Functional Analysis (MATH357) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Functional Analysis	MATH357	Area Elective	3	0	0	3	6

Pre-requisite Course(s)
MATH251

Course Language	English
Course Type	Elective Courses
Course Level	Natural & Applied Sciences Master's Degree
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)	Assoc. Prof. Dr. Erdal KARAPINAR
Course Assistants
Course Objectives	The aim of the course is providing a familiarity to concepts of the functional analysis, such as norm, compactness and convergence.
Course Learning Outcomes	The students who succeeded in this course; At the end of the course the student is expected to: 1) understand the notions of commutative metric and normed spaces and be able prove the basic facts of these theory, 2) apply this theories to operator theory, 3) know the Hahn-Banach Theorem, 4) know uniform boundedness principle, 5) know open mapping and closed graph theorems.
Course Content	Vector spaces, Hamel basis, linear operators, equations in operators, ordered vector spaces, extension of positive linear functionals, convex functions, Hahn-Banach Theorem, The Minkowski functional, Separation Theorem, metric spaces, continuity and uniform continuity, completeness, Baire Theorem, normed spaces, Banach spaces, the algebra of bounde

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	Metric Spaces Open Sets, Closed Sets	pp. 2--22
2	Convergence, Cauchy Sequence, Completeness	pp. 23--44
3	Vector Spaces, Normed Spaces Banach Spaces	pp. 50--66
4	Further Properties of Normed Spaces Finite Dimensional Normed Spaces and Subspaces	pp. 67--75
5	Compactness and Finite Dimensional Linear Operators	pp. 77--90
6	Bounded and Continuous Linear Operators, Linear Functional	pp. 91--110
7	Midterm Exam
8	Linear Operators and Functionals on Finite Dimensional Spaces Normed Spaces of Operators, Dual Spaces	pp. 111--125
9	Hahn-Banach Theorem Hahn-Banach Theorem for Complex Valued Vector Spaces and Normed Spaces	pp. 213--224
10	Application to Bounded Linear Functionals on C[a,b]	pp. 225--230
11	Adjoint Operator	pp. 231--238
12	Reflexive Spaces	pp. 239-245
13	Midterm Exam
14	Category Theorems Uniform Boundedness Theorem	pp. 246--254
15	Strong and Weak Convergence Convergence of Sequence of Operators and Functionals	pp.256-268
16	Review

Sources

Course Book	1. Introductory Functional Analysis with Applications, E. Kreyszig, 1978, John Wiley and Sons Inc. ISBN 0-471-5073-8
Other Sources	2. Elements of the Theory of Functions and Functional Analysis, A.N. Kolmogorov and S.V. Fomin, Dover, NY, 1999. ISBN: 0-486-40683-0
	3. Functional Analysis, G.Bachman and L. Narici , Dover, 1991, ISBN: 0-486-40251-7

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	-	-
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	60
Final Exam/Final Jury	1	40
Toplam	3	100

Percentage of Semester Work	60
Percentage of Final Work	40
Total	100

Course Category

Core Courses	X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area.
2	Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research.
3	Can apply gained knowledge and problem solving abilities in inter-disciplinary research.
4	Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary.
5	Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study.
6	Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework.
7	Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility.
8	Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation.
9	Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields.
10	Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge.
11	Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications.

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)	16	3	48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class	14	3	42
Presentation/Seminar Prepration
Project
Report
Homework Assignments	5	4	20
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	12	24
Prepration of Final Exams/Final Jury	1	16	16
Total Workload			150