Schools How is my Preparation for Grad School in Math?

AI Thread Summary
The discussion centers on a junior math major's concerns about pursuing a master's degree before a PhD, noting that some universities do not accept master's graduates into their PhD programs. The individual questions whether this is a common practice and if their academic background is strong enough for graduate school, having completed courses in calculus, linear algebra, abstract algebra, and real analysis, with plans to take additional advanced courses. They express uncertainty about the adequacy of their preparation compared to prestigious programs like Princeton's. The conversation also touches on the importance of taking courses in general topology and ring & field theory to strengthen their application. Overall, the individual seeks advice on their academic trajectory and course selection for a successful transition to graduate studies.
qspeechc
Messages
839
Reaction score
15
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.
 
Physics news on Phys.org
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?
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

Similar threads

Replies
3
Views
3K
Replies
16
Views
2K
Replies
9
Views
2K
Replies
12
Views
2K
Replies
14
Views
2K
Replies
2
Views
2K
Back
Top