine what a job Micromass had, and didn't mean my remarks to sound like a complaint.

 

[jackmell]

Surely you jest? You do realize that there is a limit to pointless pedanticism don't you? If you're being serious then boy...just boy.

No I don't jest. I'm simply expressing my personal opinion about the subject: I would like to see a separate sub-forum for Complex Analysis. And burying it in the Topology gang's hang-out is in my view just creating a nuisance for that group while simultaneously inhibiting members from entering "big-time" Topology and creating a baby thread in for example the Cauchy-Riemann equations or the Residue Theorem. The entire field of Complex Analysis in my opinion suffers from bad books, poor teachers, and lack of emphasis. In order to grasp mathematics more comprehensively, students should understand the underlying complex analytic structure which is the basis for much of their real analysis.

Just yesterday a student in one of the math forums was confused about the graph of the square root function. They did not understand this function is more than just the positive real values of the function. Knowing the complex analytic geometry of the entire function gives one a more comprehensive understanding of the underlying mathematics. And this is true in my opinion of other concepts such as complex solutions to differential equations.

We should place more explicit emphasis on Complex Analysis.

 

[brmath]

Jackmell -- I am with you. I agree that complex analysis tends to get shunted aside, and that this is stupid since it explains so much. I don't think the students who are confused about square roots are ready yet to benefit. But I sure have. For example I was looking for a definition of real analytic function. Everyone says it's analytic if its Taylor series converges. Great -- how would I know that? The simple definition is that it is analytic at x if it is analytic as a complex function in a neighborhood of x.

I have had only bad teachers of it, but I had a good book which taught me the subject. I was going to tell you what it is, but it seems to have vanished from my bookshelf. Grrr.

 

[WannabeNewton]

If you have a question regarding complex analysis then post it in the analysis section. If you think something as comically and ridiculously trivial as the subsection allocation of a mathematical subfield serves as an obstruction to you from physically posting a complex analysis question then you need to rethink your priorities in life.

 

[brmath]

Hi Wannabe...

Actually I'm looking to answer questions or see answers, not so much to post them. When I go to the analysis section I then have to troll through numerous questions that would not interest me. So it would be easier if the complex analysis were in a separate section. Not that I can't manage as things are; just that it would be easier. I think that might also encourage more questions in that subject.

Sometimes you may not understand why someone is requesting something "comically and ridiculously trivial"; there could be reasons why the request is valid. The reasons can even be deep instead of a matter of convenience as this one is. You just never know. Yes there are some idiots out there, but there are also a lot of people out there with a lot of situations which you might not be able to guess at.

And given that I am an idiot sometimes, although widely considered brilliant among my friends, I believe in treating idiots kindly too. So I personally avoid editorializing, although I may laugh in the privacy of my own home. Perhaps you could have worded it as: "what is stopping you from just posting your complex analysis problems in the analysis section?"

 

[jgens]

Actually I'm looking to answer questions or see answers, not so much to post them. When I go to the analysis section I then have to troll through numerous questions that would not interest me. So it would be easier if the complex analysis were in a separate section.

It would be easier for me if algebraic and differential topology each had their own sections for exactly the same reasons. Maybe we could also add a section for category theory too since I would like to answer some questions about that. It would also be great if we made a separate little section for algebraic geometry so I can save myself the effort of having to scroll through bunches of unrelated threads about groups and rings and vector spaces in the algebra forum. I get that some members want separate subforums for certain topics, but the point is that it's really not practical, especially if you want to please everyone. The current system is by no means perfect, but it does divide up the topics in a reasonable manner, and it avoids the problem of creating too many subforums.

 

[Enigman]

Perhaps just tagging the threads accurately would work...

 

[brmath]

It wouldn't hurt, but it's hard to see how you could get everyone to do that. It really comes down to balancing not getting too many subforums with not so few that people get lost in details. There is probably no one best answer to that -- various people will have different opinions, and most of those will not be wrong in any absolute sense. Also, it may be the the better solutions change over time, depending both on the mix of forum users and the directions in which math is moving.