Carol Schumacher is the author of Closer and Closer: Introducing Real Analysis (Jones and Bartlett, 2008) and Chapter Zero:Fundamental Notions of Abstract Mathematics, 2e. (Addison-Wesley, 2001).

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. 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, student-driven approach to the course. The second half of the guide more specifically addresses the nuts and bolts issues associated with the book itself.

Chapter Zero is a textbook whose goal is to introduce mathematics majors to mathematical language, logic, and proof.  It is used as a textbook in the course Foundations (Math 222) that is required for all math majors at Kenyon College.  Foundations is aimed at students who have completed three semesters of college level calculus (though this is a mathematical maturity pre-requisite;  the course does not assume any knowledge of calculus.) Click here for the most up to date set of known errors in the book Chapter Zero.

Prof. Schumacher has also authored a companion Instructor's Resource Guide. In addition to nuts and bolts information about the book, the guide describes the pedagogical philosophy and procedures that she uses when she teaches Foundations.  This portion of the book may be of interest to those seeking information about the Modified Moore Method-style of teaching.  Modified Moore Methods are sometimes called "Discovery Learning." 

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