>>12260830>>12260822Math classes are absolutely pozzed. This shit is actually not hard to understand. It would take maybe 15 minutes to provide an in depth, well motivated explanation for this identity using infinite series, but 90+% of professors just brush that shit away. People often take MULTIPLE courses on complex analysis and vector calculus, each of which generally lasts anywhere from 2-4 months depending on when and where you take such a course. All it would take is 15 minutes at the beginning of your first complex analysis or differential equations course. Professors either view this as a waste of time, or they themselves do not have the mathematical knowledge or communication skills to explain this shit.
It pisses me off. Not explaining things or providing any motivation does not improve your math classes, it does not make them more rigorous, and it does not even provide more time to cover the basics. If you have ever had a really good math professor or you have read a classic textbook on a topic like anything by John Conway or say Munkres topology, then you would know that brilliant mathematicians and brilliant expositors, are actually good at invigorating the material, so to speak. They provide intuition and they point out the beauty. They comment on how topics are inter-related and why one should be interested in some seemingly arcane lemma or obscure piece of notation. Good authors and instructors are able to create a natural sense of flow and logical progression in the material. Theorems should be strategically placed, and their names should sound cool and be easy to remember.
