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Syllabus ( MATH 671 )


   Basic information
Course title: Operator Theory And Its Applications
Course code: MATH 671
Lecturer: Prof. Dr. Mansur İSGENDEROĞLU (İSMAİLOV)
ECTS credits: 7.5
GTU credits: 3 (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, MATH 502
Professional practice: No
Purpose of the course: To teach spectral properties of some operator types and its applications by assuming to be known the fundamental concepts of Funtional Analysis
   Learning outcomes Up

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

  1. Obtain the fundamental concepts and theorems of Operator Theory

    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. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
  2. Obtain spectral properties of some operators

    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. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. Determine the areas of applying of Operator Theory

    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

    Method of assessment

    1. Written exam
    2. Oral exam
    3. Homework assignment
   Contents Up
Week 1: Banach and Hilbert Spaces
Week 2: Linear Functionals and Bounded Linear operators
Week 3: Projection Operators and Unitary Operators
Week 4: General Concepts and Propositions in Theory of Linear Operators
Week 5: The Concept of Spectrum and Resolvent
Week 6: The Graph of Operator
Week 7: Spectral Analysis of Completely Continuous Operators
Week 8: Midterm exam. Fredholm Theorems
Week 9: Fixed point Theorems, Existance of Invariant Subspace for a Completely Continuous Operators
Week 10: Spectral Analysis of Unitary Operators
Week 11: Spectral Analysis of Self-Adjoint Operators
Week 12: Completely Continuous Self-Adjoint Operators, Hilbert-Schmidt Theorem
Week 13: Theory of Extension of Symmetric Operators
Week 14: Examples on Differential Operators
Week 15*: General review
Week 16*: Final Exam
Textbooks and materials:
Recommended readings: Walter Rudin, Functional analysis,
N. I. Akhiezer and I.M. Glazman, Theory of linear operators in Hilbert space
L. A. Lusternik and V. J. Sobolev, Elements of Functional Analysis
Erwin Kreyszig, Introductory functional analysis with applications
  * 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: 8 40
Other in-term studies: 0
Project: 0
Homework: 3, 5, 7, 9, 11, 13 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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