View Full Version : Topology

08-25-2007, 11:26 PM
Hello all,

I am still thinking what courses I should take in the coming semester:

There is no topology course in my school except the graduated one which requires Abstract Algebra 4. So I gave it up.

However we have a course ' independent study'.

We can take this class with the prof only if our school does not offer that course.

As known, it s good to take topology for phd application.
And as I said we dont have it for undergraduate students.

When I checked what topology today..I found...

Topology (Greek (http://en.wikipedia.org/wiki/Greek_language) topos, "place," and logos, "study") is a branch of mathematics (http://en.wikipedia.org/wiki/Mathematics) that is an extension of geometry (http://en.wikipedia.org/wiki/Geometry). Topology begins with a consideration of the nature of space, investigating both its fine structure and its global structure. Topology builds on set theory (http://en.wikipedia.org/wiki/Set_theory), considering both sets of points and families of sets.

Ours school offers set theory.
So should I take set theory or ask the department if I can take the independent study for Topology?

For your reference, here is the description of the course: set theory at my school:
Axioms of set theory. Operations on sets. Ordinal and cardinal numbers. Well-orderings, transfinite induction and recursion. Consequences of the axiom of choice. Boolean algebras. Cardinal arithmetic.

What should I do?:hmm::hmm::hmm::hmm::hmm:

08-25-2007, 11:38 PM
I am not sure how your school works, but at my school, set theory is required in order to take real analysis. and real analysis < topology in terms of level of difficulty. so i am not sure if a course on set theory and a course on toplogy are comparable.. your description of set theory sounds exactly like the set theory i had to take in order to take real analysis.. if you are not familiar with the topics covered in set theory i think you ought to take it first.

08-26-2007, 12:32 AM
Thanks so much for your reply.

What about this course?
It says it s analysis 3.

Introduction to metric spaces. Multivariable differential calculus, implicit and inverse function theorems.

It does not requires us to take any set theory for this course.It requires analysis 2.

So is it helpful to take the set theory for taking analysis 3?
And what kind of analysis is for this analysis3?

08-26-2007, 01:03 PM
That analysis course is exactly what you want to take. Moreover, it would be good preparation for a course in topology (at least the metric spaces part of it).

08-26-2007, 07:28 PM
That analysis course is exactly what you want to take. Moreover, it would be good preparation for a course in topology (at least the metric spaces part of it).

so is it helpful to take Set Theory for analysis3?

Or I should take them together?

08-27-2007, 12:41 AM
To the OP, I don't understand why you're so obsessed with these advanced pure math courses like set theory. No, you don't need to take set theory for analysis 3. What kind of analysis is analysis 3? To me this sounds like pieces of real analysis 1 and 2 that I took at my undergrad institution. Introduction to metric spaces is usually taught during real analysis 1 (together with real numbers, single variable calculus, and function spaces.) What's taught in analysis 2 and 3 varies by school - it's usually things like lebesgue measure and integration, functional analysis, fourier analysis, analysis in R^n, implicit function theorem, etc. In any case, an advanced course in RA is usually more useful to an average economics PhD student than general topology (you should study point-set topology as part of RA courses which is all topology that you will be asked to know, at least during first year). You can also benefit more from taking courses in linear and non-linear programming (optimization), which are usually taught by operations research departments, numerical analysis, dynamic programming, linear models, advanced linear algebra, advanced probability, etc. Set theory or topology would be the second to last thing that I would consider taking if I had choice (the last thing probably would be something like advanced abstract algebra).