Aiming for Ph.D. in math - am I screwed?

[yz764527]

Aiming for Ph.D. in math -- am I screwed?

I just finished my first year of college this May, declared a double major in mathematics and philosophy, and after a lot of thought, I'm pretty sure that I want to go to a Ph.D. program in pure mathematics. Not aiming for the ridiculously top schools like Harvard/Princeton/MIT, but perhaps something along the lines of NYU/UPenn/Hopkins.

I have a good number of strengths. 3.93 overall my first year (will try to maintain ~3.90); became very familiar with the math department faculty, won two schoolwide math-related awards; doing research with a physics professor this summer and presenting at a few conferences; just asked by a math professor to do research with him in the upcoming academic year. I'm very confident that I can finish my 4 years with a stellar GPA, superb recommendations, and extensive research experience under my belt.

Problem: I go to a small, obscure liberal arts college. Due to the small size of the department, few advanced courses can be offered. Most Ph.D. programs recommend two semesters of both real analysis and abstract algebra, but only one semester of each is offered here. Other than that, I'll only have one semester of complex analysis plus some stuff like probability, graph theory, and geometry. There is an advanced "Topics in Pure Mathematics" course that's offered once every 4 semesters, and if I'm lucky, the chosen topic will be something like number theory or topology when I get to take it.

My math professors have expressed their optimism about my chances, but I'm seriously wondering how much the limited course offerings here will hurt me when it comes to grad school admissions. Can anyone give some insight?

 

[JCVD]

You are right; you will need more coursework. You should consider studying abroad for a semester at one of the following mathematics-only programs: Penn State MASS, Budapest Semesters in Mathematics, Math in Moscow.

 

[Jokerhelper]

I just finished my first year of college this May

This alone answers your thread question -- no, you are not screwed at all! You just got started, so it's easy to change.

If you are considering transferring to a bigger college with a more complete math department, then look into it now. The good thing is that probably more than 90% of first year students (myself included) have done no work with a professor. That added to your great GPA should make it easy for you to be accepted by any math department, really. Try to get in contact with the departments of any colleges you may be interested in, and see what they say.

 

[yz764527]

Thank you guys for the responses!

@ Jokerhelper
I appreciate your advice but I'm actually not looking for change. Despite the limited math course offerings, I'm satisfied with my current school. I was offered a full-tuition merit scholarship (which will make transferring anywhere a HUGE financial burden for my family), I've met amazing friends here, and I've made invaluable connections with my professors. Plus, the philosophy department here is excellent and has a wide variety of course offerings, and even though I'm planning to go the math route in grad school, I'm also absolutely committed to being a philosophy major. After all, mathematics developed from philosophy and I've found that the two majors complement each other very well.

@ JCVD
I've looked into the Budapest program and was very interested in it, but there are logistical issues. I'm taking medication for anxiety and motion sickness, and these specific medicines may not be available in Eastern Europe. (I'm originally from China and I know they don't have them there.) Also, studying abroad for a whole semester will be difficult if I am to fulfill my philosophy major. I'll keep thinking about it, but for now I'm under the assumption that I will be at my home institution every semester.


I live pretty close to the University of Maryland - College Park, so I'm thinking about taking the second semester of real analysis there (it was offered this summer, so I'm hoping it will be offered in future summers as well). As for a second semester of abstract algebra, I can probably pursue it as an independent study with one of my professors. (Recent independent studies have included ring theory and Galois theory.) Does this sound good?

I'm still wondering though, if two semesters of both real analysis and abstract algebra are necessary or just recommended. I looked in the math department handbook and activities of recent graduates include graduate study in mathematics at pretty good schools including Maryland - College Park, Rutgers, Georgia Tech, Hopkins, and even Caltech! So assuming that I'll have everything else--very high GPA, great recommendations, extensive research experience, and solid GRE scores--would that make me competitive for a somewhat-top Ph.D. math program if I'm just missing a few courses?

 

[Jokerhelper]

Thank you guys for the responses!

@ Jokerhelper
I appreciate your advice but I'm actually not looking for change. Despite the limited math course offerings, I'm satisfied with my current school. I was offered a full-tuition merit scholarship (which will make transferring anywhere a HUGE financial burden for my family), I've met amazing friends here, and I've made invaluable connections with my professors. Plus, the philosophy department here is excellent and has a wide variety of course offerings, and even though I'm planning to go the math route in grad school, I'm also absolutely committed to being a philosophy major. After all, mathematics developed from philosophy and I've found that the two majors complement each other very well.

Ah sorry, I completely misunderstood your post. In that case, then yes definitely continue to enjoy what you are doing right now. Also, I know that often colleges/universities make their graduate students complete certain undergraduate courses to fill some of their voids in certain topics. For example, one of my profs started with a bachelor in physics and went on to get a master in electrical engineering so she had to also take some undergrad classes during her master years. She eventually settled for a PhD in Radio Astrophysics

 

[yz764527]

Don't worry about it, Jokerhelper, I know you were trying to help. :) I've heard that grad students take undergrad courses to fill in voids as you said, but when crossing from one discipline to a related one (e.g. physics to engineering). I'm not sure if that applies in my case...

Anyway, can anyone help me answer the questions in my previous post?

 

[eumyang]

I live pretty close to the University of Maryland - College Park, so I'm thinking about taking the second semester of real analysis there (it was offered this summer, so I'm hoping it will be offered in future summers as well). As for a second semester of abstract algebra, I can probably pursue it as an independent study with one of my professors. (Recent independent studies have included ring theory and Galois theory.) Does this sound good?

I'm still wondering though, if two semesters of both real analysis and abstract algebra are necessary or just recommended.

I think you'll need to take two semesters each of analysis and algebra. And at least a semester of topology, too, if you can. (From what I have seen, plenty of schools at the undergraduate level offer two semesters for analysis & algebra, but not as many schools offer two semesters in topology.) Analysis, algebra, and geometry/topology make up the three main branches of pure math, so I think you need these courses if you want to go for a Ph.D. in pure mathematics.


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[yz764527]

Alright, there seems to be a consensus so far, so I'll try to take a second semester of both real analysis and abstract algebra along with a semester of topology somehow, whether it be taking courses at another institution or doing independent studies with a professor.

Question though: does the second semester of analysis or algebra have to be a general continuation of the introductory analysis/algebra course, or can it be focused on a specific topic in the subject area? For example, could I take "Intro to Abstract Algebra" and "Commutative Algebra" rather than "Intro to Abstract Algebra" and "Advanced Abstract Algebra"? Or does it not matter?