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FACULTY OF SCIENCE / MATHEMATICS / MAT4004 - FUNCTIONAL ANALYSIS II
GENERAL INFORMATION ABOUT THE COURSE
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Course Title
Theoretical
Practical
ECTS
Turkish Name of the Course
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Course Objective
Problems originating from different areas of mathematics are closely related to the structure and properties of those areas. This situation tends to reinforce a certain approach to these types of problems and, consequently, the solution is often hindered or complicated by many insignificant details. Therefore, approaching problems with an abstract approach related to their fundamental characteristics, leaving insignificant details aside, eliminates these types of hindrances and complications. The aim of this course is to implement these abstract approaches using metric spaces, normed spaces, and inner product spaces.
Brief Content of the Course
Hahn- Banach Theorem, Open Mapping Theorem, Closed Graph Theorem, Uniform Boundedness Principle, Inner product spaces, Hilbert space and sustainable approaches to their applications, Banach algebras, Spectrum.
Prerequisites
Course Objectives
Course Objectives
1
Students should be able to learn the Hahn-Banach theorem, the Open Mapping Theorem, the Closed Graph Theorem, and the uniform boundedness principle.
2
Students should be able to learn inner product spaces and Hilbert spaces.
3
Students should be able to learn Banach algebra, spectrum, ideals, and division algebras.
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Course Category
Course Category
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Mathematics and Basic Sciences
Basic Vocational Courses