MAA 6617: Analysis II

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 Course Notes(Fall = last semester)

 

 Course Notes(Spring = this semester)

(Note these my be updated semi-frequently.)

Syllabus

Instructor

James Eldred Pascoe

Time and Location

M W F Period 4, LIT 205

Office Hours Period 5 MWF

Description

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

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

Grades

Course grades will be based on participation and homework (95%) and an in class exam (5%).

See the current UF policy on assigning grade points.

Exams

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.

Text

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

An Introduction to Measure Theory 

    by Terence Tao

 

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

Accommodation for students with disabilities. 

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. http://www.counseling.ufl.edu/cwc/Default.aspx

; 392-1575; and the University Police Department: 392-1111 or 9-1-1 for emergencies.

 

Addenda. We reserve the right to make justifiable and necessary addenda or corrections to the syllabus.

Other course info

To be announced.

 

Tentative Schedule

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