Can a Spotty Academic Record Affect PhD Admissions in Mathematics?

[kilimanjaro]

Well, let me start with a bit of background info. My transcript is an absolute mess, I have dropped out twice (one withdrawal, and one semester of all F's). So basically I am finishing a 4 year degree in 5. Since my whole dropout phase I have been at 3 schools total, a community college, a local state university, and now I back at my original school, a well respected (top 15) school finishing up a pure math degree.

My GPA here is pretty poor, due to 16 hours of F's (all one semester). In terms of core coursework, things aren't so bad but still a bit spotty.

A: Analysis 1, Algebra 1, Probability, Topology, Linear Algebra, Vector Calc
B: Algebra 2, Knot Theory, Number Theory, Diff Eq
C: Complex Analysis

This semester I am probably going to get an A in Analysis 2 (measure & integration, hilbert spaces), A or B in an "applied linear algebra" class (mainly spectral theorem and applications to problems of physics) and a C in a numerical methods class.

I'm really lazy when it comes to some classes, if it doesn't interest me I have a bad habit of just not doing the work. That's a pretty gaping character flaw of mine. However, when I am interested in something I'm pretty dedicated to it, I think I would find phd level mathematics rewarding and would even be pretty good at it (relatively speaking... not a superstar but able to do good work).

Next semester I'm going to take the undergrad PDE and Diff Geometry courses, and I'll probably get A's in both of those.

I missed the GRE deadline so I'm going to apply next fall, but I expect I should have a pretty good score. So with the above mentioned grades, and 3 mediocre reference letters ("he was a top student in my class but I don't know much about the guy"), what sort of school should I be shooting for? I hope to be able to continue some independent studies this summer (if I manage to land a job somewhere around here) with a professor on topics in analysis & geometry, so it's possible that I could get at least one interesting letter.

If anyone read this far, I'd appreciate some advice. I'm probably going to go talk with a professor about this same issue to see what he has to say.

Thanks

 

[Vanadium 50]

I'm really lazy when it comes to some classes, if it doesn't interest me I have a bad habit of just not doing the work.

This is a Big Red Flag. This will make life as a graduate student extraordinarily difficult, as you will almost certainly have to learn things that don't immediately interest you.

 

[Mene]

for sharing your background and current situation. It sounds like you have had some challenges in your academic journey, but it's great to hear that you are now back at a well-respected university and are still pursuing a degree in pure math. That shows resilience and determination, which are important qualities for a scientist.

In terms of your question about what sort of school you should be shooting for in your PhD applications, it's difficult for me to give a specific answer without knowing more about your research interests and long-term goals. However, I can offer some general advice.

First, it's important to highlight your strengths and achievements in your application. This could include your strong performance in certain courses, your interest and dedication in topics that you find engaging, and any independent studies or research experiences you have had. These will help demonstrate your potential as a researcher.

Second, it's important to address any weaknesses or challenges in your application. This could include explaining your transcript and any withdrawals or poor grades, and also addressing the issue of laziness in certain classes. Admissions committees understand that everyone has their strengths and weaknesses, and it's important to show that you are aware of yours and are actively working to improve and overcome them.

Finally, when deciding which schools to apply to, it's important to consider factors such as the research areas and strengths of the faculty, the resources and opportunities available for graduate students, and the overall fit with your interests and goals. Don't be afraid to reach out to professors or current students at schools you are interested in to learn more about their programs and see if it would be a good fit for you.

Overall, I would say that with your current transcript and letters of recommendation, you may want to consider applying to a range of schools, including some mid-level and lower-ranked programs, as well as some top-ranked schools. Your strong performance in courses like Analysis 1 and Algebra 1, as well as your interest in analysis and geometry, may make you a competitive candidate for programs with strengths in those areas.

I wish you all the best in your PhD applications and future studies. Don't be discouraged by your past challenges, but instead use them as motivation to excel in the future. Good luck!