What is the correct reading order for these topics in mathematics?

[Phy_Reason]

Alright. So, internet gives me the idea that any serious research in Theoretical Physics will require me to have atleast some knowledge of the following topics in math:

Topology
Groups (Group Theory)
Differential Geometry
Calculus of Variations
Linear Algebra
Abstract Algebra

I was wondering if some of you could suggest me 'the' suitable order for these topics. eg, I know that Calculus of variations has nothing to do with, say, linear algebra; but in what order should I read the above mentioned topics; say between Linear Algebra, Topology, Groups, Differential Geometry?

 

[HallsofIvy]

There is no necessity that one be read before the other but I think Linear Algebra is a good introduction to the ways of thinking necessary in Group Theory. I would also consider Linear Algebra necessary to Differential Equations (which should be on your list). Strictly speaking, both Linear Algebra and Group Theory are part of Abstract Algebra although Linear Algebra is more often studied separately from Abstract Algebra than is Group Theory.

I would recommend this order:

Linear Algebra
Ordinary Differential Equations
Group Theory
Abstract Algebra
Calculus of Variations
Partial Differential Equations
Differential Geometry

 

[Phy_Reason]

That helps... Thanks!