Syllabus ( MATH 541 )
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Basic information
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Course title: |
Functional Analysis |
Course code: |
MATH 541 |
Lecturer: |
Prof. Dr. Mansur İSGENDEROĞLU (İSMAİLOV)
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ECTS credits: |
7.5 |
GTU credits: |
4 (3+0+0) |
Year, Semester: |
1/2, Fall and Spring |
Level of course: |
Second Cycle (Master's) |
Type of course: |
Area Elective
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Language of instruction: |
Turkish
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Mode of delivery: |
Face to face
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Pre- and co-requisites: |
MATH 350 |
Professional practice: |
No |
Purpose of the course: |
To teach the fundamental concepts and theorems of Functional Analysis |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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Adapt the fundamental concepts of Functional Analysis.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
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Acquire scientific knowledge and work independently
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Defend research outcomes at seminars and conferences.
Method of assessment
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Written exam
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Oral exam
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Homework assignment
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Recognize the main theorems of Functional Analysis
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Acquire scientific knowledge and work independently
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Defend research outcomes at seminars and conferences.
Method of assessment
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Written exam
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Gain the capability of fields of application of Functional Analysis
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
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Design and conduct research projects independently
Method of assessment
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Written exam
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Oral exam
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Homework assignment
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Contents
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Week 1: |
Introduction to Metric Spaces |
Week 2: |
Connectedness and Comleteness |
Week 3: |
Compactness and Connectedness in Metric Spaces
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Week 4: |
Normed Vector Spaces and Banach Spaces |
Week 5: |
Linear Functionals, Hahn-Banach Theorem |
Week 6: |
Inner Product spaces and Hilbert Spaces |
Week 7: |
Ortogonal Expansions and Riesz Representation Theorem |
Week 8: |
Bounded Linear Transformations, Invertible Operators and Banach Theorem for Bounded Inverse |
Week 9: |
Midterm exam. Linear Transformations on Hilbert Spaces |
Week 10: |
Compact Operators and Examples in Integral Operators |
Week 11: |
Self-adjoint, Unitar and Normal Operators |
Week 12: |
The main theorems in Normed and Banach spaces, Baire category and Banach-Steinhaus Theorems |
Week 13: |
The Open Mapping and Glosed Graph Theorems |
Week 14: |
Spectrum of a Linear Operators and Hilbert - Schmidt Theorem |
Week 15*: |
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Week 16*: |
Final Exam |
Textbooks and materials: |
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Recommended readings: |
Introductory functional analysis with applications (Erwin Kreyszig) Elements of the theory of functions and functional analysis ( A. N. Kolmogorov and S. V. Fomin) Functional analysis (Walter Rudin) Elements of Functional Analysis ( L. A. Lusternik and V. J. Sobolev) |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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Method of assessment |
Week number |
Weight (%) |
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Mid-terms: |
9 |
40 |
Other in-term studies: |
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0 |
Project: |
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0 |
Homework: |
2, 4, 6, 8, 10, 12 |
10 |
Quiz: |
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0 |
Final exam: |
16 |
50 |
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Total weight: |
(%) |
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Workload
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Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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Courses (Face-to-face teaching): |
3 |
14 |
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Own studies outside class: |
4 |
14 |
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Practice, Recitation: |
0 |
0 |
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Homework: |
7 |
6 |
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Term project: |
0 |
0 |
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Term project presentation: |
0 |
0 |
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Quiz: |
0 |
0 |
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Own study for mid-term exam: |
20 |
1 |
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Mid-term: |
3 |
1 |
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Personal studies for final exam: |
20 |
1 |
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Final exam: |
3 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)
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