Let's say you spend your weekends (15 hours / week) focussed on going through this book list. Approximately how long would it take to get through (~50% of exercises) let's say one book in each topic in the "Intermediate" section?
Where are you starting from? Are you seeing the concepts for the very first time or dusting off concepts you've learnt about years ago and then forgotten?
Also it's not worth going through all the books since there is a lot of overlap. Pick one book from each topic that interests you and start with that. Then you can perhaps go back and fill in any gaps those books might have left.
Time-wise it's basically impossible to say anything useful. It depends on the book and on you. If you get the right book that teaches a topic you find fascinating in the 'right' way for your brain, you can probably get through it in a couple of weekends. With the wrong book teaching the wrong topic using the wrong approach for you, you can beat your head against it for months and still not get anywhere.
No Principia Mathematica, or anything on Cantor or Kronecker - though they might be touched on elsewhere in the list. They do include a intro to infinity, which I've not read.
I'm not actually sure that is a bad thing. So, just a curiosity.
We're talking undergraduate here. Undergraduate level math is really just about introducing the basic concepts of mathematics. There is no way your average undergraduate student would gain anything of note from trying to read Principia.
I was a math major and consumed it while an undergrad. I also would find that a good time to start work on infinity and save randomness for graduate levels.
Kids these days! ;-)
I do suppose it may be a bit different today, as I'd expect today's foundations to include more computer-centric course. That is not a complaint, just a sign of the times. We were, for the most part, expected to figure that out on our own.
Undergraduate courses will obviously cover the core ideas discovered by Russel, Whitehead, Cantor etc. The basic concepts from their works where certainly introduced to us during the first year of my undergrad math degree, and built upon during subsequent courses. I just think that expecting undergrads to read the actual works of Russel, Whitehead, Cantor etc. is not the best use of their times.
http://math.ucr.edu/home/baez/physics/Administrivia/booklist...