Marcelo Mendes Disconzi
Department of Mathematics, Vanderbilt University

email: marcelo.disconzi at vanderbilt.edu
office: Stevenson Center 1515
phone: (615) 322 7147   fax: (615) 343 0215
mail to: 1326 Stevenson Center, Vanderbilt University, Nashville TN 37240

Vanderbilt












Marcelo Mendes Disconzi
MATH 6101 - Graduate Analysis II

General Information:
For a description of the course, including the grading policy, consult the course syllabus. Students are responsible for reading the syllabus and being aware of all the course and university policies.

Textbook: There will be no required textbook. See the course syllabus for a list of suggested references.

Classes meets on TR, 11:00am–12:15pm, at Stevenson Center 1313.

This course is a continuation of MATH 6100.

Contact Information and Office Hours:
Instructor's office: SC 1515.
Instructor's email: marcelo.disconzi@vanderbilt.edu.
Instructor's office hours: Thursdays, 1-4pm, or by appointment.
Instructor's office phone: 322-7147.

General Math Office: SC 1326, phone: 322-6672.

Exams.

Description Date
Location and Time
Remarks
Test 1 March 3 In class
Final Exam
TBA

Schedule:
Below is a schedule for the course (for the academic calendar, click here). This will be updated regularly and, therefore, students should check this webpage frequently. The due date for each assignment will be posted as the course progresses.

Date Material covered HW problems and assignments Remarks
Jan 12
Mesurability


Jan 14 Local properties of measurable functions

Jan 19 Egoroff's theorem

Jan 21 Measurability and integrability HW1 Solutions
HW1 due on Feb 2n.
Jan 26 Essentially bounded functions

Jan 28 Locally integrable functions

Feb 2 Product of a measure and a locally integrable function HW2: open-ended HW, as discussed in class. Solutions. HW2 due on Feb 18
Feb 4 No class

Feb 9 Radon-Nikodym

Feb 11 Densities and absolute continuity

Feb 16 Duality

Feb 19 Decomposition of measures HW3 Solutions
HW3 due on March 3
Feb 23 Fubini

Feb 25 Other types of convergence

March 1 Non-mesurability

March 3 Test
Solutions
March 15 Differentiability HW4 Solutions
HW4 due on April 12
March 17 Change of variables

March 24 Duals and Hahn-Banach

March 29 Baire category and its consequences

March 31 Weak topologies

April 5 Hilbert spaces

April 7 Hilbert spaces
Abstract measures


April 12 Hausdorff measures

April 12 Integration of abstract measures
Make-up class
April 14 More on integration
Examples and counter-examples involving Hausdorff measures


April 14 Rademacher's theorem
Area and co-area formulas

Make-up class
April 19 Convolution

April 21 Smoothing
List of practice questions

Anonymous feedback:
Students are encouraged to bring suggestions and to discuss with the course instructor any concerns they may have, including something they think is not being properly handled in the course. But if you do not feel comfortable doing that, here you have the opportunity to send some anonymous feedback.