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Syllabus ( MATH 541 )


   Basic information
Course title: Functional Analysis
Course code: MATH 541
Lecturer: Prof. Dr. Mansur İSGENDEROĞLU (İSMAİLOV)
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
Language of instruction: Turkish
Mode of delivery: Face to face
Pre- and co-requisites: MATH 350
Professional practice: No
Purpose of the course: To teach the fundamental concepts and theorems of Functional Analysis
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Adapt the fundamental concepts of Functional Analysis.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    3. Acquire scientific knowledge and work independently
    4. Defend research outcomes at seminars and conferences.

    Method of assessment

    1. Written exam
    2. Oral exam
    3. Homework assignment
  2. Recognize the main theorems of Functional Analysis

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Acquire scientific knowledge and work independently
    3. Defend research outcomes at seminars and conferences.

    Method of assessment

    1. Written exam
  3. Gain the capability of fields of application of Functional Analysis

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    3. Design and conduct research projects independently

    Method of assessment

    1. Written exam
    2. Oral exam
    3. Homework assignment
   Contents Up
Week 1: Introduction to Metric Spaces
Week 2: Connectedness and Comleteness
Week 3: Compactness in Metric Spaces
Week 4: Normed Vector Spaces
Week 5: Linear Functionals, Hahn-Banach Theorem
Week 6: Inner Product spaces
Week 7: Ortogonal Expansions and Riesz Representation Theorem
Week 8: Introduction to Bounded Linear Transformations
Week 9: Midterm exam. Linear Transformations on Hilbert Spaces
Week 10: Compact 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
Week 15*: General review
Week 16*: Final Exam
Textbooks and materials:
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)
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 9 40
Other in-term studies: 0
Project: 0
Homework: 2, 4, 6, 8, 10, 12 10
Quiz: 0
Final exam: 16 50
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 4 14
Practice, Recitation: 0 0
Homework: 7 6
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 20 1
Mid-term: 3 1
Personal studies for final exam: 20 1
Final exam: 3 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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