Advice for Phd in Mathematics

[Bikov]

Hello, everyone!

Here are the questions I'm concerned with. I'm an international student. Now I'm a freshman at Sofia University in Bulgaria. The department of mathematics and informatics is the best in the country (and not only) but it is hardly popular around the world. The entrance exams are really tough and the curriculum is very strong. You can compare it with the best mathematics departments in Russia. I have already decided that I want to do Phd in Math (particularly, some kind of geometry) in the USA and become a professor of Math in an American university. However, I was wondering if my bachelor degree will be strong enough to be accepted to a good math department in US. That's why I want you to see my future study plan- all the courses I plan to take. Imagine I have taken them all with exellent grades (I CAN do it). Will I be competitive enough in this way? I know that other factors as GRE, letters of recommendation, personal statement are also very important but at this time I'm wondering about my curriculum? Won't it be better to do a master degree first (probably in Utrecht Uni, the Netherlands) and then apply for PhD in the USA. Do you think that I will have even a little chance to be accepted to Harvard, MIT, Princeton or some other top-tier university? This year I started studying about GRE General so I think that in two years' time I'll have good scores not only in the quantitative part. I plan to take the GRE Math Subject during my junior year. I hope you give me some advice about what it'll be good to achieve in the next years in order to be accepted to a very good university in the USA.

I year:

Linear Algebra

Analytical Geometry

Differential & Integral Calculus I & II

Abstract Algebra I

Introduction to Programming

CS Practicum I

Subject of Geometry (topics: Erlangen Program of geometry; Geometry of Lobachevsky)

Selected Topics in Elementary Mathematics (topics: plane & solid geometry; combinatorial problems in the Number Theory)

II year:

Abstract Algebra II

Mathematical Analysis I & II

Differential Equations

Data Structures & Programming

CS Practicum II

Geometry & Topology

Introduction to Functional Analysis

Advanced Calculus I & II - workshop (based on problems given on mathematical competitions)

Differential Geometry

Numerical Analysis

Discrete Mathematics

Introduction to Number Theory

Introduction to Analytic Number Theory

III year:

Analytical Mechanics

Complex Analysis

Mathematical Logic

Partial Differential Equations

Lie Algebras & Groups

Geometrical Probabilities & Integral Geometry

Mathematical Programming

Introduction to Mechanics of Continua

Probability Theory I

Complex Analysis of Several Variables

Commutative Algebra

Functional Analysis - seminar

IV year:

Geometry of manifolds

Elements of Algebraic Geometry

Homological Algebra

Probability Theory II

Algebraic Topology & Differential Forms

General Topology

Hyperbolic Equations & Systems

Geometry & Mathematical Physics - seminar

Finite Geometries

Riemannian Geometry, Bochner Techniques & Vanishing Theorems

Theory of Groups

Descriptive Geometry

Preparation for the final state graduate exam

Thank you in advance!

[frankdux]

i have no idea how you can take that many classes. how in the hell are you taking that many math classes? do you take other classes on other subjects besides math? seriously, i was a math major in america and i took a total of about 13 one-semester math classes.

masters degrees and PhDs are a little bit different in america vs. europe.

in america, TYPICALLY when you apply for a PhD you are NOT expected to have a masters yet. you earn your masters along the way towards your PhD. the masters is included in the program.

in other words, apply for a PhD in america after your bachelors. a masters isn't necessary, and it could just be redundant. however, if you were offered a fully funded masters in your home country, it certainly wouldn't hurt to just do it anyways, then dive right in to a phd program in america that you might be able to finish a year or two early.

[Bikov]

The fact is that as a student who studies Math in Bulgaria, I have to study ONLY Mathematics. I mean that all the courses which are compulsory for me to be taken are only in Math. Our system is different from yours. That's why I've heard that foreigners have higher scores on GRE Math Subject than Americans because of the fact that you should take classes on other subjects.

Moreover, the quality and level in my university is very high and all the material is taught on a very professional level. I don't know if it is true but I've heard that you (Americans) emphasize on solving problems and spend less time on proving theorems. However, it is compulsory for me to be able to prove every theorem I use or I have been taught.

Do you mean that even at Harvard will be impressed by the broad spectrum of my bachelor degree?

[frankdux]

i think ANY school in america would be impressed by such a courseload of math. seriously, you'll have MUCH more math ability after your second year then i did after 4 years at an american university as a math major.

i suppose the only drawback to your system is that you don't have a very well rounded education. i honestly don't know how that might negatively affect your application. but if your goal is to be a researcher and a professor, then i think you are better off than most american PhD applicants. (except you'd still have to worry about funding. many schools don't have adequate funding for foreign students.)

[Bikov]

except you'd still have to worry about funding. many schools don't have adequate funding for foreign students.

Except I hope for a good funding, I do not know what else I can do. I don't know any other outside sources of funding for international students.

Besides, do you know any research projects or internship programs during the summers in US (or abroad) where foreign students may take part?

[frankdux]

i'm sorry, but i don't really have much information for you.

does your country have any sort of funding programs for students wishing to travel abroad for school?

the next best thing to do would be to directly contact graduate programs you are interested in and ask about funding for international students.

[Bikov]

We have the Fulbright Scholarship which is a good option but one of its requirements is to come back to your country after you have finished your education in US. However, as I said I want to become a professor in the USA. I have already been thinking about contacting the grad schools but don't you think it's too early in my case? I don't know if they will give me some appropriate information which is very likely to be changed in a couple of years' time.

About the summer programs, I have found some REUs in the USA which do not require to be an American citizen, but the problem is again connected with funding. I am not sure if the president of my university will be willing to pay for all.

[rising_star]

Bikov, many REUs offer housing and a summer stipend to participants, to offset income they might otherwise get from taking on a summer job. Have you looked into that as a funding possibility? Obviously, it wouldn't help with the plane ticket but it would certainly help with your living expenses.

[Bikov]

Bikov, many REUs offer housing and a summer stipend to participants, to offset income they might otherwise get from taking on a summer job. Have you looked into that as a funding possibility? Obviously, it wouldn't help with the plane ticket but it would certainly help with your living expenses.

They offer housing and a stipend but only to US citizens. The only program I have found that may offer funding for international students is Williams College SMALL Undergraduate Research Project. I don't know about others like this one.

Are such programs very competitive? When do you think it is better to apply - after my second or third year?

[hartshorneBoy]

They offer housing and a stipend but only to US citizens. The only program I have found that may offer funding for international students is Williams College SMALL Undergraduate Research Project. I don't know about others like this one.

Are such programs very competitive? When do you think it is better to apply - after my second or third year?

SMALL is extraordinarily competitive.

At any rate, Sofia is well-known here. Being a fourth-year student here at a public university in the US, I have heard great things of Sofia, so I do not think it will be much of a difference applying from Utrecht. People that come from ENS, Sofia, Utrecht, Cambridge, Roma III, Pisa, Milano, Nice, etc. I don't think have hard times getting good placements in american universities, but they may not be exactly the place you want to go. The first step is realizing that getting into a top 5 school is also luck-based and has to do with your recommenders' connections to said schools. That's honesty.

Push comes the shove, people know what Sofia is and all you can do is apply =).

But you will be at a disadvantage when it comes to funding.

With care,

hartshorneBoy

PS I haven't computed something that wasn't a theoretical computation for a non-teaching role in three years, and I am an American student.

[Bikov]

People that come from ENS, Sofia, Utrecht, Cambridge, Roma III, Pisa, Milano, Nice, etc. I don't think have hard times getting good placements in american universities, but they may not be exactly the place you want to go. The first step is realizing that getting into a top 5 school is also luck-based and has to do with your recommenders' connections to said schools. That's honesty.

Push comes the shove, people know what Sofia is and all you can do is apply =).

But you will be at a disadvantage when it comes to funding.

Which schools will you suggest me to apply to? I have already realized that getting into a top 5/10 Math department is based on luck and of course the recommendations I have. That was the reason why I was thinking of going to Utrecht first because it is definitely more popular than Sofia University and has more contacts with American universities. But know I'm considering the idea of applying to USA schools during my senior year at Sofia more seriously.

What advise can you give me about funding?

[canuck]

You are a freshman?

Probably the first thing to worry about is learning some mathematics; you could find out you are mediocre. You should probably focus on classwork and maybe even reading some papers for a couple of years to decide that you want to be a professor at an American university. You'll have to be miles better than everyone else if you want to start thinking about Harvard.