Undergrad What is the logical interdependence of mathematics?

[Anti Hydrogen]

TL;DR

I mean what is the map of mathematics? for example, what do i need to know for understanding topology? or what do i need know for understanding partial differential equations?

thanks in advance

 

[fresh_42]

Summary: I mean what is the map of mathematics? for example, what do i need to know for understanding topology? or what do i need know for understanding partial differential equations?

thanks in advance

Here is your map

but I doubt that this is of much help. However, your question is so broad that it is impossible to answer in such a generality, except that mathematics usually starts with linear algebra and calculus. These are important for anything else, esp. for differential equations.

 

[Anti Hydrogen]

Here is your map
View attachment 249703

but I doubt that this is of much help. However, your question is so broad that it is impossible to answer in such a generality, except that mathematics usually starts with linear algebra and calculus. These are important for anything else, esp. for differential equations.

i have already seen that map but thanks anyway

 

[member 587159]

You need nothing for topology, except mathematical maturity (i.e. knowing how to write proofs and being comfortable working with sets).

For partial differential equations (from a pure mathematician's point of view), you certainly need real analysis and further down the road some complex analysis and measure theoretic functional analysis.

 

[mathwonk]

When I was a student, I found this book of topology by Alexandrov helpful:

https://www.amazon.com/dp/0486401790/?tag=pfamazon01-20

 

[nuuskur]

Some understanding of propositional calculus is helpful, especially of the opertation $\Rightarrow$, which confuses the hell out of countless first year students.

Then there's nothing much to it. Take relevant definitions and try to reproduce proofs. Start with simple ideas such as introductory linear algebra or naive set theory. Topology can wait.

Don't try to fly too high too early. Get comfortable with walking, first.

 

[WWGD]

Look up Dave Rusin's Mathematical Atlas. He connects things pretty well, to my taste. http://www.math-atlas.org

 

[WWGD]

Here is your map
View attachment 249703

but I doubt that this is of much help. However, your question is so broad that it is impossible to answer in such a generality, except that mathematics usually starts with linear algebra and calculus. These are important for anything else, esp. for differential equations.

I think graffiti is against PF rules ;).

 

[mathwonk]

I suggest books by V. Arnol'd, such as Lectures on partial differential equations, where he says prerequisites for at least his book on PDE, are linear algebra, analysis, and ordinary differentil equations; which leads to my recommending his book on Ordinary differential equations.