The official site for the course is the Avenue shell (access it here once it's published). I'll try to keep general material here as well for accessibility purposes in case anybody can't access Avenue at some point, but be sure to check Avenue often for announcements.
See Avenue for an up to date version of the syllabus.
“Introduction to Real Analysis”, 4th edition, by Bartle and Sherbert, John Wiley & Sons (publishers), ISBN 978-0471433316.
Main text for the course. I'll follow the table of contents, though I'll borrow some sections from other places (in particular, the Riemann integral section will not be following this approach).
“Calculus”, 4th edition, by Michael Spivak, Publish or Perish (editors), ISBN 978-0914098911.
Very accessible intro to Calculus with proofs. I prefer this book's approach to integration.
“An Introduction to Analysis”, 4th edition, by William R. Wade, Prentice Hall (editors), ISBN 978-0132296380.
A more comprehensive intro, covering multivariable analysis as well as some abstract concepts.
"Principles of Mathematical Analysis," 3rd edition, Walter Rudin, McGraw Hill (editors), ISBN 9780070542358.
A very thorough, though abstract, introduction to the fundamentals of analysis. Unfortunately, a bit too advanced for the scope of this course. If you're interested in the topics of MATH 3A03 you should definitely give this book a look.
I'll upload some practice problems here, as well as on Avenue, once I'm done compiling a decent list. Exercises will be taken from the main book.