Mapping Mathematical Subjects: Prerequisites & Dependencies

[outis]

I'm trying to map out how certain mathematical subjects depend on each
other, i.e. which subjects could be described as prerequesites for
which other subjects, in the sense that the former define needed or
helpful concepts for the latter. In a crude ascii diagram, which
might look messed up depending on the width of your spaces, what I've
got so far is:

A
/ \
B C
|\ /|
| D |
|/|\|
E | F
| |\|
| | G
\|/
H

where:

A= set theory
B= abstract algebra
C= general topology
D= real analysis
E= Lie groups and algebras
F= algebraic and geometric topology
G= differential topology
H= differential geometry

Higher levels are prerequisites for lower levels, and connecting lines
represent strong dependencies.
As the ascii diagram might be illegible, the dependencies are:

B depends on A
C depends on A
D depends on B and C
E depends on B and D
F depends on B, C, and D
G depends on D and F
H depends on D, E, and G

Of course this partitioning of knowledge is rather arbitrary and
subjective. To explain a couple choices:
I've extracted "Lie groups and algebras" from "abstract algebra"
because I'm considering the latter as strictly the general, elementary
stuff. And both "Lie groups and algebras" and "algebraic and
geometric topology" depend on "real analysis" for its rigorous notions
about continuity, or so it seems to me.

I'm interested in people's opinions about whether this particular
organization seems reasonable, or whether some dependencies should be
added or removed, etc.

 

[neutrino]

Hi, outis. Welcome to PF.

This topic reminds of a picture I have seen in a website called Relativity on the WWW. Unfortunately, it is no longer online.

 

[rudinreader]

It's actually a pretty nice map. However, I hope you aren't making a huge intimidating list of books you may never have time to read them all.. I have mostly concentrated on analysis, and find that along the way I pick up a lot of other things..

 

[CRGreathouse]

The requirements for real analysis seem too strict to me.

 

[rudinreader]

The requirements for real analysis seem too strict to me.

Not clear if you are criticizing the "map" or if you are asking for analysis help? If criticizing the map, I agree no real need to dwell on set theory, topology, algebra before studying analysis. Analysis only really asks that you read the complete ordered archimedean field properties very carefully, and apply the "epsilon-delta" formalism with the same central importance that the "transistor" has in electronics.

Nonetheless, if I had to order the subjects in this way, I would keep set theory - general topology above analysis (for sake of organization) and put algebra near lie groups, because I'm not real big on abstract algebra..

 

[CRGreathouse]

Not clear if you are criticizing the "map" or if you are asking for analysis help?

Somewhere between criticizing and commenting on the map. Perhaps I understand the terms "abstract algebra" and "general topology" differently, but they don't really seem necessary for real or complex analysis.