How is my Preparation for Grad School in Math?

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Discussion Overview

The discussion centers around the preparation of an undergraduate mathematics major for graduate school, specifically regarding the adequacy of their coursework and the implications of pursuing a master's degree before a PhD. Participants explore the norms of graduate admissions and the necessary mathematical background for success in advanced studies.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • The original poster questions the standard practice of some graduate programs not accepting students with a master's into their PhD programs, expressing concern about their own academic trajectory.
  • Some participants suggest that taking courses in general topology and ring & field theory would be beneficial for the poster's preparation.
  • The poster inquires about the suitability of using Munkres for general topology and expresses intent to take a topology course in the upcoming year.
  • The poster expresses uncertainty about their mathematical background, particularly in relation to the expectations of prestigious programs like Princeton.
  • There is a concern about the adequacy of the poster's current coursework and whether self-study in abstract algebra would fill gaps in their knowledge.

Areas of Agreement / Disagreement

Participants have not reached a consensus on whether the poster's background is sufficient for graduate school or if pursuing a master's before a PhD is advisable. Multiple viewpoints regarding the necessary coursework and the implications of different graduate paths remain present.

Contextual Notes

The discussion reflects varying standards and expectations across different universities and programs, highlighting the subjective nature of what constitutes adequate preparation for graduate studies in mathematics.

qspeechc
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Hello everyone.

I am currently in my third year (junior year I think it's called in the USA) of undergrad, as a maths major, hoping to get into a masters program. I go to a small university.

I looked at some universities graduate school's websites, and I've seen quite a few that say they do not accept students with a masters into their Phd programs. This seems a bit odd to me, it's certainly not the case at my university; is this standard? I mean, I seriously doubt I'll know by the end of next year which area I want to specialise in, so I'll want to do a masters first. Is there anything wrong with this route?

Also, I suspect my background is quite weak for a typical undergrad. What kind of courses should an undergrad looking to get into grad school have? I've taken the calculus sequence. As for real maths, I have taken: linear algebra; a little abstract algebra (mostly group theory); real analysis in one variable, at the level of Rudin. At the end of this academic year you could add complex analysis in one variable, from Conway.

My background looks suspiciously weak to me, especially when I look at the undergrad curriculum for Princeton (a family friend went to Princeton). Next year, my final year (senior year?) I will be taking only maths courses (which is typical at my uni). That said, I can probably add multi-variable analysis and abstract algebra to the list of courses I know, by going through the books myself, before my senior year. Does this sound sufficient? I know very little about what my senior year courses are going to be like.

As for non-math courses, I have taken:
Two years of physics (general physics; EM and QM)
Applied maths (numerical analysis; ODEs, PDEs, mathematical methods, GR)
First year stats

As you can probably tell, my uni has a good applied maths program; I'm not so sure about the pure maths program. The physics program is also good from what I hear.
So, is my background sufficient, or weak? Is taking masters instead of going straight into a Phd program a good ora bad idea?
Thanks for your help.
 
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General topology and ring & field theory would be good courses to take.
 
General topology like Munkres, is that fine? I think I will take a topology course next year. Like I said, I can probably polish off the holes in my abstract algebra knowledge on my own. Otherwise, does my background look fine?
 
Anyone?
 

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