Programs From CS Major in Europe to Math PhD in USA/Canada?

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A senior CS major from Bulgaria, who has shifted focus from programming to mathematics, is seeking advice on pursuing a PhD in Mathematics. With a nearly perfect GPA and a solid foundation in various math courses, the student has also participated in math competitions and is writing an undergraduate thesis in Numerical Analysis. They are contemplating whether to apply for a PhD directly after self-studying complex topics or to enroll in a Master's program first. Feedback from peers suggests that the current GRE score is acceptable and that applying now could be beneficial, especially considering upcoming deadlines. The student is also exploring the possibility of pursuing a Master’s degree in Italy.
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This will be a long post but I will be thankful if you read it.

I,m a CS major, senior year from Bulgaria. Wanted to go to Mathematics but in my city (actually in the city i bought an apartment) there wasn't a Math Major. Since my freshman year i found that wasn't interested in Programing so I decided to study the topics that i don't like only for grades, and focus more on Math classes. I also enrolled in Cisco academy because i like networking and i realized that i must have some work options for my future.
Finally i took a decision to pursue a PhD in Mathematics. Here is my progress so far in this direction and some question I would like to ask you. Any comments welcomed.

Math classes i have took in the university:

Mathematical Analysis 1 & 2 (differential, integral & vector calculus)
Linear Algebra and Analytic Geometry
Abstract Algebra
Mathematical Logic (including Predicate calculus)
Differential Equations with applications
Discrete Mathematics (don't know if it is a CS or a Math class acording to American notation)
Mathematical Optimization
Differential Geometry
Numerical Analysis
Probability and Statistics
Graph Theory with Applications
Mathematical Optimization in Extreme Value Problems ( Nonlinear Optimization)

My GPA is almost 4.00.

I have take part in various Math Competitions with mediocre results.

I will write a Undergraduate Thesis in Numerical Analysis ( involving discrepancy and diaphony and with a computer algorithm to link CS, because the thesis should be in my Major field)

I have take the Math GRE in October and received 690 pt, 64% but without any preparation, and without knowledge in Complex Analysis and Topology. I should say that I'm happy with the result. Will retake it in April and expect and 80-90 result. Not sure how will be with the General GRE but have plenty of time to prepare.

So here is the question:
When to apply to PhD?
1. Study independently Complex Analysis and Topology and with a 80-90% GRE score apply to Phd.
2. Enroll in a Master Study at some local University(which take 1.5 to 2 years) take one year of important topics i have missed and (without finishing the Master) apply to PhD.
3. Enroll in a Master Study and receive a Master Degree, then apply to PhD.

Please give me so advises.
Thanks in advance.
Rade.
 
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You should definitely apply...what do you have to lose besides the application fee?

If you are planning on applying for Fall 2009, then you should already be in the process of applying since deadlines for grad school with funding are almost here.

Plus your math GRE looks fine to me. Had a friend who got 71% and got into a good school...of course, there has to be more to your application than just 1 test.
 
I don't have any more time to apply for the 2009/2010 admission. yesterday I got the name of my undergraduate thesis:

" Quasi Monte-Carlo integration over weighted Hilbert spaces. Representation of the error in terms of the Walsh functional system. Mathematical models and computer realizations. "

Now am considering doing Master Study in Italy and will appreciate any thought about this.
 
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