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#1 15-11-2017 10:53:34

RyanCaleb
Banni(e)
Inscription : 06-11-2017
Messages : 12

Which order to learn math topics in?

Hi there,

I've been teaching myself mathematics from textbooks and webpages for a while. I have never had formal math education, though, so I am unfamiliar with how this is usually done.

An example: I was reading a graph theory textbook when, about a tenth of the way in, the author assumes knowledge of linear algebra for the rest of the book. This annoys me because I'd prefer not to stop-and-start textbooks.

So, in what order are you supposed to learn things? I'm looking for a sort of 'technology tree' of math; what are each subfield's dependencies? What should I know before getting a textbook about abstract algebra or topology?

I am currently pretty much up to speed with high-school math; I am more-or-less familiar with calculus, I know (extremely) basic number theory, but beyond that I know nothing. I am interested in basically all math, maybe slightly biased to the discrete side. I'm learning this for fun.

Thanks for any help






I didn't find the right solution from the internet.
References:
http://forums.xkcd.com/viewtopic.php?t=69851

whiteboard animation

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#2 15-11-2017 21:48:33

Yassine
Membre
Inscription : 09-04-2013
Messages : 1 090

Re : Which order to learn math topics in?

Hi RyanCaleb,
May be you can follow the Bourbaki road : they tried to rewrite a great deal of math from the ground up.
I guess the published books follow a logical order :
Livre I :      Set theory
Livre II :     Algabra
Livre III :    General Topology
Livre IV :    Single variable functions
Livre V :     Topological vectorial spaces
Livre VI :    Integration
Livre VII :   Commutative algebra
Livre VIII :  differential  and analytical manifolds
Livre IX :    Groups and Lie algebras
Livre X :     Spectral theory


L'ennui dans ce monde c'est que les idiots sont sûrs d'eux et les gens sensés pleins de doutes. B. Russel

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