Michael Kleber suggested Mattuck's book. Mattuck is a good teacher, but I suspect that he wrote the book for MIT students, so I'm not sure how suitable it'd be for UMass Lowell students. UML does have some fine students, but the average UML math major is not as well- prepared as the average MIT math major. I should also say that I'm NOT looking for a book that constructs the reals (via Dedekind cuts or Cantor sequences or Conway games). My view is that a student's first exposure to real analysis should be based on an axiomatic DESCRIPTION of the reals, not a formal CONSTRUCTION of them. My point of view might be expressed succinctly, with only a small amount of distortion, in the slogan "Why construct the reals when they already exist?" Don't get me wrong; one of the formative experiences of my young mathematical career was getting a copy of Kirshner and Wilcox's "The Anatomy of Mathematics" as a gift when I was thirteen and devouring it from cover to cover. I loved the thrilling progression from Peano Postulates to the construction of the real numbers, with each successive number system incorporating the one before. But most of my students won't become mathematicians, let alone logicians or model theorists (constructions are good for establishing relative consistency but it's a rare student who would worry about this). I want my students to become principled and savvy practitioners of real analysis who know what the main tools are and who know when caution is required in wielding them. So I'm looking for a book by someone who shares that spirit. On the other hand, I love a good (friendly) argument, so if any of you think I'm going in the wrong direction, please offer your counter-arguments! Jim