Course Content and Objectives

This year long course treats the fundamentals of measure and integration theory, including Lp spaces and the Radon-Nikodym theorem; and an introduction to functional analysis, including Banach spaces, Hilbert spaces, and the theory of linear operators. Other topics that may be included (depending on time and interest) are harmoinc analysis and the Fourier transfom, the theory of distributions, the spectral theorem, and an introduction to probability.

References
Real and Complex Analysis, by Walter Rudin.
Real Analysis: Modern Techniques and Their Applications, by Gerald B. Folland
Real Analysis, by H. L. Royden.
Measure Theory, by Paul Halmos.
An Introduction to Measure Theory, by Terence Tao.

Suggested Problems
Selected problems from the text will be assigned on a daily basis.

Homework
Homework problems, selected to complement each students interests and course of study, will be assigned, collected, and graded.

Exams
For those planning to take the PhD qualifying exam in analysis, there will be a self administered midterm and final exam with times to be arranged.

Grading

Course grades will be based on participation, homework and/or exams. See the current UF policy on assigning grade points.

Attendance
Attendance is recommended.

Additional Information:

Grades.
Grading will be in accord with the UF policy stated at
https://catalog.ufl.edu/ugrad/current/regulations/info/grades.aspx

Academic Honesty.
The course will be conducted in accordance with the University honor code and academic honesty policy, which can be found in the student guide

Accommodations for Students with Disabilities.
“Students with disabilities requesting accommodations should first register with the Disability Resource Center (352-392-8565, https://www.dso.ufl.edu/drc/) by providing appropriate documentation. Once registered, students will receive an accommodation letter which must be presented to the instructor when requesting accommodation. Students with disabilities should follow this procedure as early as possible in the semester.”

Online Evaluations.
“Students are expected to provide feedback on the quality of instruction in this course by completing online evaluations at https://evaluations.ufl.edu Evaluations are typically open during the last two or three weeks of the semester, but students will be given specific times when they are open. Summary results of these assessments are available to students at https://evaluations.ufl.edu/results/.”

Contact information for the Counseling and Wellness Center.
https://www.counseling.ufl.edu/; 392-1575; and the University Police Department: 392-1111 or 9-1-1 for emergencies.

Tentative weekly schedule

Week 1: Section 20.