The curriculum will consist of some parts of the following two books:
J. N. McDonald and N. A. Weiss, A course in real analysis, 2nd edition, Academic Press. We will cover material from sections 1.2, 10.3, 10.5, 11.3, 12.4-12.6, 14.4-14.6.
G. K. Pedersen, Analysis Now, 1989. Springer. ISBN: 978-0-387-96788-2. Corrected 2nd printing. We will cover material from sections 3.2-3.4, 4.1-4.6 and 5.1. Link to Springer's homepage for this book.
Some additional notes will possibly be posted during the semester. A more precise curriculum (with regard to the final oral exam) will be posted within the end of May.
The final curriculum is available here.