COURSE INFORMATION
Code
Semester
L+P
Hour
Credits
ECTS
MATH 551
1-2
3+0
3
10
Course Title
FUNCTIONAL ANALYSIS I
Prerequisites
Language of
Instruction
English
Course Level
Graduate
Course Type
Course Coordinator
Prof. Dr. Yusuf Ünlü
Instructors
Prof. Dr. Yusuf Ünlü
Assistants
Goals
Topological structure. Basic topological concepts. Compact topological
spaces. Continuous functions. Connectedness. Metric topology and metric
spaces. Convergence, completeness and compactness. Contraction
mappings. Urysohn's theorem. Normed linear spaces. Bounded linear
operators. Continuous linear operators.
Content
Teaching
Methods
Assessment
Methods
1) Learns basic concepts of topology, especially of
metric spaces
1,2
A
2) Learns completeness and its applications
2,2
A
3) Learns applications of the concept of compactness
1,2
A
4) Learns the concepts of connectedness and
separation
1,2
A
5) Learns Ascoi-Arzela Theorem
1,2
A
6) Learns Baire Category
1,2
A
Learning Outcomes
Teaching
Methods:
Assessment
Methods:
1: Lecture, 2:Problem solving
A: Written Examination, B: Homework
COURSE CONTENT
Week
Topics
1
Basic concepts of topological spaces.
2
Continuity. Metric spaces.
3
Complete metric spaces. Completion of metric spaces.
Study
Materials
4
Contracting mapping theorem and its applications to Differential
equations
5
Totally bounded metric spaces and compactness
6
Properties of compact spaces, Stone-Weirstrass Theorem
7
Baire Spaces
8
Ascoli-Arzela Theorem
9
Connected spaces and intermediate value theorem
10
Seperability, second countability
11
Normality. Urysohn, Tietze Theorems.
12
Normed linear spaces. Banach spaces.
13
Review of measure spaces and Lp –spaces
14
Bounded linear operators between normed spaces
RECOMMENDED SOURCES
Textbook
1. Topology of Metric Spaces, S. S. Kumaresan
2. Topology, A First Course, J. Munkres
3. Functional Analysis, Y. Eidelman, V. Milman, A. Tsolomitis
Additional Resources
MATERIAL SHARING
Documents
Assignments
Exams
ASSESSMENT
IN-TERM STUDIES
NUMBER
PERCENTAGE
Mid-terms
1
100
Quizzes
Assignments
Total
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL
GRADE
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL
GRADE
Total
COURSE CATEGORY
COURSE'S CONTRIBUTION TO PROGRAM
100
60
40
100
No
Contribution
Program Learning Outcomes
1
1
2
3
4
5
6
7
Acquires a rigorous background about the fundamental fields in
mathematics and the topics that are going to be specialized.
Acquires the ability to relate, interpret, analyse and synthesize on
fundamental fields in mathematics and/or mathematics and other sciences.
Follows contemporary scientific developments, analyses, synthesizes and
evaluates novel ideas.
Uses the national and international academic sources, and computer and
related IT.
Participates in workgroups and research groups, scientific meetings,
contacts by oral and written communication at national and international
levels.
Acquires the potential of creative and critical thinking, problem solving,
research, to produce a novel and original work, self-development in areas
of interest.
Acquires the consciousness of scientific ethics and responsibility. Takes
responsibility about the solution of professional problems as a requirement
of the intellectual consciousness.
2
3
4
5
X
X
X
X
X
X
X
ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Quantity
Duration
(Hour)
Total
Workload
(Hour)
Course Duration (14x Total course hours)
14
3
42
Hours for off-the-classroom study (Pre-study, practice)
14
10
140
Mid-terms (Including self study)
1
25
25
Quizzes
-
Assignments
-
Final examination (Including self study)
1
35
35
Activities
Total Work Load
242
Total Work Load / 25 (h)
9,68
ECTS Credit of the Course
10