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I am a first-year mechanical engineering PhD at a Canadian university. I had by undergrad and a master's degree in materials engineering. My previous master's research was mostly experimental with some implementation of a mathematical model in Matlab and Fortran. All graduate courses were on programming or simple mathematical modeling or experimental analysis.

Now for the PhD degree, my research topic involves continuum mechanics, variational mechanics, and finite element analysis. There are no courses available in my university for the next two semesters. I had taken an "advanced" course last semester which had some continuum mechanics in it, but I found it fairly introductory.

My advisor says that in graduate school one must learn topics by oneself. And no one will look for these courses in the CV if one can publish papers using the methods.

I am starting to learn these from online courses and books. But I feel inadequate because of my poor undergraduate background in mathematics and these topics.

My PhD funding is for three years (can be extended to one more year). I need to start my research by the second year. I don't know what to do.

My advisor just points me towards relevant literature. I wonder if she has my best interests in mind.

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  • Is there any sort of summer institute tradition in this field? In Econ we have various summer institutes where you go and take one-day courses on key topics from the experts.
    – Dawn
    Jun 11 '20 at 15:40
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    When you say, "There are no courses available in my university for the next two semesters", do you mean "no courses in my selected topics", or "no courses whatsoever being held at the university"? In other words: Is this the normal schedule, or has it been specially disrupted by covid-19? Jun 12 '20 at 14:40
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    The solution to your specific problem is to watch the finite element video series by Wolfgang Bangerth (math.colostate.edu/~bangerth/videos.html), and the computational science and engineering video series by Gilbert Strang (ocw.mit.edu/courses/mathematics/…).
    – Nick Alger
    Jun 13 '20 at 4:28
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Part, or most, of a PhD is about self-learning, so you have to step up and work on those subjects you need.

A PhD is usually to push the boundaries of knowledge in topics / areas etc so learning methods or techniques relevant to moving your research forward is what you have to do - simply said your supervisor is correct.

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    While this is absolutely true, a good supervisor should also understand that there is nothing wrong with asking for help (on the contrary), and do anything he can to make the projects of his students a success. Unfortunately this does not appear to be the norm in academia, making this answer a good one.
    – Louic
    Jun 11 '20 at 11:19
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    @Louic I'm not sure what you are suggesting the advisor do differently?
    – chepner
    Jun 12 '20 at 11:54
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    I do not know how much effort the supervisor has put into this already, but OP has the feeling that he is not getting enough help and that issue needs to be addressed. The supervisor could possibly try to find a colleague or student with the desired expertise who could help the student with his questions, schedule some time to do so himself, or even better: ask the student what he thinks would be the most helpful solution. He has a PhD student who is eager to learn and has spent the effort to read books and online courses, but still needs some help. This help should be provided somehow.
    – Louic
    Jun 12 '20 at 13:24
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For context, I am a third-year PhD student in physics who has completed all my coursework.

I think that your experience is the norm. As you get more advanced in your education and transition into focusing on research, it becomes less and less likely that your department will offer courses that cover exactly what you need (though this might depend on your research area). At some point, there will be topics that you will have to teach yourself by finding the right textbook, deciding what is important, and learning it.

It may be helpful to take courses that are tangentially related to your research area. I did this a few times when in your situation and found that many of these courses happened to come in handy later. However, I've found that the most efficient way to learn specific topics was by teaching myself. Taking a course is not always the fastest approach because it sometimes forces you to jump through hoops that you don't need to go through.

I think your advisor is right to point you towards relevant literature related to your project, as these will give the best indication of what topics you really need to learn for your research. Then you can aim your self-learning so that you get up to speed with the most essential skills as quickly as possible. Good luck!

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You say "But I feel inadequate because of my poor undergraduate background in mathematics and these topics."

Given that, you should consider the possibility of taking some less specialized courses. Do not depend on getting the actual knowledge you need from the courses. Your advisor is right that you should be learning to learn from papers and books. Instead, aim to fill any gaps in your background knowledge and skills that are making it harder to learn independently.

Since you do not need any grades or diplomas from the background courses, you can consider on-line courses if they work for you and are available in the topics you need.

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Many people, including myself, have had similar frustrations to this. What I have learnt, over time, is that courses in the things I needed to learn simply didn't exist. Any where. The things I was interested in were simply too cutting edge to ever be taught in a classroom like setting. At the time I felt like this counld possibly be true. Surely there were lots of poeople out there that needed to know these things? What about all the people publishing papers in the field? Where did they learn?

Well it turns out, you just have to muddle through. No one is going to "teach" you these things.

Okay, now that i've effectively said the same as everyone else, what can you do about it and how can you get help?

The first thing is that you need materials. Collect together any papers, books etc, any online courses. It sounds like you've already done this - well done.

Now you need a general overview of the field. What are the main uses of the field. What categories do the main techniques fall into etc. Get a grasp of the things you don't know. Turn the unknown unknowns into known unknowns. Do this by reading broadly but shallowly. Read the introductory chapters in books and the introductions to papers etc.

Now set your self specific goals. Not "I want to understand the field" or even "this week I will understand this subfield". One of the first things any training in pedagogy will teach you is that "understand" is not a useful word. A good goal would be "I would like to know when it is appropriate to use tool X". Or "What are the steps in derviving the main model in approach Z". Its good to focus all this on a particular question or application, presumably the one you will be tackling in your PhD.

If you are feeling that you lack the background in a particular sort of mathematics, then organise to do a course in that piece of missing background.

How can your supervisor help in this? They can't "teach" you the subject. They do not have the time. Instead, arrange for your supervisor to help you plan with sub-bit you will tackle next and give you some accountability on your progress. They can help steer you to what sub-fields are most appropriate. You can also get them to help with with specific problems "Can you help me with thisstep in this derivation?" Or "I keep getting a different answer to the authors in this paper, can you see why?". Make sure the questions you are asking are specific.

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You could theoretically take one or two courses at a different university, that's close enough for you to travel there once a week. This is often officially sanctioned and counted towards your course requirements after some intra-university and cross-university paperwork; and if it isn't, you could still probably just "take" it unofficially.

Now, I'm not saying that this will necessarily be a good idea. You will have to get used to self-study - since most subjects you'll need to study up on don't have courses online, nor anywhere. Many will not even have any books, just a bunch of papers.

But - it might save you time and effort despite the travel; and you might even make academic contacts.

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You should look into the Western Dean’s Agreement in Canada. It allows graduate students to take courses at other universities without paying additional fees of attending another university program. It is incredibly powerful and can help you to address the needs of courses your institution does not offer.

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This is very sad.

Is this research something that the advisor actually wants to do? Has she published in this area? Or is this just something that there was grant money available for? If so you are being used as cheap labor just so that your advisor can appear to be active and engaged.

That most certainly should not be norm, but it is not unknown. You have been assigned to a project for which you have expressed no enthusiasm and in which you have no training or experience. If this is the case what can you do about it? Others have made practical suggestions, but how approachable is your Head of Department? This one of the things that they are paid to sort out. They might be able to point you toward suitable resources. They could assign you to a new advisor. Your Department should also have a Graduate Chair,which might be a better place to start.

It could be however, that doing anything to make the department look good on paper is a deliberate policy. In that case, you may really be on your own. Ombudsman?

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    I don't see any evidence of this. In fact, their advisor is pointing them towards relevant literature, and letting them know that they are expected to self-study (which is how a PhD typically works). I also don't see them say anywhere that they were assigned this project, or that they have no enthusiasm. Oct 1 '20 at 19:41
  • If the OP really lacks background as they describe, it takes a bit more than just pointing them in the right direction.In fact it should always take more than pointing in the right direction.
    – Philip Roe
    Oct 2 '20 at 2:51

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