What are the best resources for teaching myself the basics of real and complex analysis?I know they rehash a lot from math classes I took some time ago, so I figure I will need a fair bit of handholding and prep./g/ suggested Abbott and Needham respectively for more introductory works and Rudin and Alhfors generally.
you sure do seem to like talking about yourself on social media
>>16260313This is a genuine question. Is this image from a blogger?
>>16260218Papa Rudin of course.
>>16260218Abbott is a great book for an introduction to real analysis. If you are already comfortable with real analysis, Rudin might be better for you. For complex analysis, Alhfors is my favourite, Stein and Shakarchi is good as well. Papa Rudin is an amazing book, but in my opinion, you should use it as a reference rather than as a textbook.
>>16260218I’m in a similar situation, went through a calculus sequence (single variable) and I’m not happy with how things were presented. To begin with, the course began with limits without a shred of motivation. Then we were told to pretend dx, dy could be treated as fractions even though they are not. Later we were given a bunch of convergence tests and asked to determine if some sum converges or not. It was absolutely soulless. Calculus looked like something out of Mary Shelley’s Frankenstein. I think you’d do well if you approached analysis chronologically. Work on physical problems with infinitesimals as seemed to be the case in the 1700s. Study differential equations and how to solve them, especially the heat equation. Eventually your math will present subtleties/absurdities and you’ll see first hand the need for rigor. At least it won’t feel as misplaced.
>>16261092(cont.)If I’m going to take a course on real analysis, I’ll make sure I have a good grasp of complex variables first. Flanigan covers this subject with applications to heat. Get a decent book on DE’s like Braun’s. Then the one by Flanigan. At the same time follow the history which led one discovery to the other (Stillwell).
Read "Mathematical Analysis I" by Vladimir A. Zorich. Zorich has two volumes and has 4.9 stars on amazon.
