Math 5350/6350 - Applied Functional Analysis - Fall 2017
Dr. Radu C. Cascaval

Welcome!

On this main page you will find all the latest annoucements throughout the semester, so please bookmark it and check it often during the semester. You may also access this page via Blackboard (where you can also find grades, solutions to HMW exercises, handouts, etc)

Final Exam (PDF) - Take Home, due Wed, Dec 13 at 5pm.

HMW #8

Sect 4.2: #3, 4, 5, 10
Sect 4.3: #4, 11, 15
Sect 4.5: # 3, 8, 10

HMW #7:

Sect 3.5 # 6,7
Sect 3.6 # 4, 7, 10
Sect 3.8 # 5, 8,12

HMW 6:

Section 3.2: # 5, 7, 9
Section 3.3: # 6, 8, 10
Section 3.4: # 5, 7, 9

Sample Midterm PDF

HMW #5: Due Mon, Oct 9

Sect 2.10 #4, 10, 12
Sect 2.8 #3, 6, 12
Sect 2.7 #6, 7, 9, 12

HMW #4 : Due Mon, Sep 25

Sect 2.6 #5, 10, 14
Sect 2.5 #2, 8, 9, 10
Sect 2.4 #5, 8

Relevant Optional Reading

Kalton & Albiac "Topics in Banach Space Theory", 2nd ed, Springer 2016
https://link.springer.com/book/10.1007/978-3-319-31557-7 (free access for UCCS students)

HMW #3 : Due Wed, Sep 13:

Sect 2.3 #6, 10, 14
Sect 2.2 #10, 11, 14, 15

HMW #2: Due, Wed, Sep 6

Sect 1.6 #12, 14
Sect 1.5 #3, 8, 10
Sect 1.4 #2, 3, 4, 6

HMW #1 : Due Wed, Aug 30:

Sect 1.3 #6, 8, 10
Sect 1.2 #6, 8, 11
Sect 1.1 #8, 10, 12

Course Info:

Time: Mon & Wed 1:40 - 2:55 pm (Aug 21 - Dec 13) 
Place: OSB B136
Office Hours: Mon & Wed 11:00-12:00pm or by appointment
Website: http://academics.uccs.edu/rcascava/Math5350

Course Description:

Basic concepts, methods, and applications of functional analysis. Complete metric spaces, contraction mapping, and applications. Banach spaces and linear operators. Inner product and Hilbert spaces, orthonormal bases and expansions, approximation, and applications. Spectral theory of compact operators, including self adjoint and normal operators. Prer., MATH 4/5320 - Modern Analysis II

Textbook (required):

Introductory Functional Analysis with Applications, by Erwin Kreyszig: Wiley Classics Library 1989

Supplementary readings (optional):

- Elements of the Theory of Functions and Functional Analysis, by A.N. Kolmogorov & S.V. Fomin, Dover Publications 1999
- Functional Analysis, Sobolev Spaces and Partial Differential Equations, by Haim Brezis, Springer Verlag 2011

Grading:

The grade will consist of weekly HMW (30%), a midterm exam (30%) and the final exam (40%). For Math 6350, students will be expected to compete a report on an advanced topic related to the material covered in class, which will count as 10%, part of the final exam grade.

Other policies:

To make the most of your class, you are required to attend every class session. Students should notify (in advance) the instructor if they need to miss more than one session. Supporting documentation may be required. Drop dates: Please seek counseling from the Dean's office before dropping any course and note the following important dates: Sept 7,2017 – last day to drop and receive a full tuition refund; Oct 27,2017 – last day to drop without special permission from the Dean.

Academic Dishonesty:

Academic honesty is fundamental to the activities and principles of a university. All members of the academic community must be confident that each person's work has been responsibly and honorably acquired, developed, and presented. Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful. The academic community regards academic dishonesty as an extremely serious matter, with serious consequences that range from probation to expulsion. When in doubt about plagiarism, paraphrasing, quoting, or collaboration, consult the course instructor.

Disability Services:

Students with disabilities should contact the Office of Disability Services (Main Hall 105, 255-3354) and also notify the instructor of any special needs. They should provide a letter of certification from the Office of Disability Services within the first 2 weeks of classes.