I'm currently studying mathematics in UK and am going to graduate in a 4-year undergraduate masters program. I would like to know where else (other than UK and US) can I apply for PhD? As almost all European PhD programs require a master degree and that European masters usually consist of 2 years rather than 1, would I be eligible to apply to those? Are there other options?
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Consider Canadian universities. If you're looking for the best, check out the Canadian U15 Research Universities.
If you only have a bachelor's degree or equivalent, you can apply for what are usually called a "direct-entry" PhD program. For example, on the University of Toronto graduate admissions page:
Direct entry from the bachelor's to the Ph.D. is possible for some eminently qualified applicants.
By eminently qualified they likely mean a few things:
- Grades: you will likely need to be near the top of your class.
- Research Potential: you will likely need to have qualifications demonstrating your "research potential" such as journal articles to your name, research terms with professors during/after your undergrad. An honours thesis might also count. They will also gauge your potential by your application, which generally requires submission of an outline of proposed research.
- Awards: you will likely need to have a history of getting awards and scholarships in your undergrad.
It would also help your cause if you contact potential supervisors before applying. It is common in Canada to establish who you'll be working with before you apply for a PhD. They can then help speed your application along and coach you on some of the details (like your outline of proposed research).
As a non-citizen you will need to get a study permit but considering that Canada is a Commonwealth country it shouldn't be much of a problem for a UK citizen.
If you can't qualify for "direct-entry" you'll have to slog it out like the rest of us in a Master's degree first. That being said, there are options to transfer from Master's to PhD after your first year at most Canadian universities, if you demonstrate the aptitude. It's easier to transfer than it is to get direct-entry. It will also give you time to gauge whether or not you are ready for the full four-to-five year commitment of a PhD.
Take a look at this international degree equivalency chart for the University of Toronto. It won't be exactly the same for all Canadian universities (UofT is pretty top notch) but it can give you a pretty good idea of how you stack up.