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Measure Theory

Anonymous Wed 03 Mar 14:02:39 2021 No.12780398 View Reply Original Report

Quoted By: >>12780435 >>12780437 >>12780470 >>12780533 >>12780602 >>12780752 >>12780785 >>12780809 >>12785356 >>12785430 >>12786257

What are the prerequisites for Measure Theory?

Anonymous

Anonymous Wed 03 Mar 2021 14:12:39 No.12780435 Report

Quoted By:

>>12780398
Bump

Anonymous

Anonymous Wed 03 Mar 2021 14:13:00 No.12780437 Report

Quoted By: >>12780452

>>12780398
A priori there actually aren't any, in practice you'll want to know real analysis and point set topology.

Anonymous

Anonymous Wed 03 Mar 2021 14:17:07 No.12780452 Report

Quoted By: >>12780472 >>12780521 >>12780913

>>12780437
What are the prerequisites for topology? Sorry that I have to ask.

Anonymous

Anonymous Wed 03 Mar 2021 14:20:47 No.12780470 Report

Quoted By:

>>12780398
it's a pretty foundational subject, so technically not much, you just need to be comfortable with set operations and with real numbers (including limits and infinite series). however, you should know Riemann integration for motivation and a little bit of point set topology and functional analysis to put things in context.

Anonymous

Anonymous Wed 03 Mar 2021 14:22:08 No.12780472 Report

Quoted By: >>12780791 >>12786235

>>12780452
There aren't any. Just be familiar with how a mathematical proof works.

Anonymous

Anonymous Wed 03 Mar 2021 14:32:46 No.12780521 Report

Quoted By:

>>12780452
naive set theory

Anonymous

Anonymous Wed 03 Mar 2021 14:36:54 No.12780533 Report

Quoted By: >>12780715

>>12780398
You must have a big penis.

Linear Algebro

Linear Algebro Wed 03 Mar 2021 14:52:55 No.12780602 Report

Quoted By: >>12780715

>>12780398
autim

Anonymous

Anonymous Wed 03 Mar 2021 15:21:32 No.12780715 Report

Quoted By:

>>12780533
>>12780602
Contradiction

Anonymous

Anonymous Wed 03 Mar 2021 15:27:48 No.12780752 Report

Quoted By:

>>12780398
Some real analysis maybe

Anonymous

Anonymous Wed 03 Mar 2021 15:35:22 No.12780785 Report

Quoted By:

>>12780398
Baby rudin ( do it completely if possible )Stephen Abbott, perhaps undergrad spivak if u have sufficient time

Anonymous

Anonymous Wed 03 Mar 2021 15:36:52 No.12780791 Report

Quoted By:

>>12780472
Well a rigorous course in proof based math (primarily analysis) will definitely be helpful as those ideas would be invoked quite often in general topology

Anonymous

Anonymous Wed 03 Mar 2021 15:41:25 No.12780809 Report

Quoted By: >>12781210

>>12780398
Since we're asking these types of questions, what would be the prerequisites of homotopy theory?

Anonymous

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Anonymous Wed 03 Mar 2021 15:41:42 No.12780812 Report

Quoted By: >>12780820

what is the science behind this?

Anonymous

Anonymous Wed 03 Mar 2021 15:43:09 No.12780820 Report

Quoted By:

>>12780812
Meme magick

Anonymous

Anonymous Wed 03 Mar 2021 16:01:24 No.12780913 Report

Quoted By: >>12780919

>>12780452

*Technically* all you need is set theory, since point-set topology basically generalises analysis to a more general setting. It would therefore be possible to do topology, then whiz through real analysis getting a load of theorems for free. However there's a reason why it's not done this way, mathematical maturity is useful and you should know some real analysis.

Anonymous

Anonymous Wed 03 Mar 2021 16:02:56 No.12780919 Report

Quoted By:

>>12780913

[of course, I'm mainly talking about stuff like continuity, connectedness, compactness, etc. Stuff like differentiation and integration doesn't generalise so nicely and requires specific work. You could argue that the most "logical" progression is topology -> complex analysis -> real analysis]

Anonymous

Anonymous Wed 03 Mar 2021 16:59:53 No.12781210 Report

Quoted By:

>>12780809
Point set topology. Allen Hatcher has a 50 page document called "notes on introductory point set topology" which serves as the barebones necessary amount to start doing homotopy theory. We used it in my topology class since our instructor wanted to get to algebraic topology as fast as possible. He called point set topology boring but necessary.

Anonymous

Anonymous Thu 04 Mar 2021 00:21:32 No.12785356 Report

Quoted By:

>>12780398
You just need to know introductory set theory and what a sequence is.

-t. took measure theory after real analysis

Anonymous

Anonymous Thu 04 Mar 2021 00:30:00 No.12785430 Report

Quoted By: >>12785995

>>12780398

Rudin, REal and Complex analysis, chapter 1, 2, 6, 8

Anonymous

Anonymous Thu 04 Mar 2021 02:35:29 No.12785995 Report

Quoted By:

>>12785430
why is papa rudin a prereq?

Anonymous

Anonymous Thu 04 Mar 2021 03:55:01 No.12786235 Report

Quoted By:

>>12780472
What are the prerequisites for proofs?

Anonymous

Anonymous Thu 04 Mar 2021 03:59:50 No.12786257 Report

Quoted By:

>>12780398
A nonzero penis

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