Programs PhD in Pure Math with BSc in CSE

[Deep water]

I am unsure there is any thread similar to this. Today in morning I was making a thread but I can not find it. Anyway,
When I enrolled to CSE I was crazy about it but gradually I found myself in love of Math and I also found I am actually not good in CSE but in Math. I read in the best uni of my country. My university offers only following math courses
1. Calculus I, II, III
2. Discrete Math
3. Complex Analysis
4. Statistics
5. Differential equations
6. Linear Algebra
7. Basic Fourier and Laplace transformation
8. Mathematical Analysis for CS
9. Numerical Analysis
10. Graph theory
I am planning to take all of them. But I am in such a state that I can not leave CSE. There is no opportunity for Math major in my university and its a technical university. I also must admit if I leave CS now I have no opportunity to enroll in Math in other university. So my question is:
1. Is there any university in Japan, UK, USA, Canada, Germany, France, Russia, Australia (since almost all top ranked universities for Math are situated in these countries) who will accept me as a student of Pure Math MS program or Pure Math PhD program?
2. If I have some research paper in Pure Math then can I apply to PhD in Math directly?
3. How to apply for PhD in Pure Math directly with research paper in Pure Math?
Any advice is appreciable.

 

[Deep water]

Somebody please enlighten me...

 

[ZeroZero2]

Somebody please enlighten me...

I'm not too sure, but you maybe could transfer as an international student to an american university as an undergrad (your current grades would determine which schools accept you). Transfer the credits you already have then get a bachelor's degree in math? After you earn your B.S., you could attend to a more "prestigious " university if you'd like for a higher degree.

 

[JasonMode]

I'm in a similar situation...
but I'm a 1st year econ major, and my university is extremely weak at natural sciences, no math courses to choose for most majors...

I think a master in math is the best way to solve the problem (if possible...)
so you stay where you are, earn some money and finish a bachelor degree first

you're a CSE major, and your university offers much more math courses than mine
if you can't make it, there's no reason why I can do it...

 

[Deep water]

ZeroZero2, thank you, but my current financial condition is not good. Moreover my result is not good to transfer credit or to receive a scholarship
JasonMode, thank you, I'm also thinking of a MS in Math.
I actually want to know if I have some research paper in Math can I apply for PhD in pure Math directly?
Somebody help me...

 

[Cod]

The University of Maryland is a viable option. From the graduate catalog, under Mathematics (MATH):

Admissions Information
Admission is granted to applicants who show promise in mathematics as demonstrated by their undergraduate record. Unless courses in advanced calculus and (undergraduate) abstract and linear algebra have been taken, admission may be on a provisional basis (conditioned on passing MATH 410, 403, and/or 405 with a grade of B). Both the Subject Test and the General Test of the Graduate Record Examination are required for admission.

So as long as you have a solid mathematics background, do well on the GREs (general and subject), and meet the other requirements set forth by the university...you may have a valid chance of getting accepted.

 

[iratern]

May I ask you which country you are in?

 

[mrb]

Deep Water,

It is unlikely you would be able to produce research in pure math that would be worth anything without lots of guidance, which it sounds like is not available to you.

You could probably be admitted as a Masters student at a halfway decent school. This would let you play catch up and move on to a good PhD program. But you would probably not be funded for a Masters.

A PhD program at a top school is a different story. Regarding Cod's quotation from U Maryland's graduate catalog: I found that several schools, including very prestigious schools, include information like that which makes it sound like almost anyone can get in with minimal qualifications. But it just doesn't reflect reality; students need much stronger backgrounds to be admitted than these statements would lead one to believe.

 

[eof]

mrb is right. On my department's website the description of what we look for is something like: We expect you to have taken calculus, abstract and linear algebra, real analysis, you are familiar with proofs and that you have mostly As in these courses. However, the reality is that American students usually come from top 20 unis/LACs have honorable mentions from the Putnam, publications or have done some prestigious REUs and every international student outside of China or India in my class had a medal from the IMO. I also think everyone had taken more than one graduate course. None of the students in at least the past 3 years have had a MSc/MA, so everyone came straight from their undergrad. This year every accepted American was from an Ivy League school... though it was a tough year.

We are higher ranked than Maryland, but I don't think Maryland is that much easier to get into. Unfortunately, good programs in pure math are extremely competitive. It's also quite hard to tell from that list of courses whether or not these courses are heavily proof based? I don't see any real analysis, but in some European countries the US equivalent to real analysis is called Calculus. However, if you take the toughest courses your school has to offer and ace them, get 850+ on the math GRE and get really good recommendations that stress the fact that you've exhausted all your schools math offerings, then you can just hope that some school values your potential and will accept you based on that.

 

[Deep water]

Thanks everyone.
Cod, I've also found this information in many university's website...I shall also apply to them...but I am also thinking over what mrb said.
iratern, I live in Bangladesh.
mrb, you're right. No guidance is available to me. But I do self study (learned Calculus 3, Linear algebra by self study). I am currently self studying Topology (from Munkres) and Abstract Algebra (from Michael Artin) and yet have not faced any big problem. I am thinking of a Master's in Math too after my BSc
eof, it is difficult for me to get a good recommendation because there is almost no good mathematician in my country.
I am planning to self study Algebraic geometry and Commutative algebra after I have finished Abstrat algebra and Topology.
I am asking a question again can I apply to PhD in Math directly if I have some papers in Math? If yes, how to do it?

 

[mrb]

I am asking a question again can I apply to PhD in Math directly if I have some papers in Math? If yes, how to do it?

Yes, you can. Just do it. If you have real research in math before grad school, and done all on your own, that will certainly get you noticed. The only gap will be recommendations. Find some way to make contact with some mathematicians who can get to know you and your abilities and could recommend you, along with possibly a recommendation or 2 from your current professors.

BUT, let me reiterate what I said before, maybe a little more strongly: Beginning to do original research in modern mathematics without guidance is very difficult. It's so difficult that almost no one ever does it. It's good that you are working through Munkres and Artin, but understand that these books are elementary introductions to their subjects (not to say that they are not challenging, especially for a student who is new to them). In particular, algebraic geometry has a reputation as an area in which the amount one must learn before making an original contribution is huge, and the literature very hard to navigate.

I don't want to discourage you, but I think it's important for you to understand that this plan is not likely to work out. If you really want to go that route, you should probably look into an area like combinatorics which is more accessible and where the amount of knowledge you would need to even read papers is not so huge.

Make sure you're making the best of your current situation though. I'm assuming that CSE stands for Computer Science and Engineering? If there are theoretical CS classes available to you, take as many advanced classes as possible. If some of your profs do theoretical CS (as opposed to engineering), try to work with them and get to know them, so they will be able to write you letters of recommendation.

 

[Deep water]

mrb, thank you very much for your valuable advice and encouragement.

Combinatorics is actually not for me and I am interested in Algebra, Complex analysis and Representation theory (very soon I shall choose one of them)