I have a 2-3 week recess from university for winter break. In this time, I would like to learn analysis, starting with Walter Rudin's Principles of Mathematical Analysis, and then, if at all possible, continuing with Walter Rudin's Real and Complex Analysis. If necessary, I would be willing to complete the second book after returning to college (that is, outside of the 2-3 week time frame).
A few questions come to mind:
How reasonable are these goals?
My background in maths is an elementary Moore method single-variable calculus course, and the beginning of (undergraduate) introductory real analysis. However, most of my time during the break will be available for mathematics. Is only the goal of completing the first book reasonable, with the second book requiring additional time?
Is Principles of Mathematical Analysis sufficient for reading Real and Complex Analysis?
If not, what else should I know?
What advice can you give me?
I'm reading these primarily for entertainment, and I hope with this to learn enough mathematics to do interesting things. (I am a maths student in college, but have just started undergraduate analysis. My courses do not use either Rudin book.) This does not need to be advice on the books themselves, perhaps it could be advice on how to learn math quickly (and properly) if one has sufficient time to think about it exclusively.