When I took the course on Real Analysis, it made me very nervous. I was having fever dreams from the past when I took undergraduate real analysis and the epsilon-delta definitions just did not make a lot of sense. In retrospect, taking MA504 has been one of the best academic decisions, especially as an engineer.
It has helped me a lot in how to concretely formulate definitions, and what ‘approaching’, ’tending’, ’limiting’, and other weasel words mean in a mathematical sense.
I tried to make notes of the course throughout, and am making entirety of them available here. How, I feel, these differ from the textbook (Baby Rudin) and the course notes, is in the sense that they are more concise, I skip over the proofs, and (I think) they are more approachable to an undergraduate level audience. Please feel free to collaborate as this is an ongoing repository and I will add/subtract from it whenever I get time.
These notes at places are shameful regurgitations of Prof. Petrosyan’s amazing course notes and Baby Rudin.