It so happened that I entered the PhD program in mathematics at Stanford University. I would like to talk about what is required for admission, and why trying to enroll is not very difficult. I am sure that my experience is relevant not only for mathematics, so in some places I write more generally.
What is required for admission?
- TOEFL ($ 260) (English exam)
- GRE Subject Mathematics ($ 150) (math exam)
- GRE general ($ 205) (school math and English)
- At least three letters of recommendation
- Statement of Purpose (Essay)
- Curriculum vitae (scientific autobiography)
- (sometimes) Personal History Statement (another essay)
- (preferably) publications and papers at conferences
- Money (on average $ 150 for each university)
And now - in order!
TOEFL
TOEFL is an exam in English, which consists of four parts: Reading, Listening, Speaking and Writing. A detailed description of the exam can be found on the official website . The maximum score is 120.
Instead of TOEFL, you can take the IELTS exam, which is also suitable for American universities. But I did not write IELTS and I don’t know anything about it, so I’ll write further about TOEFL.
As far as I know, for admission you need to collect more than the minimum threshold, which each university has its own direction. After passing this threshold, the difference in points should not matter. For example, for the commission there is no difference between 100 and 120 points, but a result of less than 90 can cause problems. For most areas, 100 points is a sufficient result.
On the Internet you can find a lot of materials to prepare for the TOEFL. However, it should be noted that the number of complete tests on the Internet is limited (especially with listening). Therefore, it is better to carefully work out the mistakes in the test done, than to immediately begin the next one.
I used the following materials:
The book Cracking the TOEFL contains many good exercises and a couple of complete tests with listening. However, the text of the book itself is too detailed, and, in my opinion, it is not necessary to read it. It is better to just solve problems along the text, returning to explanations only when problems arise. The same goes for the Official Guide to the TOEFL.
Be sure to look at examples of good essays to understand what the ETS experts expect from you. Examples can be found in this file or on the official edX course (which I do not advise to go through entirely).
I was preparing to surrender for about a month with deep immersion and got 108 out of 120. Many advise to devote more time to training, and this depends on the level of proficiency in the language. However, even for people with good English, it makes sense to prepare for an unusual test format. I did not study with a tutor, did not go to paid courses and used only the materials that are available on the Internet. But I do not claim that this is the right approach.
GRE mathematics
GRE mathematics is a math exam. There are a lot of tasks in it and not enough time to solve them. 50% of problems in mathematical analysis, 25% in linear algebra, and the remaining 25% are different branches of mathematics. To successfully pass this exam, you must be able to quickly solve problems. Details can be found on the official website . The score range is 200 to 990.
On this site you can find exams of past years with solutions. The Princeton Review also released the book “Cracking GRE Subject Mathematics”, in which there are many tasks, but the text is, again, too detailed. It is better to solve problems and return to theory if necessary.
The result of this exam is one of the main factors for the selection committee. I scored a low score (760 out of 990), because I do not know how to solve problems quickly (unlike those who studied at the time), and this was the weakest point in my application for admission.
GRE general
The test consists of two parts: school mathematics and surprisingly difficult English (test and two essays). On the official website you can find a complete description and examples of the problem. The rankings are rather strange: from 130 to 170 for each part, and essays are ranked on a scale from 1 to 6.
For a person with a technical education, school mathematics should be trivial, and the commission expects a result close to the maximum (170). English, on the contrary, is incomprehensible (at least for me). Honestly, I don’t know how to prepare for and successfully pass this exam if I don’t know literary English for many years. Difficult vocabulary assignments made me literally guess the answer without any considerations. The book Cracking the GRE of the same Princeton Review did not help much.
On the other hand, as I understand it, it does not matter much. Probably, this exam is a part of the bureaucratic system, and the result in English does not affect anything (in a reasonable sense). However, in mathematics, of course, you should score the maximum score.
All my friends who entered the United States gained an absurdly low score in the language part of this test. However, in other areas things may be different (probably, English literature requires a high score).
Letters of recommendation
Main idea: “Give material to those who write a recommendation!”
If you are a good student, you can write about your studies.
If you speak at seminars - about academic activity.
If you are doing research - about the scientific results.
If there is nothing, then there is nothing to write about.
Letters of recommendation are best obtained in a natural way: study well, do non-trivial term papers, speak at seminars and conferences, discuss scientific results or research questions with professors. It is not necessary to “beat out” recommendations for yourself, specially crossing with famous scientists, if you do not have a common scientific theme. This is unprofessional.
One letter of recommendation must be from the faculty member where you study. Other letters of recommendation can be from anyone, but the right to choose those people who can tell something specific and at the same time - good.
Statement of Purpose
Statement of Purpose is an essay where you need to explain why you and the chosen university are ideally suited to each other. There are many conflicting opinions about what needs to be written in the Statement of Purpose, and no one really knows what works and what does not.
I think that it is not necessary to write about interests other than the direction of interest. If you are an outstanding athlete, play in an orchestra, or speak six languages, it may be better to indicate this in your resume. An exception can be only if it fits perfectly into the text or hobby is indirectly related to the chosen direction (programming for mathematics is quite good).
In my essay, I wrote about the work done, why I decided to study mathematics, what goals (or dreams) I want to achieve, and why the chosen university is the ideal place to realize them. I think it is appropriate to indicate specific people, if it is not randomly chosen names, but people whose results you know and are really interested in working with them.
It is important to show (if this is true) that you are ready to become part of the academic world or indicate other goals that you pursue. After all, universities expect their students to be great scientists and develop an academic environment: write books, teach, and hold conferences.
Curriculum vitae
CV is the easiest part, because it contains only facts and nothing more. In CV you need to indicate your education, Olympiads, teaching experience, speaking at conferences, published works, knowledge of languages and, possibly, other interests (somewhere at the end).
By and large, CV is a brief scientific autobiography.
Personal History Statement
Some universities (for example, Berkeley) are asked to write another essay about the difficulties that you have overcome in your career. Problems with discrimination, prejudice or anything like that. I did not really understand what they wanted to hear, so I wrote rather casually about changing institutes twice to be in Moscow, where there are more chances for a good career. I'm not sure that this essay is important at all. Perhaps this is just a bureaucratic requirement.
Publication / Conferences
Having a research experience before applying for a PhD may be useful, but it is not necessary. This experience shows that you are able to deal with scientific issues, and not just study well. In addition, scientific results will be the content of reference letters and CV. However, in general, students are not expected to have any results at this stage and, theoretically, this should not seriously affect admission.
Money
On average, the fee for applying to the university costs $ 100. But in addition to collecting, you need to send the results of TOEFL and GRE, which cost $ 20 and $ 27, respectively (however, the first four shipments TOEFL provides for free). Thus, on average, applying for one university costs $ 150.
You also need to pay for the exams, which in total costs $ 260 (TOEFL) + $ 150 (GRE subject math) + $ 205 (GRE general) = $ 615.
What is the result?
Of course, you need to make some efforts for admission, but on the other hand, the admission process is linear and understandable. You can prepare and pass exams well. Instead of a course or diploma, you can ask a research question from a supervisor and speak with him at seminars and conferences. You can study well and get a high grade point average (GPA), which in many places pay a lot of attention (especially if your university has established itself as a good education). And everything will work out!
Briefly about meI graduated from school in Krasnoyarsk, and there I entered the Polytechnic Institute as a programmer. However, I soon realized that I wanted to study mathematics, so I transferred to the Institute of Mathematics in Krasnoyarsk. After another year and a half, I transferred to the Faculty of Mathematics at the HSE in Moscow.
I always asked to give me research tasks instead of coursework. This allowed me to participate in seminars and conferences. Dating at conferences and having research experience helped me a lot in the future.
I entered not only Stanford, but also Columbia University. My subjective comparison of these schools I wrote here .
About how the PhD works in the USA (at least in math)In the US, education is paid, but you can go to the PhD almost “for free”. PhD students are required to help lead professors in courses: check homework, answer questions, and conduct seminars (at senior courses). For this work, the university pays tuition and grants a scholarship, which is usually enough for a living.
At the end of the first year, the student must often pass a qualifying exam, for which they are preparing for the first year of study. In the future, the main task is to write PhD thesis.
Students are prohibited from working off campus, and on campus you can work no more than 20 hours a week. For violation of these rules can only student visa and deport from the United States.
Write about any errors and inaccuracies in private messages.