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.