I'm a sophomore and I'm taking my introductory real analysis course this summer.
What I'm not sure about is the proper textbook to use in order to learn it properly, at MIT they jump to Rudin at once, they don't bother studying any lowered down books before it so I know that I do not have to study mathematical analysis from lowered down books before I jump to the real deal.
Courses I have taken so far:
- Calculus (although I'm bad at the multivariable calculus I still can revise anything I need whenever needed).
- Elementary Set Theory
- Abstract Algebra (Group Theory)
and I'm taking topology this semester as well. I know nothing of linear algebra though but I do not think its really necessary. So what do you think is the proper textbook to use?
Is it Rudin/Pugh/Apostol or Do I have to learn from books like Abbott/Kenneth Ross/Bartle first? I have already studied few sections from Bartle regarding Continuity and Differentiation and I find the exposure to the material quite weak, doesn't matter if I do all the problems I still do not taste the beauty of analysis from this *hit textbook because all I can find in it is just a bunch of definitions with no explanation on why are they there or what is the point of having them and the problems are just direct random applications so if I do them I still feel like I learned absolutely purely nothing new just calculus written in a different way really.