I currently have Jost (as well as a few other texts), and have been working through it - I am a master's student who is trying to prepare for thesis work in closely related areas. However, it is far too dense to make me feel comfortable. On top of this, I have found what I consider to be an unacceptable number of errors which can regularly trip up a beginning student (at least a half dozen in the first 30 pages). It is frequently listed as one of the top texts for this subject, but for someone trudging through it alone, I find this makes it a huge pain to get through. I have a solid background in abstract algebra, and have taken a beginning topology course, but am not well versed in complex analysis or modern geometry. I frequently feel lost, and like I am trying to memorize theorems, corollaries and lemmas by rather than having them soak into my math schema from a true understanding of their development. My undergrad Calc classes used Bartles Introduction to Real Analysis text (simplified); I have not started a true grad-level Real Analysis Course yet.

I am looking for resources which introduce an individual to Riemann Surfaces while requiring as little background information as possible (perhaps including additional necessary info in an appendix, if required), and which also works step by step explicitly through the proofs of corollaries, lemmas, theorems, etc. (Jost does not do this). Also, Jost only offers a couple exercises per section (if that), so a larger set of exercises would probably help a lot as well. In a perfect world, the text would include (like Gamelin and Greene's Introduction to Topology text) an outline of the solutions to the corresponding exercises, so that I can build my own confidence that I can write the proofs/perform the calculations on my own (working with such a dense text has increased my anxiety about the subject significantly, and made it hard for me to have confidence in anything I do manage to try to compute). These resources could be anything from videos, to online lecture notes from someone else's course, to a set of recommended texts.

  • $\begingroup$ Have you tried Forster's book? Miranda's is also great! As far as I know, there aren't many books on this topic in which all the details are given. At some time, you have to fill in some details. Good luck. $\endgroup$ – YYF Sep 3 '16 at 18:31

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