**Spring 2011. MATH5341. Section 001. **

**Instructor:**
Luan Thach Hoang

Office: MA 234. Phone: (806) 742-2580 Ext 232.
Fax: (806) 742-1112

Email address: *luan.hoang@ttu.edu*

Homepage:
*http://www.math.ttu.edu/~lhoang/*

Office hours: MWF 3:00 pm - 4:00 pm

**Classroom and Time:** MA 011, MWF 2:00 pm - 2:50 pm.

**Course website:**
*http://www.math.ttu.edu/~lhoang/2011Spr-M5341/*

**Text:** *A course in Functional Analysis*, 2nd edition by John B. Conway, published by Springer.

Supplementary texts: *Functional Analysis*, by W. Rudin, published by McGraw-Hill; *Functional Analysis*, by K. Yosida, published by Springer.

**Course Description:** Linear operators on a Banach space and spectral theory, normal operators on Hilbert space, unbounded operators, Fredholm theory, and applications.

**Course Outline:** Selected topics among the following:

- Chapter V: Weak topologies
- Chapter VI: Linear Operators on a Banach Space
- Chapter VII: Banach Algebras and Spectral Theory for Operators on a Banach Space
- Chapter IX: Normal Operators on Hilbert Space
- Chapter X: Unbounded Operators
- Chapter XI: Fredholm Theory
- Additional Topics: Distribution Theory, Fourier Analysis, Theory of Semi-groups.

**Expected Learning Outcomes:** Bounded operators on Banach and Hilbert spaces and their spectral theories, Fredhom theory, unbounded operators, and applications.

**Methods of Assessment of Learning Outcomes:** Assessment of the learning outcomes will be achieved through homework assignments, two midterm exams, and a final exam.

**Grading policy:** Homework will be assigned weekly and will count for 30% of the grade. There will be two midterm exams in class, each will count for 20% of the grade. The final exam will count for 30% of the grade.
All in-class exams are closed-book. No make-up exams are given unless
legitimate documents for excuses are presented to the instructor at
least a week in advance. Grading Scale: A: 90%-100%, B: 80%-89%,
C: 70%-79%, D: 60%-69%, F: below 60%.

**Attendance Policy:** Students are expected to attend every class and are responsible for all information given in class.

**Examination Schedule:**

Midterm 1: Friday, February 18.

Midterm 2: Friday, April 8.

FINAL EXAM: Monday, May 9, 4:30 p.m. - 7:00 p.m., Room MA 011.

**Critical Dates:**

- Jan. 12: Classes begin.
- Jan. 17: Martin Luther King Jr. Day. Holiday.
- Jan. 28: Last day to drop a course and receive a refund.
- Mar. 12 - 20: Spring Break.
- Apr. 25: No classes.
- Apr. 27 - May 3: No exams.
- May 3: Last day of classes.

**Academic Misconduct:** Academic dishonesty is intolerable and will be
punished to the full extent allowed by the University policy.

**Civility in the Classroom:** Students are expected to assist
in maintaining a classroom environment that is conducive to learning.

**Students with Disabilities:** Any student who because of a
disability may require special arrangements in order to meet course
requirements should contact the instructor as soon as possible. *"I would appreciate hearing from anyone who has a disability that may require special accommodations. I am sure we can work out whatever arrangements are necessary. Please see me during my office hours."*

*NOTE:* When needed, the instructor will communicate with the
students using their TTU email addresses. At the beginning of the
semester, the instructor will send out a message to confirm the students' email addresses.