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

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Discussion Overview

The discussion revolves around potential areas of specialization for pursuing a Master's or PhD in Mathematics, including considerations for career prospects and personal interests in various mathematical fields. Participants explore the breadth of mathematical disciplines and seek guidance on how to navigate their academic choices.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant asks for a list of areas of focus for Master's/PhD in Mathematics and inquires about the best career prospects.
  • Another participant suggests that statistics or numerical analysis may have better career prospects but criticizes the vagueness of the initial question.
  • A participant expresses uncertainty about the areas of focus in Mathematics and indicates a preference for Pure Mathematics, questioning the long-term enjoyment of the field.
  • One participant outlines four main branches of Mathematics: algebra, topology, analysis, and geometry, noting their overlaps and active research areas.
  • It is suggested that exploring these branches through coursework is essential for determining a suitable specialization.
  • Resources, including Wikipedia links and a list of introductory books, are provided to help participants explore the subject further.
  • Several participants express gratitude for the resources shared and discuss access to books through libraries.

Areas of Agreement / Disagreement

There is no consensus on specific areas of specialization or career prospects, as participants express differing opinions and experiences regarding the breadth of Mathematics and its applications.

Contextual Notes

Participants mention the need for more specific questions to facilitate better responses, indicating that the discussion may be limited by the initial vagueness of the inquiry.

Who May Find This Useful

This discussion may be useful for students considering graduate studies in Mathematics, those exploring different branches of the field, and individuals seeking resources for further learning.

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

All of them.

smize said:
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.
 
espen180 said:
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).
 
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
 
Thank-you very much Espen :D That should help. When I get some spare money, I'll work on getting those books.
 
smize said:
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
 
jk said:
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!
 

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