Fall 2010. MATH5340.

Functional Analysis

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.