TR
11111

COURSE INTRODUCTION AND APPLICATION INFORMATION

dm.ieu.edu.tr

Course Name
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
Spring
Prerequisites
 MATH 301To attend the classes (To enrol for the course and get a grade other than NA or W)
Course Language
Course Type
Required
Course Level
-
Mode of Delivery -
Teaching Methods and Techniques of the Course Problem Solving
Q&A
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives
Learning Outcomes The students who succeeded in this course;
  • will be able to define inner product spaces and explain the relationship between Hilbert spaces, Banach spaces and metric spaces.
  • will be able to know properties of orthogonal sets
  • will be able to know the differences between convergences of sequences of operators and functionals.
  • will be able to understand and apply fundamental theorems of functional analysis
  • will be able to understand and compare strong convergence and weak convergence
Course Description

 



Course Category

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

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Inner product spaces and their properties, Hilbert Spaces Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
2 Inner product spaces and their properties, Hilbert Spaces Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
3 Orthogonal complements and direct sums Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
4 Orthogonal complements and direct sums Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
5 Orthonormal sets and sequences Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
6 Fourier series and their properties Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
7 Total orthonormal sets and sequences Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
8 Representation of functionals on Hilbert spaces Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
9 Hilbert-Adjoint operator Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
10 Self-adjoint, unitary and normal operators Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
11 Fundamental theorems of functional analysis: Zorn's lemma, Hahn-Banach theorem and Banach fixed point theorem Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
12 Fundamental theorems of functional analysis: Baire category theorem, Uniform boundedness theorem, Open mapping theorem and Banach fixed point theorem Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
13 Weak and strong convergence Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
14 Convergence of sequences of operators and functionals Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
15 Course Review
16 Course Review
Course Notes/Textbooks

Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
Suggested Readings/Materials Walter Rudin, Functional Analysis 2/E, International Series in Pure and Applied Mathematics.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
1
10
Laboratory / Application
Field Work
Quizzes / Studio Critiques
6
15
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
35
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
8
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

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
14
3
Field Work
Quizzes / Studio Critiques
3
Portfolio
Homework / Assignments
2
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
28
Final Exams
1
36
    Total
182

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
 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 up-to-date, 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,

 X
14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

 X
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.

 X

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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