Syllabus

See online syllabus at MATH 6321

Gerald B. Folland, "Real Analysis", Wiley Inter-Science, 2nd Edition.

**First week**

- Material covered
- I.1 to I.6: The complex Number
- II.1 to II.6: Metric Spaces and the Topology of C

- Exercises
- I.6: 4
- II.2: 4
- II.4: 5
- II.5: 4, 9
- II.6: 1

**Second week**

- Material covered
- III.1: Power series
- III.2: Analytic function (first part)

- Exercises
- III.1: 6, 7
- III.2: 2, 6, 15

**Fourth week**

- Material covered
- III.2: Analytic function (second part)
- III.3: Analityc Function as mapping. Möbius transformations.

- Exercises
- III.2: 19
- III.3: 9, 18

Fifth week

- Material covered
- IV.1: Riemann-Stiltjes integral.
- IV.2: Power Series reppresentation of analytic functions.

- Exercises
- IV.1: 13, 21,23
- IV.2: 4, 8, 10, 11

Second HW due on February 11. First midterm on Wednesady February 18.

Solution set for first midterm.

- Material covered
- IV.3: Zeros of analytic functions.
- IV.4: The index of a closed curve.
- IV.5: Cauchy's Theorem and Integral Formula

- Exercises
- IV.3: 8
- IV.4: 3
- IV.5: 1, 7, 10

- Material covered
- IV.6: The homotopic version of Cauchy's Theorem and simple connectivity.
- IV.7: Counting zeros; the Open Mapping Theorem.

- Exercises
- IV.6: 1, 4, 6, 10
- IV.7: 3, 4

Third HW due on March 23. Here is a pdf file with the exercise from my copy of the textbook.

Second Midterm will be on Wednesday April 1. Solution set for first midterm.