What's the right moment to learn Set Theory?

Question

I've seen a question in which the OP asked when is the right moment to learn Category Theory, it seems this moment comes a little after a course of algebra, and indeed some books on abstract algebra brings concepts of Category Theory, such as Jacobson's Basic Algebra or Paolo Aluffi's ALGEBRA, Chapter 0.

But until the present date, I've seen no such question about set theory. What is a good moment to learn it?

I subscribe to the above comment ! :-) Albeit an even better one would be yesterday. ;-) — Lucian, Dec 26 '13 at 16:07
@Lucian: As long as it isn't "Every other day", it's fine. :-) — Asaf Karagila, Dec 26 '13 at 16:29
For reference, that other question is http://math.stackexchange.com/questions/21128/when-to-learn-category-theory — Mark S., Dec 28 '13 at 16:54
For me, it was the realization that all other branches of mathematics are too interconnected. I wanted to do one thing and one thing only, and Set Theory fit the bill perfectly. By the way, I study just to amuse myself; am a writer otherwise. :-) — ankush981, Jul 23 '14 at 05:38

score 4 · Accepted Answer · answered Dec 26 '13 at 14:41

The question is whether or not you refer to axiomatic set theory, or naive set theory. If the former, then the answer is probably "after you've seen a bit of mathematics"; if you mean the latter then "right now" is probably the right answer.

In my undergrad studies, the naive set theory course was the perquisite for all other math courses (even those on the first semester, which you were obviously allowed to take in parallel).

In other universities a lot of the topics covered in that course (basic Boolean operations, relations, functions) would be covered in the first two-three weeks of calculus, or algebra, or they might have a course called discrete mathematics covering that.

On the other hand, axiomatic set theory requires to understand what does it mean to deal with an axiomatic theory. It is usually taught to people that already seen a bit of mathematics, and learned a few basic definitions from logic.

Axiomatic set theory, in its basic form anyway, fits better a third year undergrad course, rather than a freshman level course.

score 1 · Answer 2 · answered Dec 26 '13 at 14:04

You can learn axiomatic set theory after you have done some math courses to give you some familiarity with dealing with sets in a naive manner. It is good to treat both mathematical logic and set theory in the same course as they are highly related. Any time after say an advanced calculus course is fine. Cambridge for example has a course called Logic and Sets in the third year for undergraduates.

What's the right moment to learn Set Theory?

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