Time and Location
MWF 4, Little 205
Office hours: M 5th, W 7th, F 3rd
Description and Goals
This 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.
Text: There is no required text for this course. A complete set of lecture notes will be posted on the webpage as the course progresses.
Some standard texts that treat the material covered in this course are:
Real Analysis: Modern Techniques and Their Applications by Gerald B. Folland
Real and Complex Analysis by Walter Rudin
Real Analysis by H. L. Royden
Real Analysis: Measure Theory, Integration, and Hilbert Spaces by Eli Stein and Rami Sharkachi
Some additional references for the first part of the course (on measure theory) are:
Measure Theory by Paul Halmos
An Introduction to Measure Theory by Terence Tao
Current lecture notes (updated 20 September 2019)
Homework 4 (due Monday 7 October) – Problem 13.16.
Homework 3 (due Friday 27 September) – Problems 7.29 and 13.7
Homework 2 (due Wednesday 16 September) – Problem 7.27
Homework 1 (due Friday 6 September) – Problems 7.11 and 7.12 (see lecture notes)
Grading will be trivial provided you participate and do the homework. There will be a midterm and possibly a final exam, depending on interest.
Attendance is recommended.
University policies and resources
Grades: Grading will be in accord with the UF policy stated at https://catalog.ufl.edu/ugrad/current/regulations/info/grades.aspx.
Honor Code: “UF students are bound by The Honor Pledge which states, “We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honor and integrity by abiding by the Honor Code. On all work submitted for credit by students at the University of Florida, the following pledge is either required or implied: “On my honor, I have neither given nor received unauthorized aid in doing this assignment.” The Honor Code specifies a number of behaviors that are in violation of this code and the possible sanctions. Furthermore, you are obligated to report any condition that facilitates academic misconduct to appropriate personnel. If you have any questions or concerns, please consult with the instructor or TAs in this class.”
Class Attendance: “Requirements for class attendance and make-up exams, assignments, and other work in this course are consistent with university policies that can be found at: https://catalog.ufl.edu/ugrad/current/regulations/info/attendance.aspx.”
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://counseling.ufl.edu/, 392-1575; and the University Police Department: 392-1111 or 9-1-1 for emergencies.