Many students have over the past couple of years been asking me how to prepare for their studies abroad (outside India). I have been telling them almost the same answer over these years, so I have decided to put everything I know in one place as easy reference.
The page will be updated from time to time, to reflect changes in the procedure or to give out new information.
A salient disclaimer is in place. The information provided below is to the best of my knowledge true. If anyone has any corrections or additions to make, then please feel free to contact me. The things mentioned below, works for any subject actually, not only mathematics (for which I give examples, because I am a mathematician).
Now coming to applying abroad for your education, I usually tell the following to prospective students. This is divided into three sections below (depending on what you want to apply for):
Masters studies: For your masters studies abroad usually very few scholarships will be available. You first need to decide on what subject you want to study and then look for universities that fit your aims. For the US, it is absolutely necessary that you get a TOEFL and GRE score before you start applying. Once the university accepts, if they do not provide you with scholarship then you should look into various scholarship schemes available in India from either the ministry of human resources or from corporate sectors. For the UK, the process is similar as the US, but some universities want an IELTS score instead of a TOEFL score. For the rest of Europe, however test scores do not matter much at this stage and you apply directly to the universities. There are however almost no scholarships here, unless you apply in a specific program, like say Berlin Mathematical School. In all the cases, one would need at least two (sometimes three) letters of recommendations from either your teachers or from people with whom you have worked with.
Pre-PhD Diploma at ICTP: There is an admissions page which has all the information you require. However, I do not suggest this to Indian students as selection is extremely rare. I was the first student from India selected into the mathematics programme ever and since then there has been none. I have put this in place here, because I get specific queries from time to time about ICTP.
PhD studies: The process of application in similar to masters application, but now you would need more focus into your application then before. (See below for some tips as well.) For the US, you will need a TOEFL, a general GRE and a subject GRE score in almost all universities. Aim for a score of at least 90/120 in TOEFL and 315/340 in the general GRE. This is however no guarantee that you will be accepted as the application consists of many other components. You will need to write a general statement of why you are interested in the particular school that you are applying to. This statement should be not longer than two pages double spaced. You should write in simple language and try to give a general idea about your interests in the subject and what you wish to achieve with your PhD. For the UK, the process is similar to the US with the caveat that some universities require an IELTS score instead of a TOEFL score and some do not require any GRE scores. For the rest of Europe, unless you are applying to some specific program like say Berlin Mathematical School or Max Planck PhD programme, then normally all universities consider PhD students as employees. That means, you will need to first contact suitable professors in the area you wish to work in and then talk to them about possible projects that they might have where they might consider recruiting you as a project fellow. After this, if the professor shows some interest then you apply for the job which is usually advertised in the particular university’s website with all your grades and scores and then you either give an interview or you get selected without one.
In all these cases, you would need at least two to three letters of recommendation from either your teachers at the university or from someone who knows your work.
The European Mathematical Union has a jobs page which is sometimes used by prospective employers to post information about PhD opportunities. There will be similar job pages for other subjects. In fact, a good way to keep up with the latest job postings is to subscribe to some newsletters or mailing lists for your specific subject. As an example of what they might look like, I mention here the Discere Mathematics and Algorithms mailing list and the mailing list of Ramesh Kasilingam.
Here are some more general tips:
If there is some specific query which is not answered by this post, then you can contact me and I will try to answer it. I will be fairly comfortable in answering questions about the process for admissions in North America, UK and Europe. There are several other people, who have country specific knowledge and they have kindly agreed to share there expertise with someone in need. I list them below, with a link to their Facebook profile and the country where they are situated at the moment.
If you wish to give your expertise to the student community, then you can contact me and I will add your name in the list above.
(This page was last updated on 5 November, 2018.)