What can one specialize in for a MS/PhD in Mathematics?

[smize]

What is a list of areas of focus for Masters/PhD pursuers for Mathematics? What has the best future prospect for careers?

 

[espen180]

What is a list of areas of focus for Masters/PhD pursuers for Mathematics?

All of them.

What has the best future prospect for careers?

Probably statistics or numerical analysis.


Your question is too vague! Try to be more specific and people will be able to help you. Don't expect people to put more effort into their replies that you put into your question.

 

[smize]

Your question is too vague! Try to be more specific and people will be able to help you. Don't expect people to put more effort into their replies that you put into your question.

I do not know what the areas of focus are for Mathematics. A link to an outside source would be amazing, but I do not know how to expand upon the question. I am primarily interested in Pure Mathematics though. I want to know if it's worth me going into mathematics (to see if I'll enjoy it in the long run).

 

[espen180]

Mathematics can be loosely divided four main branches, called algebra, topology, analysis and geometry. They have a lot of overlap, and each has many subfields, almost all of which are under active research.

To begin with, you should find out which of those four you like best. Then you should start thinking about a specialization. The only way to make such a decision is to take courses in all of them and find out which you like.

To get a feel for each, browsing Wikipedia goes a long way. Try reading these and clicking the links to go more in depth.
en.wikipedia.org/wiki/Mathematics
http://en.wikipedia.org/wiki/Areas_of_mathematics

I have also listed some elementary books to get you started, assuming you know some calculus and linear algebra. Some of the books are harder then others (Here, especially Munkres). I tried to put them roughly in order of difficulty.

"The elements" by Euclid (free on the web)
"Elementary number theory" by Burton
"Calculus" by Spivak.
"A first course in abstract algebra" by Fraleigh
"Topology" by Munkres

 

[smize]

Thank-you very much Espen :D That should help. When I get some spare money, I'll work on getting those books.

 

[jk]

Thank-you very much Espen :D That should help. When I get some spare money, I'll work on getting those books.

Library cards are free

 

[smize]

Library cards are free

I just remembered I am actually going to a University now so I can use their library! Yeah, I'm not used to having access to books in math/physics. My town library is a bit small, and usually have to use inter library loan to get books like these. Thanks for the reminder!