Honors | Honors Course in Analysis I
S413 | 3434 | W. Ziemer
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.