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/sci/ - Science & Math

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3478660 No.3478660 [Reply] [Original]

Practically every math book ever starts with a chapter on set theory. Do I really need to go through this every time, or can I just try to get through the most rigorous one, or just ignore it until I get stuck later and hope my math foundations class good enough in the mean time?

>> No.3478682

set theory is useless.
I don't even remember ever using it in my life, except to find the values of some sums.

>> No.3478686

you mean you read textbooks from the start? lol. its not a story book. you read the chapter you want to know about.

>> No.3478698

Set theory is fun, zero is an empty set, one is a zero, two is a one and empty set etc...

good times..

>> No.3478745

>>3478682
The hilarious thing is that set theory is what all of math was based on, until category theory came along. Pretty much everything else can be reduced to sets and functions over sets.

>> No.3478767

>>3478660
that stuff isn't really set theory. it's just a naive set theory perspective on the most basic set operations and constructions.

>> No.3478784

>>3478686
I did not know that. My only higher math experience was a second semester abstract algebra course on rings and fields. Sure, I skipped the stuff on groups, but I did skim it, and all the stuff on rings and fields was built up from rings. If I had jumped right to extension fields because I wanted to learn about extension fields, I would have been so lost.

That said, I've Analysis I and Abstract I coming up this Fall, and I've got three books I'm looking through for metric spaces, and I noticed that they're all preceded by set theory.

In case anyone is curious, I'm looking at baby Rudin, Introduction to Analysis by Maxwell Rosenlicht, and Introduction to Topology by Bert Mendelson.

Am I too focused on metric spaces for a first-semester analysis class? I have no idea how much we'll cover, or in what order. In fact, people who have been through both analysis I and II at my school said they didn't even see metric spaces, balls, etc. until very late in analysis II, which tells me my priorities are probably screwed up.

However, every analysis book I've seen, (the two above, plus Elementary Real and Complex Analysis, by Gregori Shilov) has started off with metric spaces before doing anything really "analysis-y", so I can't even imagine how I would approach the subject with metric spaces, balls, etc. They said they were just shown epsilon and delta proofs and went with it.

>> No.3478794

>>3478745
math isn't based on category theory. category theory just organizes mathematical objects which in turn are constructed using set theory...

>> No.3478816

Some of the better written books actually provide diagrams on which chapters that belong together and which path to take to reach your goal chapter fastest without getting lost.

>> No.3478829

>>3478745
the hilarious thing is that you don't need to understand set theory to do such maths.

>> No.3479142

>>3478784
OP here. Does my classmates' experience sound typical of undergrad math education or does it sound like I go to a shitty school?

I think I already know the answer, though...