Wondering what educators / researchers in the field think is the most important and logical flow of topics. The way I was instructed was solving Schrodinger's wave equation, SWE, for every possible problem that could be solved with a pen and paper in say 2 or 3 pages max. The problems were instructive toy problems which I assume are standard. The next phase was solving similar if not the same problems but slightly less contrived where numerical techniques were used. That was all great but when I first looked at the literature it did not resemble anything I had ever seen, it was all logic, set theory, abstract algebra...not a differential equation in sight. The question is what is the progression in terms of topics to go from SWE to abstract algebra and logic/set theory of QM. Why is SWE the standard (as far as I know) way into QM, can the more abstract approach be done from the start.