Ders Planı

Lesson Information

Course Credit	4.0
Course ECTS Credit	7.0
Teaching Language of Instruction	Türkçe
Level of Course	Bachelor's Degree, TYYÇ: Level 6, EQF-LLL: Level 6, QF-EHEA: First Cycle
Type of Course	Compulsory
Mode of Delivery	Face-to-face
Does the course require compulsory or optional work experience?	Z
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Purpose and Content

The aim of the course	This course aims to give the properties of metric spaces, vector spaces normed vector spaces, Banach,inner product and Hilbert spaces.
Course Content	This course covers The metric spaces,Linear and normed spaces. Linear operators and bounded linear operators. Linear functionals. Dual spaces. Hilbert spaces. The system of orthonormal and exact vectors. Bessel s inequality. Parseval s identity. Hilbert adjoint operator and self-adjoint, unitary and normal operators. Hahn-Banach Theorems. First and second category sets. The uniform boundedness principle. Strong and weak convergence. Open mapping theorem. Closed graph theorem and Banach's fix theorem.

The aim of the course

This course aims to give the properties of metric spaces, vector spaces normed vector spaces, Banach,inner product and Hilbert spaces.

Course Content

This course covers The metric spaces,Linear and normed spaces. Linear operators and bounded linear operators. Linear functionals. Dual spaces. Hilbert spaces. The system of orthonormal and exact vectors. Bessel s inequality. Parseval s identity. Hilbert adjoint operator and self-adjoint, unitary and normal operators. Hahn-Banach Theorems. First and second category sets. The uniform boundedness principle. Strong and weak convergence. Open mapping theorem. Closed graph theorem and Banach's fix theorem.

Learning Outcomes

Have advanced theoretical and practical knowledge in mathematics and computer science.
Gain an in-depth knowledge on Computer Science including computer programming, word processing, database functions, accessing the internet and softwares.
Possess the knowledge of advanced research methods in mathematics-computer field.
Possess theoretical and practical knowledge in mathematics, computation and computer science.
Define computer programming, word processing, data functions, internete access and software programs.
Describe advanced research methods in the field of Mathematics-Computer Science.
Evaluate and interpret data using the knowledge and skills gained in the fields of mathematics and computer science.
Identify, define and analyze problems in the fields of mathematics and computer science; develop solutions based on research and evidence.
Identify, define and model mathematics, computation and computer science problems; select and apply appropriate analysis and modeling methods for this purpose.
Design and apply interactive experimental environments to get the definitions and first solutions of the problems of computer science and computer science and evaluate these environments.
Having the discipline of mathematics, understand the operating logic of the computer and gain the ability to think based on account.
Perform all phases of life cycle in computer based systems.
Work effectively as an individual and as a team member to solve problems in the areas of mathematics and computer science.
Have the ability to act independently, use initiative and creativity.
Work effectively either individually or in multidisciplinary teams.
Evaluate advanced knowledge and skills in the field with a critical approach.
Follow current developments about the awareness of the necessity of continuous professional development and information and communication technologies.
Have the consciousness of the necessity of lifelong learning and continuously develop professional knowledge and skills.
Use the time effectively in the process of getting the conclusion with analytical thinking ability.
Have at least one foreign language knowledge and the ability to communicate effectively in Turkish, verbally and in writing.
Be aware of the effects of information applications on individual, institutional, social and universal dimensions and have the awareness about entrepreneurship, innovation.
Have the awareness of professional and ethical responsibility and legal consequences of information applications
Use the knowledge about the field for the benefit to society.

Weekly Course Subjects

1	The metric spaces.
2	Linear and normed spaces.
3	Completeness,Banach Spaces.
4	Linear operators and bounded linear operators.
5	Linear functionals. Dual spaces.
6	Hilbert spaces.
7	The system of orthonormal and exact vectors.
8	Hilbert adjoint operator and self-adjoint.
9	Bessel s inequality,Parseval s identity.Midterm Exam.
10	Unitary and normal operators .
11	Hahn-Banach Theorems.First and second category sets.
12	The uniform boundedness principle.
13	Strong and weak convergence.
14	Open mapping theorem. Closed graph theorem and Banach's fix theorem.

Resources

1-Mustafa Bayraktar, Fonksiyonel Analiz,2010
2-Musayev,Bnali.Fonksiyonel Analiz,Balcı Yayınları,2000.
3-Rudın.W., Functional Analysis,Tata,Mc Graw-Hill.

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CLASS 3

CLASS 4

Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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