It’s weird how true this is. Complex Analysis was a little weird conceptually sometimes, but it made sense once you wrap your head around the complex plane structure. Proofs in Real Analysis felt like they were basically just gibberish created to support the existing calculus.
I had a 2-part real analysis course. I took the first one alongside complex analysis and the second alongside topology.
Shit was wild I kept leaning the same thing in 2 different classes in 2 different contexts, which made relating everything so much easier.
Definitely not as easy as the first semester of my BS, though. I took logic (as a philosophy credit), foundations, Algebra 1 (because the day before classes started I asked the teacher if the course would cover octonian algebra; I wanted to learn about non-associativity) and a bioethics class. That entire semester was learning how to argue and it was awesome.
Well, those properties are only for holomorphic functions, otherwise it’s just as hard or worse. Edit: ’
it’s* just as hard
Holomorphicity is equivalent to (or defined as) being differentiable in a nonempty, connected, open set, so it’s not asking much. Even then, functions which fail to be holomorphic can often be classified in a similarly rigid way.
