General appeal to CU math professors:
Please, please, please, please, *please* stop teaching analysis as simply Rudin, expanded. Please.
I believe that there are good ways to use Rudin, but they are not to plunge us into Rudin and hold our heads down. There is very little of the beauty of math in this process; it retains its purity in the sense that it is true and very little is assumed, but not its elegance, as it has no meaning; it is just words (prove [this statement]) that expand into more words (ok, so [this statement] means [this expansion of this statement] which means [stuff with epsilons and deltas] then we can apply a theorem which means very little to us although we vaguely remember proving it so we suppose it's true and which seemingly came out of nowhere to get more different epsilons and deltas, and then TA-DA! QED) as a logical or memorization game.
If you _do_ assign Rudin (please don't!!!), please explain what these things mean--- as pictures, or intuitions, or explanations of the desires mathematicians have for their definitions--- in class instead of simply following the damn book. Also, please give us a reference text, as I have not been able to find one that isn't just completely different.
The homeworks were fine. (A little long, but that's to be expected in this sort of math class.)
I wish the tests were not repeats of the practice tests, as this means it is not at all valuable to try to actually understand the concepts and methods of analysis and instead is important to train ourselves on the practice exams and more or less memorize the answers given by the professor. As a result, people for whom rote memorization or test-training is incredibly hard (yes, this includes myself) do poorly. What are we testing, here? Speed? Memorization? I may be biased, but am I not right?
Sometimes I close my eyes and dream of a world where analysis is taught as a subject to love, understand, and admire--- perhaps in a project-based class (as apparently they have in UChicago). Where my effort in the course is driven by honest desire to learn and absorb the material instead of guilt and fear of the exams. Where I exit lectures with a fuller understanding of math instead of a vague sense dread (oh God, what will it be like next semester) and horror at my own incomprehension and inability to follow the class.
Due to no fault of the professor, I honestly believe that if it were not for my other math class this semester, I would drop out of the math major entirely because of Modern Analysis I.
The professor: Professor Dimitrov was quite a good instructor. He was very calm and friendly, which I really appreciate, and his lectures made sense (he was always well prepared and answered any questions that came up fully). He had us ask questions on Piazza as well, and was always really prompt in responding. I think Professor Dimitrov tried to make Rudin more palatable, and indeed, some proofs which I could not follow in Rudin (who is, to put it lightly, terse) made sense in lecture. But I wish he just ditched Rudin and taught us. If it weren't for Professor Dimitrov, though, I don't think I'd've made it through the course.