Theoretical foundations or lack thereof

It has been a nagging thought at the back of my mind for a while now; the thought that I am uniquely deficient in fundamental knowledge. I have been climbing up the knowledge genealogy tree lately. Seeing that I have 4 years to do something, I decided not to rush much to produce results in little superficial chunks. This is when I realized that the climb is long and steep, and it feels like many have done this climb in reverse in their undergraduate years.

I started by trying to understand Optimality Criterion, a structural topology optimization method proposed by Rozvany in the 70s. The right way to go about understanding this field, i thought, was to start at the beginning after reading a review paper or two, and work my way to the present. Those pointed me to Mitchell’s original paper published in 1904. Then I discovered problems immediately, I cannot follow the math. I get hopelessly lost in trying to understand the simplest derivations. The starting point of this method is the principle of virtual work.

So I looked that up on Wikipedia. Failing to understand that article, I went further in the past, and read up on Principle of least action, then Lagrangian, which led me to Calculus of Variation. Finally something I can understand, with the help of many Calculus “cheat” sheets containing Chain rules, produce rules, integration by part, by substitution, etc.

Along a similar path, Mitchell’s truss optimization is proven to be an convex optimization problem, which can be solved with many analytical methods. The problem? I cannot follow the linear algebra, inequalities, and absolute values.

What had I been doing in my undergrad years?