Course Name  Functional Analysis I 
Code  Semester  Theory (hour/week)  Application/Lab (hour/week)  Local Credits  ECTS 

MATH 301  Fall  3  0  3  5 
Prerequisites  None  
Course Language  English  
Course Type  Required  
Course Level  First Cycle  
Mode of Delivery    
Teaching Methods and Techniques of the Course  
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 Managment Skills Courses  
Transferable Skill Courses 
Week  Subjects  Required Materials 
1  Metric Spaces (Introduction and examples)  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
2  Topology: Open set, Closed set, Neighborhood, Topological space, Dense and separable sets, Continuous functions on metric spaces  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
3  Sequences: boundedness, convergence, limit of a sequence, Cauchy Sequence, Seperability  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
4  Completeness and incompleteness (Examples and proofs).  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
5  Review  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
6  Completeness and incompleteness (Examples and proofs).  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
7  Completion of metric spaces.  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
8  Vector spaces, subspace, dimension, Hamel basis.  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
9  Review  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
10  Normed spaces and Banach Spaces  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
11  Further properties of Normed spaces  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
12  Finite dimensional Normed spaces and subspaces, Equivalent norms  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
13  Compactness and finite dimension, Maxmin theorem  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
14  Linear operators  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
15  Some properties and applications of bounded and linear operators.  Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. 
16  Review of the Semester 
Course Notes/Textbooks  The extracts above and exercises will be given. 
Suggested Readings/Materials  Walter Rudin, Functional Analysis 2/E, International Series in Pure and Applied Mathematics. 
Semester Activities  Number  Weigthing 
Participation  
Laboratory / Application  
Field Work  
Quizzes / Studio Critiques  
Portfolio  
Homework / Assignments  10  15 
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterm  2  50 
Final Exam  1  35 
Total 
Weighting of Semester Activities on the Final Grade  12  60 
Weighting of EndofSemester Activities on the Final Grade  1  40 
Total 
Semester Activities  Number  Duration (Hours)  Workload 

Course Hours (Including exam week: 16 x total hours)  16  3  48 
Laboratory / Application Hours (Including exam week: 16 x total hours)  16  
Study Hours Out of Class  5  1  
Field Work  
Quizzes / Studio Critiques  
Portfolio  
Homework / Assignments  10  1  
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterms  2  25  
Final Exams  1  30  
Total  143 
#  Program Competencies/Outcomes  * Contribution Level  
1  2  3  4  5  
1  To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics.  X  
2  To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics,  X  
3  To be able to define and analyze problems and to find solutions based on scientific methods,  X  
4  To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials,  X  
5  To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,  X  
6  To be able to criticize and renew her/his own models and solutions,  X  
7  To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way,  X  
8  To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge uptodate, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,  X  
9  To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,  X  
10  To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,  X  
11  To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,  X  
12  By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,  X  
13  To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,  
14  To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,  
15  To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. 
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest