FACULTY OF ARTS AND SCIENCES
Department of Mathematics
MATH 441 | Course Introduction and Application Information
Course Name |
Functional Analysis I
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
MATH 441
|
Fall
|
3
|
0
|
3
|
6
|
Prerequisites |
None
|
|||||
Course Language |
English
|
|||||
Course Type |
Required
|
|||||
Course Level |
First Cycle
|
|||||
Mode of Delivery | - | |||||
Teaching Methods and Techniques of the Course | Q&ALecture / Presentation | |||||
Course Coordinator | - | |||||
Course Lecturer(s) | ||||||
Assistant(s) |
Course Objectives | This twotier course provides deep understanding of introductory functional analysis. The objective of this course is to cover fundamental topics of functional analysis such as General results about metric spaces: Cauchy sequences, completeness and completion, Normed and Banach spaces: Elementary properties and results. |
Learning Outcomes |
The students who succeeded in this course;
|
Course Description | This course aims to teach basic theory and applications of Functional Analysis |
|
Core Courses |
X
|
Major Area Courses | ||
Supportive Courses | ||
Media and Management Skills Courses | ||
Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
Week | Subjects | Related Preparation |
1 | Metric spaces, Topology: Open set, closed set, neighborhood, topological space, dense and separable sets, continuous functions in metric space. | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 1.1,1.2,1.3 |
2 | Sequences: boundedness, convergence, limit of the sequence, Cauchy series, separability. | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 1.4 |
3 | Completeness, completeness of metric space | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section1.5 |
4 | Vector spaces: subspace, dimension, Hamel bases | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.1 |
5 | Normed spaces, Banach spaces | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.2 |
6 | Properties of normed spaces | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.3 |
7 | Finite dimensional norm spaces and subspaces, equivalent norms. | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.4 |
8 | Compactness and finite size, max min theorem. | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.5 |
9 | Linear operators and some of their properties, some properties and applications of bounded and linear operators | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.6-2.7 |
10 | Linear Functionals | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.8 |
11 | Inner product space and Hilbert space | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 3.1 |
12 | Properties of inner product space | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 3.2 |
13 | Orthogonal and orthonormal sets. Key features | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 3.3-3.4 |
14 | General Review | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 |
15 | Semester review | |
16 | Final exam |
Course Notes/Textbooks | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978-0471504597 |
Suggested Readings/Materials | '' Functional Analysis'',by Walter Rudin McGraw-Hill Science/Engineering/Math; 2nd edition ,1991,ISBN-13:978-0070542365 |
EVALUATION SYSTEM
Semester Activities | Number | Weigthing |
Participation | ||
Laboratory / Application | ||
Field Work | ||
Quizzes / Studio Critiques | ||
Portfolio | ||
Homework / Assignments | ||
Presentation / Jury | ||
Project | ||
Seminar / Workshop | ||
Oral Exams | ||
Midterm |
2
|
60
|
Final Exam |
1
|
40
|
Total |
Weighting of Semester Activities on the Final Grade |
2
|
60
|
Weighting of End-of-Semester Activities on the Final Grade |
1
|
40
|
Total |
ECTS / WORKLOAD TABLE
Semester Activities | Number | Duration (Hours) | Workload |
---|---|---|---|
Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
Study Hours Out of Class |
14
|
5
|
70
|
Field Work |
0
|
||
Quizzes / Studio Critiques |
0
|
||
Portfolio |
0
|
||
Homework / Assignments |
0
|
||
Presentation / Jury |
0
|
||
Project |
0
|
||
Seminar / Workshop |
0
|
||
Oral Exam |
0
|
||
Midterms |
2
|
20
|
40
|
Final Exam |
1
|
22
|
22
|
Total |
180
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
1
|
2
|
3
|
4
|
5
|
||
1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. |
X | ||||
2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. |
|||||
3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. |
X | ||||
4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. |
X | ||||
5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. |
|||||
6 | To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project. |
|||||
7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. |
|||||
8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. |
|||||
9 | To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security. |
|||||
10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. |
|||||
11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. |
|||||
12 | To be able to speak a second foreign language at a medium level of fluency efficiently. |
|||||
13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. |
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
NEWS |ALL NEWS
9th Workshop of Association for Turkish Women in Maths
9th Workshop of Association for Turkish Women in Maths will take place from May 03 to May 05, 2024 in Izmir, Turkey,
Our 2009 Graduate Has Been Appointed to the South Marmara Development Agency (GMKA) as the General Secretary
Onur Adıyaman, General Secretary of the Eastern Black Sea Development Agency, appointed as the General Secretary of the South Marmara Development Agency.
Young mathematicians came together at IUE
The award ceremony of the Turkish Mathematical Olympiad, which is organized to increase the interest of primary, secondary and high school students