Carol S. Schumacher
Professor of Mathematics
Carol Schumacher is the author of Closer and Closer: Introducing Real Analysis (Jones and Bartlett, 2008).
Closer and Closer is a first introduction to Real Analysis. As the title suggests, the emphasis is on the limiting processes that underly analytical thinking. It is aimed at junior and senior mathematics majors who have had some introduction to proof. The book approaches the subject from the point of view of a general metric space, but does so in a user-friendly manner that keeps important concrete examples like the real line and n-dimensional Euclidean spaces at the forefront of the discussion. It can be used for a one- or two-semester sequence in real analysis.
Professor Schumacher maintains detailed webpages that show the pace of and assignments in the course she teaches out of this book. If you are interested, click on the link to get back to her homepage. Then navigate through current or past courses to find the webpages for "Real Analysis I" and "Real Analysis II."
For the most complete set of known errors for Closer and Closer, click here.
Prof. Schumacher has also authored a companion Instructor's Resource Guide. The first half of the Instructor's Resource Guide describes the pedagogical philosophy and class procedures that Carol Schumacher uses when she teaches a course out of the book . This portion of the guide may be of interest to anyone who is teaching a real analysis course, particularly if the instructor wishes to use a very active, inquiry-based approach to the course. The second half of the guide more specifically addresses the nuts and bolts issues associated with the book itself.
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