Theory of numerical analysis

[Jacek Podlewski]

As a math undergrad I completed an introductory proof-based course of numerical analysis and in further education focused rather on practical implemetnation of numerical methods. However, I recently feel I lack some theoretical knowledge, especially in the field of convergence and stability of ODE/PDE methods. I also read an interesting article on QN (https://www.quantnet.com/state-of-financial-engineering/) which, close to the end, has an interesting list of important concepts in numerical analysis - I found, to some disappointment, that I'm not familiar/comfortable with some of the topics listed there. Do you guys agree with the list? What other knowledge in this field is important from a quant's point of view (I mean can really help with designing and implementing numerical procedures for more or less typical mathematical finance problems)?