I may add a further text (unlikely) - the total net cost will, however, be much much less than the cost of Rudin.
The syllabus will be reorganized and I will post the revised syllabus sometime in the next month or so. Roughly speaking, the emphasis in 4331 will be on 1-variable theory and results from "classical analysis" (EG: Euler Maclaurin formula, uniform convergence, Fourier series and the Gamma-function). Semester 2 will develop metric spaces and include applications of the contraction mapping lemma. There will be some calculus on RN (self contained, MATH 3334 not essential; though it will not hurt having done it).
One big difference from the existing syllabus will be the order of material. The focus of the course will be to end your undergraduate mathematics career with a bang rather than a whimper. In particular, I will avoid ending the course with unmotivated and dull technical material that amounts to little more than preparation for graduate courses. We will see the applications - they will not be deferred to later.
Metric spaces will now be in the second semester. Lebesgue theory will not be discussed.
PREREQUISITES: The information on the department website is a little out-of-date. MATH 3334 is NOT a prequisite for the MATH 4331/2 sequence. It is not even particularly useful for MATH 4331, though it might well be of some use for MATH 4332. MATH 3333 is strongly advised. If you have not done MATH 3333, but have done courses beyond Calculus I-III (for example, MATH 3363) then you may be able to take the MATH 4331/2 sequence. However, going into the MATH 4331/2 sequence immediately after doing the calculus sequence is not advised. If you are in doubt, email me at mikefield@gmail.com and let me know what maths courses you have already taken and with what grades. Even if you have taken MATH 3333, I advise reading the introductory chapter(s) of Kaplansky over the summer - they are not long and not hard and they give some of the flavor of what we will be doing in both the first and second semesters.
Syllabus (PDF file - from department web page. This gives an idea of some of the content but note that the order will be completely different in 2008-2008 and the text book will NOT be Rudin.)