**Fall 2010. MATH5340. **

**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: M W F 2:50pm - 3:50 pm

**Classroom and Time:** MA 011, M W F 2:00pm-2:50pm.

**Course website:**
*http://www.math.ttu.edu/~lhoang/2010Fall-M5340/*

Updates
about the course and other related announcements will be posted on
this webpage.

**Prerequisite:** Intermediate analysis MATH 5318, 5319 and Real Analysis MATH 5322.

**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:** Theories of Hilbert spaces and operators on Hilbert spaces, Banach spaces and operators on Banach spaces, fundamentals of topological vector spaces.

**Course Outline:**

- Chapter I - Hilbert spaces
- Chapter II - Operators on Hilbert space
- Chapter III - Banach spaces
- Chapter IV - Locally convex spaces
- Chapter V - Weak topologies
- Chapter VI - Linear operators on a Banach space

**Expected Learning Outcomes:** Fundamentals of functional analysis:

- Hilbert spaces, Riesz representation theorem
- Operators on Hilbert spaces, compact operators, spectral theorem
- Basic properties of normed spaces and Banach spaces, Hahn-Banach theorem, open mapping and closed graph theorems, principle of uniform boundedness.
- Weak topologies, duality, Alaoglu's theorem, Krein-Milman theorem
- Compact operators on a Banach space and invariant subspaces

**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, October 8

Midterm 2: Friday, November 19

FINAL EXAM: 1:30 p.m. – 4:00 p.m., Monday, December 13

**Critical Dates:**

- August 26, Thursday: Classes begin.
- September 6, Monday: Labor Day. University holiday.
- September 13, Monday: Last day to drop a course and receive a refund.
- October 11 – 12, Monday – Tuesday: Student holiday.
- November 1, Monday: Last day for student-initiated drop on MyTech with penalty.
- November 24 – 28, Wednesday – Sunday: Thanksgiving holiday.
- December 2 – 8, Thursday – Wednesday: No examinations.
- December 8, Wednesday: 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.