Mathematics (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH452

Course Name:

Linear Analysis

Semester:

Spring

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Araş. Gör. GAMZE AKAR UYSAL

Course Lecturer(s):

Prof. Dr. Selçuk Demir

Course Assistants:

Course Objective and Content

Course Objectives:	The course aims to introduce normed vector spaces, their properties and applications to problems of mathematical analysis.
Course Content:	The content of the course consists of the concept of norm and normed spaces, their properties and significance in stating and solving proplems of mathematical analysis.

Learning Outcomes

The students who have succeeded in this course;
1) will be able to understand Banach and Hilbert spaces and their metric properties.
2) will be able to understand the orthonormal bases of Hilbert spaces, the l_2 spaces and its relation to other Hilbert spaces.
3) will be able to understand the basic theorems of functional analysis: open and closed mapping theorem, uniform boundedness..
4) will be able to find Taylor or Laurent expansions and analytic continuation of a function

Course Flow Plan

Week	Subject	Related Preparation
1)	Hölder and Minkowski Inequaties
2)	Norms, their equivalence
3)	topology of normed spaces, bounded linear operators
4)	finite dimensional normed spaces, riesz' lemma
5)	completeness, new Banach spaces from old ones
6)	Hahn Banach theorem (geometric form)
7)	Hahn Banach theorem (analytic form)
8)	Midterm Exam
9)	Baire category theorem, uniform boundedness
10)	Open mapping and closed graph theorems, applications
11)	inner products, Cauchy-Schwartz inequalities
12)	Hilbert spaces, examples
13)	Linear operators in Hilbert spaces,
14)	Compact hermitian operators, spectral theorem.

Sources

Course Notes / Textbooks:	B. Bollobas: Linear Analysis, Cambridge University Press
References:	Kesavan: Functional Analysis, Springer

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4
Program Outcomes
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4) Have the ability to think analytically and use the time effectively in the process of deduction.
5) Have the ability to search the literature, understand and interpret scientific articles.
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7) Have the ability to work efficiently in interdisciplinary teams.
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.	2
2)	Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3)	Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.	2
4)	Have the ability to think analytically and use the time effectively in the process of deduction.
5)	Have the ability to search the literature, understand and interpret scientific articles.	3
6)	Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7)	Have the ability to work efficiently in interdisciplinary teams.
8)	Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9)	Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10)	Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.	3
11)	Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	3		39
Application	13	0			0
Study Hours Out of Class	13	0	3		39
Midterms	1	0	15		15
Final	1	0	25		25
Total Workload					118