View Full Version : What book would be best for self-studying set theory and topology?

persistence

08-05-2007, 08:40 PM

I'm doing self-study for topology and I was wondering if anyone had recommendations on a book that's not too dense. I've taken two semesters of calculus, two semesters of stats and I just did some self-study on linear algebra, since my professor in the last course was terrible and went off on tangents unrelated to the subject.

Thanks.

SunnyDutt

08-05-2007, 09:10 PM

If you want self study and want a cheap, awesome introduction to Topology, go with "Introduction to Topology" by Bert Mendelson. If your willing to shell money, then go with "Topology" by James Munkres.

quantwanabe

08-05-2007, 10:02 PM

I'm doing self-study for topology and I was wondering if anyone had recommendations on a book that's not too dense. I've taken two semesters of calculus, two semesters of stats and I just did some self-study on linear algebra, since my professor in the last course was terrible and went off on tangents unrelated to the subject.

Thanks.

Do you have the opportunnity to audit topology at some school, if yes do so. I think it is quite hard to learn topology by yourself

persistence

08-05-2007, 10:30 PM

Is "Topology" by Munkres as easy to understand as Mendelson's, or does it require more mathematical maturity? I'd be willing to shell out the money if it'll really help.

Unfortunately, I won't have the opportunity to audit the course.

And is my understanding correct that Set Theory is part of Topology, or should I be studying a different branch of math if I wanted a deeper understanding of sets?

Thanks.

buckykatt

08-05-2007, 11:49 PM

My understanding is that set theory is the foundation for topology (and real analysis), but they're distinct fields.

I worked through a bit of Stoll's Set Theory and Logic, which I liked a lot as an introduction. I did stumble over the notation, and it is probably somewhat outdated, though. (There is a nice Dover reprint of it, but I don't know whether it's at all updated.) It does have the virtue of being cheap, though. I got mine for a quarter years ago at the library, and the Dover reprint is like $10 or so IIRC.

KingOfConvenience

08-06-2007, 01:43 AM

I've only ever used Munkres' text Topology, but I found his exposition and style appealing and manageable.

TruDog

08-06-2007, 02:34 AM

This isn't a perfect fit for topology, but I would recommend parts of Principles of Mathematical Analysis by Rudin (usually known as Baby Rudin). It's also a great book for basic real analysis.

crutchboy3

08-06-2007, 02:10 PM

Another book to look at is Introduction to Topology by Gamelin and Green. The book is very good for self-study as it has several hundred solved problems. Its fairly terse, but provides you with a good understanding of metric spaces before moving onto more abstract topological spaces.

ForTheWin!_08

08-07-2007, 07:21 PM

I second what TruDog said. I think it's going to be hard to appreciate what topology generalises (metric spaces, or, even more concrete, calculus on Euclidean space) without understanding it first. I'd go for Rudin first.

By the way, Set Theory (as an area of mathematical research, not the naive set theory you need for analysis) is more closely related to logic than topology... it's important stuff, crucial to giving mathematics a solid foundation, but as far as applying that mathematics to economics goes, it's pretty irrelevant. It would be like studying tons and tons of books on linguistics and the philosophy of language when all you wanted to do was learn to speak English.

persistence

08-08-2007, 12:10 AM

I have Baby Rudin but I haven't had the chance to go over it, as I'm concentrating on Simon and Blume. I shall check it out based on your advice. Thanks to all for the book recommendations.

Buckykatt, is Set Theory and Logic largely pertinent to real analysis and topology? I'm intrigued by it, but I ask in light of ForTheWin's last point.

buckykatt

08-08-2007, 07:06 AM

You're probably better off with something else if you're not interested in set theory as such.

.

asianeconomist

08-10-2007, 01:54 PM

There is a book called "Topology without Tears". You can download the book from the Lecture Notes section of Econphd.net.

Although the book is not VERY advanced, I found it quite relevant. It has quite a lot of worked-out examples too. Check it out!

persistence

08-20-2007, 09:35 PM

That last one looks interesting! Thanks, asianeconomist.

econyun

08-21-2007, 02:58 AM

I second what TruDog said. I think it's going to be hard to appreciate what topology generalises (metric spaces, or, even more concrete, calculus on Euclidean space) without understanding it first. I'd go for Rudin first.

By the way, Set Theory (as an area of mathematical research, not the naive set theory you need for analysis) is more closely related to logic than topology... it's important stuff, crucial to giving mathematics a solid foundation, but as far as applying that mathematics to economics goes, it's pretty irrelevant. It would be like studying tons and tons of books on linguistics and the philosophy of language when all you wanted to do was learn to speak English.

I have done

Matrix Algebra, all calculus up to advanced one, linear algebra, statistics, probability, introduction to analysis and ODE.

I going to take Functional Analysis this fall.

My school offer the following course this fall, which one do u recommend to take:

I m allowed to choose one of the following courses. Which one do u prefer to impove my profile for Phd application to the greatest extend？

Numerical Analysis

Set Theory

PDE

Regression and analysis of variance

Nonlinear Dynmaics and Choas

snappythecrab

08-21-2007, 06:21 AM

Munkres really seems to be a/the standard.

KingOfConvenience

08-22-2007, 06:03 PM

Nonlinear Dynamics and Chaos is awesome, but only if you are interested in dynamical systems and/or macro.

Regression and ANOVA sounds like an econometrics class to me, so that would be useful if you haven't taken econometrics.

Set Theory is strictly dominated by all the other choices.