Honors | Honors Course in Analysis I
S413 | 3227 | Bennett


This course covers elementary metric space topology and its application to
the study of functions of a single variable, especially continuity,
differentiability, and Reimann integrability. The emphasis will be on the
construction of a completely systematic and rigorous theory, rather than
on exploring the more computational aspects, as occur in elementary
calculus courses.
One of the most important goals of this course is to get students to
discover and write clear, correct proofs. This is the essence of creative
mathematics! Students will get a great deal of practice formulating and
writing their solutions to theoretical problems, and this writing will be
evaluated and graded carefully. These problems will count for a
substantial portion of the course grade. There will be three
non-cumulative exams; the purpose of these is to insure that students
review and synthesize the material, rather than to test their ability to
think creatively under pressure. For this reason, evening exams will be
given, and ample time will be allowed.
The most important prerequisites for S413 are a demonstrated success in
third-year mathematics courses, especially S312 and S303, and a talent for
thinking creatively and rigorously in abstract contexts.