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I will give some background. I am from a third world country, and I am doing my math PhD in Europe. During high school and university years I participated in many maths competitions, and even got to the pre-national team. (I mention this just to show how interested I have been over the years with the topic.)

Here is my problem: my education is not the best. I would say it is mediocre at best. By education I mean the whole system of the country. I pretty much had to learn everything on my own during those years, starting from Analysis. So, even though I took courses, they were meaningless, because the level was very low and in many cases the professors were not experts in the field. On top of that, the interaction with other students was almost null, I was very ahead of all of them.

Despite that, as I said, I studied very hard to get to where I am now. However, I have to admit that due to this personal training, there are many topics that should be basic with which I don't feel comfortable about: ODEs, PDEs, Numerical Linear Algebra, etc. This is due to time constraints because I feel capable of learn anything.

To summarize so far: I have been a lonely man in a cave with a book for the last 7 years. That being said, I managed to get some decent knowledge in the area I am currently working in.

Fast forward to the PhD program. As usual in Europe, there are no courses involved: only research. And there is were my conflict lies: I am very unsure of myself because I think that everyone has a better education than me and hence they are better prepared. Another issue is that the institute were I am is very small and hence there is no ‘big purpose’: no one seems to care about you. Also, the institute is not well known, so that I am also afraid that the ‘brand’ issue will affect me later.

I feel like I don't belong there, and that I could do much better if I go to another Program that starts the courses from the beginning. However, the way I am doing it right now has got me very demotivated and it is starting to affect my research: I have been here for a year already and so far I am only at the middle stage of a first paper. The paper is not that strong, because after I got the results I found that someone has done it before (I lost months on this).

I guess that what troubles me most is the fact that, due to lack of data, I can not compare myself (main source of motivation, in a healthy sense of course) with the rest of my peers and that is the main reason for my insecurities. The comparison is in the sense of me being sure that I am roughly at the same level of my colleagues. I know no other way to do this other than taking the same courses and tests. This comes naturally with a program in which one take courses on the first year but, as explained earlier, I didn't have this interaction with really good students. Due to this, I am thinking of quitting and starting all over again somewhere else. Also, I don't think this is a case of the Impostor Syndrome: I am sure that with proper training I could get far, I just haven't had the opportunity to take a bunch of graduate courses.

Should I proceed?

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    I broke your wall of text into paragraphs so I could read it, then voted to close your question. I think what you're asking calls for opinions that, if they were to be particularly useful, would depend on knowing you as a person, the institution and program you're in now and what others around you experience. There's no way we can know that. So my opinion has to be on just what you've written. But my takeaway so far is that you're probably very lucky to be in the PhD program you're in right now. – Nicole Hamilton Jan 11 '18 at 14:12
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    @NicoleHamilton thanks for the input. However, I didn't followed you on the last lines. "So my opinion has to be on a lot less. But my takeaway so far is that you're probably very lucky to be in the PhD program you're in right now." Does that means that you think I should stay because I am not capable enough? – jhndoe Jan 11 '18 at 14:19
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    @jhndoe Far from imposter syndrome, you seem to have a very high opinion of yourself and appear to feel your current institution isn't good enough. But I didn't see evidence in your essay that convinced me of either. – Nicole Hamilton Jan 11 '18 at 14:54
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    This is exactly the case of impostor syndrome. – Ander Biguri Jan 11 '18 at 16:21
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    This is not the kind of question one should close. It's very relevant to anyone trying to get a scientific education from a third world country. – user21264 Jan 12 '18 at 7:26
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As someone who studied in a third world country, then did a PhD in US and came back to the country, I have a few comments to this question.

The first is about the quality of education. Funding for science in a country like mine is unpredictable and doesn't have a long term objective or a specific target. The bureaucracy makes you wish you were in a Kafka novel. As a result, the few existing specialists always contemplate leaving. I know I do. A large percentage of faculty and research staff gave up on research and they stay there just to game the system. Their bad attitude infects future generations of students and many of them simply leave the academia utterly disgusted. The same people get really upset if an outsider comes in with a strong research record and tries to make a serious research group. One of my colleagues (who happens to have the strongest research record in my institute) was forced to leave though he has two projects running right now, because he was upsetting the balance of the force.

Second, about getting a proper PhD education in my country. This is not possible. A good student like OP would be isolated. Since many people don't understand the subjects they are teaching, most students are weak and have a hard time self-evaluating. They are also much more insecure than the students in Western countries.

Someone like OP find themselves alone. I know I did, and it still has negative impact on my career. It is very important to break the isolation if you want to get proper education and make a significant scientific contribution. Yet, isolation is very beneficial to the weak professors who don't want to be exposed as frauds by discussing to their peers abroad. There is a ton to discuss about the issue, but I only want to say that my institution and university in my town are completely disconnected from the rest of Europe. We simply don't have PhDs and postdocs coming and going, we have a 10k/year travel budget for a 50 people department for a whole year, no subscription to main journals in our fields of research, and I could go on.

In conclusion, this is not the environment in which a good student becomes a good scientist. I had my own student who was in OP's situation and I advised him to leave and get a PhD at a serious institution where he has constant contact with peers at his level and scientists who do science for pleasure. He could learn a lot of my own trade by staying, and do quite well at my institution, or go abroad and become a real scientist. And guess what, he's abroad now and already has two publications with his new group, while I'm still fighting with a paper from last year by myself.

To list the advantages of going:

  • more motivated and diverse peers
  • more predictable funding
  • more travel opportunities (conferences, summer schools)
  • better access to literature, labs
  • much more qualified professors
  • more likely to get into a good research group
  • more and higher quality seminars
  • more opportunities at the end of PhD (if you pay attention).

The main disadvantage is that you may lose touch with people at home and you have to re-make your friend network which is crucial for your well being.

  • Is this biology or math field? – SSimon Jan 12 '18 at 8:36
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    (+1) Thanks for the answer!! You described it exactly the way it is in my case. However, did you note that I am not in my country anymore, right? – jhndoe Jan 12 '18 at 8:51
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    You did not answer OP's question at all. I don't get how he could accept your answer. – usr1234567 Jan 13 '18 at 23:24
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In the European programs I have been involved in, there is no (or a very minimal) fixed curriculum students need to go through. However, students do follow specific courses to learn specific techniques. Typically/ideally the student discusses with her/his advisor what is needed for the project, what is needed for her/his future career, and where the gaps in her/his knowledge is, and how to fill those gaps. This is the kind of discussion you need to have with your advisor.

  • in Math?? are you sure? – SSimon Jan 11 '18 at 14:36
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    I don't understand that comment. Do math PhD students not talk to their advisors? – Maarten Buis Jan 11 '18 at 14:58
  • It is different concepts of study, on both unies in EU and one in Asia, concept how Math advisors behave toward Phd students is different from other departments. – SSimon Jan 11 '18 at 15:01
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    @SSimon I have several friends that are currently doing PhDs in math in Italy, Germany, France and the UK. AFAIK all of them have to follow some courses during the first year of the PhD, and some of them will have to follow some courses also the following year. Obviously the departments also do some non-mandatory courses and/or series of seminars for both the PhDs and professors that want to hear about specific topics of research. – Bakuriu Jan 11 '18 at 17:20
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    +1, "talk to your advisor" is the best advice in my opinion. Also, have some confidence. Unless you lied and cheated your way into the program, you're there because they think you're qualified to finish. See also this: academia.stackexchange.com/questions/2219/… – Allure Jan 11 '18 at 21:09
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The university's name is not nearly important as your contributions. If you believe you have the talent required for a top university, but you say you don't have the education, then get the education.

Doing research requires you to be able to self-educate and then use that knowledge to push the boundaries and discover new solutions -- whether it is by inventing the method yourself or applying other people's methods to these problems.

This whole case sounds like you need to step back and evaluate yourself honestly. Then, buckle down and learn the things you think you need to know. You've already done the hard part of getting accepted, now do the harder part of making a plan and sticking to it. Talk to your adviser, figure out what you need to know, make a plan to learn it, and make sure you keep your eye on your research goals while doing so.

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    Thanks for the answer(+1) That is exactly what I have done(evaluate myself), hence the question on this site. I feel very comfortable in my area right now, I am just afraid that not knowing other topics can harm me somehow in the future. – jhndoe Jan 11 '18 at 21:40
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I'm not from mathematics, but your progress sounds reasonable to me. Midway to a paper after the first year is pretty good. That you missed closely related work is unfortunate, but not unusual: it's more or less the first time you are doing a real literature search. Ideally, your advisor should have checked that too.

I would caution against thinking that just because classwork is mandatory in other places, it will be good or useful. The classes offered at postgraduate level can vary wildly, and are often a motley collection of the research topics of the professors who get assigned to teach one. In my department, most of the postgraduate courses are too far from my work to be of practical use, and the one class I think I really could benefit from is taught by a professor that everyone has warned me to stay far away from.

The classes don't have to be mandatory for you to attend them. Especially when it is for your own learning, rather than for a grade, it is quite easy to just sit in on classes that you think you could benefit from. At the beginning of the semester, look through the classes offered at your local university and attend the first lecture of any that interest you. If it seems useful, talk to the professor at the end and ask if you can sit in informally. Usually there will be no problem, although if the exercises are only accessible through an online platform requiring students to be registered, like moodle, you may need to ask for access or for the prof to email you the materials separately (or you just find your own, different exercises).

This way, you can find out if extra classes would really be of as much value to you as you think they would be, without going to the drastic step of abandoning your PhD first.

5

Changing topic, advisor, or university came to the mind of every PhD student facing serious problems. Still, most students must tackle their problem and get their research done. After that, you can wrap up and write the thesis and you are done.

Having a PhD without major detours is a good sign. You can move around to prestigious names during your post-doc time. Maybe you can stay a couple of week within your PhD program at another institute.

In general, you don't need to know everything, just your topic. You can still learn about ODEs and numerical methods once you need them. If you are good in your topic and have above-average contributions, everything will be fine.

3

How did you manage to get into a Phd-position if you think that you have a lower education. In most departments that I know it is really hard to become a phd-student. Do you think that you get there because of a rate?

Another point is that on one hand you think "my education is not the best" and on the other hand you think that "Also, the institute is not well known, so that I am also afraid that the ‘brand ’ issue will affect me later". Why do you think that a well known and popular institute should accept you, if you think that your knowledge isn't even good enough for the small unknown one?

  • "Why do you think that a well known and popular institut should accept you, if you think that your knowledge isn't even good enough for the small unknown one?" Because I know I have the talent, I just haven't had the right opportunity – jhndoe Jan 11 '18 at 13:56
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    Coming from a third world country, I didn't had many choices. If I could, I would have applied to a PhD program in the US: this was just not possible for me back then – jhndoe Jan 11 '18 at 13:58
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    @SSimon: "why didn't you publish a paper until now". Uh? Who publishes a paper in their first year of a Ph.D. in math? Do you know anything about doctorates in math? – Martin Argerami Jan 11 '18 at 21:52
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    That's pretty close to unbelievable. Which university are you at? If you are understandably unwilling to tell us, can you give us an example of a (different) university with a similar policy? – SolveIt Jan 12 '18 at 9:21
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    @SSimon: it's not about comparing with my institution. In mathematics, it is very rare for a Master's thesis to result in a paper, and even more unusual to publish in the first year of a Ph.D. Before qualys, what a math student does is to take classes and study for the qualys. Example: not long ago I had to referee the grant application of one of the best mathematicians (worldwide) of my area; for this top mathematician, in a top university (who obviously gets top students), his expectation is that a Ph.D. student will defend with two papers submitted; and this is already beyond the norm. – Martin Argerami Jan 12 '18 at 13:41
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Anyone who answer this question might be expressing his/her opinion that must be biased towards his/her own experiences. Mine, for example: I was starting a cientific initiation in algebra and automata to achieve a master's degree in computer science. I was working at a federal university as a technician, not teacher, and my "dream" at the time was to work as teacher and do R&D. But after sometime I knew for sure that it was only to gain a 30% raise in my wage due to degree's incentive given by institution where I worked. I was starting a 4 year (or more) study just for 30% raise? Does it makes sense? Afterwards I realized that I should be happier working with my REAL dream as a DBA. Then a friend of mine invited me to join he in a company and we opened up a Database Administration startup. It was 2 years ago and I can't say that I would be happier with just a degree more into my resume. My income today is far better than 30% raise and my challenges are new everyday. So, you must think what makes you happy. Do you think yourself as a researcher or a teacher in the future? The PhD will add something pleasure in your life? Does the area (math) you choosed is really what you like to do? Work in something you love and you will not work a single day in you life. Best wishes from a "third world country" too (Brazil).

2

I suspect your intuition is correct. I'd either take the extra time during summer to get to the level of expertise of your peers, or drop out of a PhD program, and re-enter as an undergraduate at the same school to arrive at the level of beginning PhD students.

That's perhaps a bit extreme, and you should consider a serious discussion with your advisor about something that approximates this trajectory.

  • Thanks for the answer! I think that is a little bit extreme too, given that I feel very comfortable in my area right now. I am just afraid that not knowing other topics(not needed now for the research) can harm my academic career. – jhndoe Jan 11 '18 at 21:43
  • It's definitely good to be concerned about that. Once you slip a little, you slip a lot and it's very hard to climb back up. – TheDoctor Jan 11 '18 at 21:45
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    Re-entering another PhD program after having difficulties with your first one came to the mind of virtually every PhD student. Stick to your problem, work around or solve your problems, learn about yourself and focus on get research done. After that write up your thesis. Good luck! – usr1234567 Jan 11 '18 at 21:45

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