AMCS/MATH 608:  Analysis I

Fall 2014
Instructor: Charles L. Epstein

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The Course

This year the Analysis I-II sequence is being redesigned to cover Complex Analysis, Real Analysis (Measure Theory), and Functional Analysis.  The first semester of analysis provides an introduction, at the graduate level, to functions of one complex variable and the first half of real analysis.

For the first ten weeks, we cover the basic Cauchy theory, we will focus on more analytic features of the subject, highlighting its connection to PDE and Fourier analysis. As references for complex analysis we use E. Stein and R. Shakarchi, Complex Analysis; Lars Ahlfors, Complex Analysis; Zeev Nehari, Conformal Mapping. More advanced material on the d-bar equation can be found in T. Napier and M. Ramachandran, An Introduction to Riemann Surfaces

For weeks 11-14 we begin our discussion of Real Analysis, which will be followed by 4 more weeks  in the second semester. In the first semester we will cover Measure Theory and Lebesgue Integration in Euclidean space. References for Real Analysis are Real Analysis by E. Stein and R. Shakarchi, Real Analysis by Gerald Folland, and Real Analysis by H. Royden.

A problem set will be assigned every week on Tuesday, due the following week on Tuesday. I very much prefer that students do the problem sets alone. We may have midterm and final exams.



Problem sets
  1. Problem set 0, These problems in advanced caclulus do not have to be handed in, but should be done this week, so you are ready for our discussion of contour integration.
  2. Problem set 1, due September 16, 2014.
  3. Problem set 2, due September 23, 2014.
  4. Problem set 3, due September 30, 2014.
  5. Problem set 4, due October 7, 2014.
  6. Problem set 5, due October 21, 2014.
  7. Problem set 6, due October 28, 2014.
  8. Problem set 7, due November 11, 2014.
  9. Problem set 8, due November 18, 2014.
  10. Problem set 9, due November 25, 2014.
  11. Problem set 10, due December 9, 2014.
  12. Problem set 11, due December 16, 2014.

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