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

Numerical Analysis in Extreme Value Problems ( Nonlinear Optimization)

Theoretical Basics of Informatics (some in depth study of computability and mathematical background of Informatics)

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).

Name of the 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. "

I have take the Math GRE in October and received 690 pt, 64% but without many 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 (considering Italy because am fluent in Italian) and receive a Master Degree, then apply to PhD.

Please give me so advises.

Thanks in advance.

Rade.