How to feel confident with knowledge if I have not taken relevant classes during my postgraduate degree?

Question

Taking relevant courses builds up confidence, exposure and depth. I managed to get my master's degree and PhD degree in computational chemistry without taking any graduate level mathematics and modeling courses.

On top of this, the only maths I had was till my 3rd year undergrad and I struggled with it. I scored a C grade in every exams and I was/and still am not comfortable with it.

I am decent with linear algebra and multivariable calculus and work with tensor analysis in my research. Each of these I had taken only in my undergrad.

I should have taken relevant courses during my master's and PhD. Though I can perform well in my research (currently a postdoc), I feel unconfident and uncomfortable with my level of knowledge as I have never explored the depth of the subjects as is done in graduate courses. I only self-studied what was needed in my research.

How to feel confident with knowledge if I have not taken relevant classes during my postgraduate degree?

Answer 1

The classes from undergrad and what you took from them enabled you to self-study all the relevant maths on your own. That is a much more valuable thing than the knowledge on its own and should give you the confidence.

If you absolutely need the "external validation" to build the confidence: As a postdoc you are still in a University setting? Then why not take some time out of your schedule and take the classes now? Or take some online courses that include tests and a certificate.

Answer 2

In addition to the good points made by asquared, you might consider going back to the first course you struggled with and taking it again or going through a book on it. You might be rusty on some points, but you could very well find that you understand parts of it better than you did the first time around.

Also, what made the courses harder as you went along? Was it more assumed knowledge, a faster pace, a shift from computation and calculation to proofs, a greater level of abstraction/complexity? If you can identify the stumbling blocks, you can work on them. For instance, take time to strengthen your knowledge of the prerequisites, study at your own pace if possible and, if relevant, take an introductory course on proof-based mathematics. Increased abstraction or complexity can be harder to deal with, but sometimes you can find a book or other resource that helps bridge the gap between where you currently are and where the new material starts, with a gentler learning curve.

You may also need to make peace with not knowing everything to the same depth. The seeming paradox is that the more you know, the more you find there is to know, so it feels like your knowledge is increasingly inadequate. This is a game you can't win - none of us can. By all means learn things as you need to or want to, but ease back on your expectations of yourself.