Are the major math branches prerequisites for each other?

[Simfish]

As we know, there are three major branches of mathematics: algebra, geometry, and analysis. The question then is - is understanding one of those branches necessary in understanding another one of those branches? Is it conducive? Is it possible that someone can do analysis on the research level without knowing any abstract algebra at all? Or differential geometry?

Are any of those branches particularly conducive to understanding applied mathematics or statistics or theoretical microeconomics?

 

[Stevedye56]

There was a lot of algebra involved in Geometry, at least there was in the class I took. There was a lot of rearranging and different laws, ex. law of sines, and law of cosins. This isn't difficult Algebra, but Algebra was still involved in the process. Does this help at all?

 

[mathwonk]

yes indeedy.

 

[Simfish]

Umm, I was talking about abstract algebra, real/complex analysis, and differential geometry/topology at the upper-div undergrad/grad level (esp. at the research level). Of course people are expected to graduate with all three areas covered - but some people may jump into one of them without a degree specifically in math.

 

[neurocomp2003]

as an applied mathematician(focus in sci&eng) you should at least no the basics of all 3. eg uniqueness & existence. I'm surprised u didn't list any computational mathematics/discrete types of subjects like combinatorics/graph/computational theory/complexity