Programs PhD in Math: How high can I aim for?

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The discussion centers on selecting PhD programs in mathematics, particularly for a candidate with a strong academic background, including a double major in math and physics with a 4.00 GPA. Key points include the importance of having a solid foundation in advanced mathematics courses, such as multiple semesters of Real Analysis and Algebra, as well as coursework in topology. Some participants suggest that the candidate may face challenges in gaining admission to competitive PhD programs due to the perceived lack of advanced coursework. There is also a recommendation to consider applying to a master's program first as a potential pathway to a PhD. Additionally, the importance of aligning school choices with personal research interests and geographical preferences is emphasized, along with the urgency of finalizing applications due to approaching deadlines.
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Hi,
I am trying to decide what schools to apply to for PhD program in math. I will be getting my B.A. in math and physics in May (double major) from pretty a public university. I have had Real Analysis, Linear & Abstract Algebra, Complex Analysis, College Geometry, Differential Equations, some pretty advanced statistics. I have 4.00 GPA in all my math and physics classes. I have done some minor physics research. I can get recommendation letters from any/all professors I've ever taken classes with. So, the question is how high can I aim for without looking too ridiculous?
 
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I don't think you've taken enough math classes. That will probably be a big hurdle for competitive programs.
Did you take one or two semesters of Real Analysis and Algebra? If you've only had a semester of analysis, a semester of algebra, and no topology, it's going to be hard to be competitive.
 
I am entirely sure if this is correct, but you may have an easier time getting into a masters program, finishing that and then applying to a phd program.
 
I honestly don't see you as lacking in the number of classes you have taken...plus you should apply to whatever school fits you as far as research, geography, etc. and consequently no one on this board will be able to do that for you. But if you are applying for fall 09 then you should probably already have chosen your schools since deadlines are closely approaching, if not already passed.
 
I’ve been looking through the curricula of several European theoretical/mathematical physics MSc programs (ETH, Oxford, Cambridge, LMU, ENS Paris, etc), and I’m struck by how little emphasis they place on advanced fundamental courses. Nearly everything seems to be research-adjacent: string theory, quantum field theory, quantum optics, cosmology, soft matter physics, black hole radiation, etc. What I don’t see are the kinds of “second-pass fundamentals” I was hoping for, things like...
TL;DR Summary: I want to do a PhD in applied math but I hate group theory, is this a big problem? Hello, I am a second-year math and physics double major with a minor in data science. I just finished group theory (today actually), and it was my least favorite class in all of university so far. It doesn't interest me, and I am also very bad at it compared to other math courses I have done. The other courses I have done are calculus I-III, ODEs, Linear Algebra, and Prob/Stats. Is it a...

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