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My PhD thesis is on numerical modeling using finite element methods and non-linear continuum mechanics. My university did not offer these courses during the first two years of my PhD. So, I had to self study them from different books to the best of my ability. As I got completely engrossed in my research after my second year, I decided to not take the courses which were then being reintroduced.

I am finishing up with my PhD thesis and have started writing a CV for postdoc applications. In many sample postdoc CV's, I have seen people mention about the relevant courseworks carried out. I think that my lack of relevant coursework will be a huge negative in my applications. Is there a way, I can address the self-studied courses in my CV?

Additionally, since in the future, I will be applying for tenure track positions, do courses taken during graduate school carry weightage in shortlisting a candidate for a position if they are expected to teach exactly those courses too? Like, I might be required to teach finite element methods and non-linear continuum mechanics at the university, won't it be an issue as I have not done the courses in a structured manner myself?

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I think that my lack of relevant coursework will be a huge negative in my applications.

I seriously doubt this. While I cannot speak to all cultures and fields, I find it hard to imagine that anyone will doubt your ability to understand and teach underwater basket weaving if you have published original research in underwater basket weaving.

So, I would not give this undue weight in your mind, and certainly not in your application. In particular, I really recommend against raising this issue in your application, and certainly not in a prominent place such as your introductory paragraph. Your application should focus almost entirely on your research. A rule of thumb is that successful post-docs act like faculty members while unsuccessful post-docs act like students -- and giving undue weight to coursework risks placing yourself in the latter group.

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I had to self study them from different books to the best of my ability.

This sounds an awful lot like you simply researched topics that were relevant to your research. Under this definition, I have taken enough classes in my PhD/Postdoc/Professorship to have several extra degrees. Taking a course usually is reserved for actual courses you studied for and were examined on. It's generally expected that graduate students do what you described in order to be skilled researchers.

For grad students, the best way of proving you know something is to conduct research on the topic. If you have papers/manuscripts using finite element methods and non-linear continuum mechanics, then it's reasonable to assume that you are skilled in using these things, and listing them separately is redundant.

If you took some free online classes that may count: in that case you actually have some proof that you've taken these courses (say, a certificate of completion from Coursera or EdX).

Is there a way I can address the self-studied courses in my CV?

If you really insist, you could add them under the "skills" section (with your programming proficiencies and stuff like that). They will not carry much weight for general applications; however, if you are applying for a position that specifically asks for these skills (or that you know that the group's research interests focus on these topics) it may be worth mentioning. You can also say this in my application email.

When emailing my CV I'd say something like

"Dear Prof. X,

See below my attached application for your consideration. I would like to highlight that despite not having taken any formal courses on method A, I am proficient in finite element methods and non-linear continuum mechanics. Thus, I believe I would be a good fit to your group. "

do courses taken during graduate school carry weightage in shortlisting a candidate for a position if they are expected to teach exactly those courses too?

Not much. I am currently teaching classes I've never taken in my undergrad or graduate studies. If your studies are in the general topic that the department specializes in (e.g. a physics major applying to a physics department), there is an implicit expectation that you'll be able to teach a good chunk of classes, even if they're not in your area of specialization. Of course, no one wants you to teach stuff you're not good at, but things happen (manpower issues, someone is sick or leaves abruptly etc.). People often end teaching statements with a list of courses they're willing to teach - just list those you're happy teaching.

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