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James Eldred Pascoe
Time and Location
M W F Period 4, LIT 205
Office Hours Period 5 MWF
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 transform, the theory of distributions, the spectral theorem, and an introduction to probability.
Homework problems, selected to complement each students interests and course of study, will be assigned, collected, and graded.
- Course grades will be based on participation and homework (95%) and an in class exam (5%).
There will be an in class exam on 1 April. You should take the exam if you intend to take the qualifying exam.
Attendance and Late Policy
Attendance and punctuality are highly encouraged. Furthermore they are necessary for participation, and to find out what the homework is.
The official text will consist of notes that have been developed over several years several colleagues, including Mike Jury and Scott McCullough. Minor updates to the notes may occur throughout the semester, so printing is discouraged.
Additional, but not required references include:
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
- by Terence Tao
Accommodation for students with disabilities.
Contact information for the Counseling and Wellness Center. http://www.counseling.ufl.edu/cwc/Default.aspx
Addenda. We reserve the right to make justifiable and necessary addenda or corrections to the syllabus.
Other course info
To be announced.
Week 1: Banach Spaces
Week 2: Banach spaces
Week 3: Dual spaces and Hahn Banach Theorem
Week 4: Dual spaces and Hahn-Banach Theorem
Week 5: Hilbert Spaces
Week 6: Hilbert Spaces
Week 7: Lp Spaces
Week 8: Lp Spaces
Week 9: Spring Break
Week 10: Fourier Transforms
Week 11: Fourier Transforms
Week 12: Banach Algebras
Week 13: Banach Algebras (There is an exam April 1)
Week 14: C*-algebras
Week 15: C*-algebras
Week 16: Special topics and review