Pure PhD Program Advice

[cwatts]

I am applying for a Pure Math PhD for Fall 2013.

I am currently in a Pure Master's program at my undergrad institution and should graduate May 2013 (assuming all goes well of course!).

My Bachelor's is in Pure Math and I am a white female student.

My GRE scores are V 610 (88%), Q 800 (94%), and Writing 4.5 (67%).

As a graduate student I have already taken:

Intro to Real Analysis (Pugh/Rudin) [A]

Topology (Munkres) [b, retaking for an A this fall]

Advanced Linear Algebra (Axler) [A]

Abstract Algebra (Lanski, studying Dummit and Foote for comp exam) [b+]

Complex Analysis (undergrad level) (Matthews and Howell) [A]

I will be taking:

Measure Theory (Bartle)

Topology (retaking) (Munkres)

Numerical Linear Algebra and Optimization (undergrad level) (Kincaid)

Complex Analysis (graduate level)

Mathematical Statistics

Numerical Solutions of Differential Equations (undergrad level)

I have an undergrad research paper that has been accepted for publication this fall. It is an applied modelling paper, which unfortunately is not my area of interest.

I have had my own precalculus class to teach for Fall, Spring, and Summer semesters, and feel very comfortable teaching (I really enjoy it).

I think I would like to research more in to abstract algebra. My school is more focused on the applied and statistical areas so I have not had much in-depth exposure to the areas I would like to study more. I have not had any courses in number theory or graph theory and not very extensive courses in abstract algebra.

As an undergrad, I was in Pi Mu Epsilon and Mortar Board. I took several years of French so I am not too worried about any language qualifiers.

If anyone had suggestions on schools that they know of being more geared towards the algebras or that have a good breadth of research areas in pure mathematics it would be greatly appreciated.

Here is a (very random) list of schools I am considering already:

University of Kansas - Lawrence

University of Minnesota - Twin Cities

Penn State

Dartmouth

Purdue

University of Nebraska - Lincoln

University of Colorado - Boulder

Thanks in advance for your help!

[lonelymonk]

Your GRE scores are well above cut-off. Ensure that you get good grades in sub GRE too. You seem to have the requiste background needed for a graduate program in pure math. And a publication always helps. The list is quite random. You must definitely consider some safety schools i.e worst case scenarios. Make sure you space out your application. Two or three in the top places , Bulk in the midlevel and two safety schools.

Since you have mentioned that you are looking for a big department, you can strike off Dartmouth from the list.

You already have decent background in Analysis. Try taking Algebra courses this year. What about graduate level courses ?

I didn't have any publication or outstanding academic record. However I think it helpled my application when I mentioned that I had taken some graduate level courses like Functional Analysis, Measure theory and Distribution theory.

[ANDS!]

You need to take the subject GRE. Perhaps there are some exemptions that are made on a case by case basis - but as a graduate student I would think that the expectation would be that it is a cakewalk for you.

[cwatts]

Thanks for the responses guys! I am scheduled to take the subject GRE this fall as I did not need it for entrance into my current graduate program. As to the algebra courses, I have unfortunately already completed the highest level of courses at my university (as I said it is a very applied university). The two algebra courses I have listed under the graduate study are our graduate versions. I completed all of the equivalent undergrad sequences while completing my bachelor's.

[ANDS!]

The algebra is fine. You should do fine with the schools you are applying to; at worst they have you take some courses to bring you "up to speed. . ." with where they want their students to be. Are these one semester courses?

[cwatts]

These are one semester courses. I will be taking comprehensive exams this Christmas in Linear Algebra, Abstract Algebra, Real Analysis, and Topology. Consequently, I expect to have a strong background in each of these subjects.