MATHEMATICS (TURKISH, PHD) | |||||
PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT4003 | Functional Analysis I | Fall | 3 | 0 | 3 | 6 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | En |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Assoc. Prof. MAKSAT ASHRAYYEV |
Course Objectives: | This course aims to provide deep understanding of introductory functional analysis. |
The students who have succeeded in this course; Will be able to understand the need for functional analysis and infinite dimensional vector spaces. Will be able to compare the notions of Metric, Banach and Hilbert spaces. Will be able to construct formal proofs. Will be able to compare function,functional and operator. Will be able to derive the dual space of a given Banach space. Will be able to explain representation of functionals on Hilbert spaces. |
This course aims to teach basic theory and applications of Functional Analysis |
Week | Subject | Related Preparation | |
1) | Introduction: Metric Space, Open set, Closed set, Neighborhood. | ||
2) | Sequences: Boundedness, Convergence, Cauchy Sequence, Seperability. | ||
3) | Completeness and Completion of Metric Spaces. | ||
4) | Examples. Completeness Proofs. | ||
5) | Vector spaces: Subspace, Dimension, Hamel Basis. | ||
6) | Normed Spaces, Banach Spaces: Normed Space, Banach Space, Further Properties of Normed Spaces. | ||
7) | Finite Dimensional Normed Spaces and Subspaces, Compactness and Finite Dimension. | ||
8) | Linear Operators: Some Properties. | ||
9) | Applications of Bounded and Linear Operators. | ||
10) | Functionals: Linear Functionals, Normed Spaces of Operators. | ||
11) | Dual Space: Algebric Dual and Continuous Dual. | ||
12) | Inner Product Spaces, Hilbert Spaces: Inner Product Space Hilbert Space, Further Properties of Inner Product Spaces, Parallelogram Law. | ||
13) | Orthogonal Complements and Direct Sums. | ||
14) | Total Orthonormal Sets and Sequences, representation of Functionals on Hilbert Spaces, Hilbert adjoint Operator. |
Course Notes: | Walter Rudin, Functional Analysis 2/E, International Series in Pure and Applied Mathematics (1991). |
References: | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley (1989). |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | 14 | % 0 |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | % 0 | |
Homework Assignments | 7 | % 20 |
Presentation | % 0 | |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 2 | % 50 |
Preliminary Jury | % 0 | |
Final | 1 | % 30 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 70 | |
PERCENTAGE OF FINAL WORK | % 30 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Laboratory | 0 | 0 | 0 |
Application | 0 | 0 | 0 |
Special Course Internship (Work Placement) | 0 | 0 | 0 |
Field Work | 0 | 0 | 0 |
Study Hours Out of Class | 14 | 5 | 70 |
Presentations / Seminar | 0 | 0 | 0 |
Project | 0 | 0 | 0 |
Homework Assignments | 7 | 6 | 42 |
Quizzes | 0 | 0 | 0 |
Preliminary Jury | 0 | ||
Midterms | 2 | 15 | 30 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 41 | 41 |
Total Workload | 225 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |