So here are the lecture notes. If you notice any mistakes or have any suggestions, feel free to e-mail me at firstname.lastname@example.org. Thanks! And I'm probably typing up more lecture notes as you're reading this, so look out for them.
06/21/2011: Finally finished with the lecture notes! I added Lectures 25 and 26, so these lecture notes are now complete, if not completely correct. I still have not gone through the corrections I've received, but I will go through them and improve these notes. Thank you for bearing with me!
06/10/2011: Sorry for the delay, but I'm still alive! Added Lecture 24, and fixed some more errors.
06/04/2011: Added Lecture 23, added a small section from Lecture 24 to Lecture 20, and fixed a variety of errors and such.
06/03/2011: I'm starting these up again. This isn't really a significant update, and I'll have more coming later, but I have fixed the problem with the proof of the differentiability of power series (with help from Professor Jones).
05/12/2011: Alright, I never finished these... But the Stone-Weierstrass Theorem is outlined in Scott Morrison's notes on Professor Jones's website, and the rest of the stuff (integration) is in the book, mostly... But I'm sorry if you were looking forward to it. As I keep studying, I wish everyone the best of luck!
05/08/2011: Added Lecture 22.
05/07/2011: Added Lecture 21.
05/06/2011: Added Lecture 20 (though the proof of the Differentiability of Power Series is not fully complete; if anyone could help me out, that would be great), and fixed a small error in the definition of the Radius of Convergence.
05/04/2011: Added Lecture 19.
05/03/2011: Uploaded Version 1, complete up to Lecture 18 (that is, until Spring Break).