Meets MWF 8:45-9:50

Choate House Seminar Room

Choate House Seminar Room

While the content of Math 103 will depend on the interests and backgrounds of those enrolling, I hope to give a course which will help students prepare for the analysis certification examination. At present, I'm planning to start with abstract measure theory loosely following chapters 1, 2, 6, and 8 of the text. We will finish with a review of the theory of functions of a single complex variable loosely following chapters 10, 11, 12, and 14 in the text.

Familiarity with the Lesbegue integral on the real line would be very
helpful as would an elementary course in complex variables. However,
neither is required for Math 103 (although each is an essential part
of the certification syllabus). Ideally, prospective students should
have had undergraduate courses in both abstract analysis (e.g.,
Math 63), and in complex analysis (e.g., Math 43). In particular,
students will find Chapters 1-4 of Royden's *Real Analysis* and
Churchill and Brown's *Complex variables and applications* (or
any comparable book) to be excellent supplementary texts.

The pace will be
fast as we can manage, and the students will be expected to fill in
considerable detail on their own. The goal is to help prepare
graduate students to take (and *to pass*) the certification exam
at or near the end of the winter term.

Dana P. Williams

201 Choate House

6-2990

`http://math.dartmouth.edu/ m103f99`

201 Choate House

6-2990