Syllabus ( MATH 541 )

Basic information


Course title: 
Functional Analysis 
Course code: 
MATH 541 
Lecturer: 
Prof. Dr. Mansur İSGENDEROĞLU (İSMAİLOV)

ECTS credits: 
7.5 
GTU credits: 
4 (3+0+0) 
Year, Semester: 
1/2, Fall and Spring 
Level of course: 
Second Cycle (Master's) 
Type of course: 
Area Elective

Language of instruction: 
Turkish

Mode of delivery: 
Face to face

Pre and corequisites: 
MATH 350 
Professional practice: 
No 
Purpose of the course: 
To teach the fundamental concepts and theorems of Functional Analysis 



Learning outcomes


Upon successful completion of this course, students will be able to:

Adapt the fundamental concepts of Functional Analysis.
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics

Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results

Acquire scientific knowledge and work independently

Defend research outcomes at seminars and conferences.
Method of assessment

Written exam

Oral exam

Homework assignment

Recognize the main theorems of Functional Analysis
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics

Acquire scientific knowledge and work independently

Defend research outcomes at seminars and conferences.
Method of assessment

Written exam

Gain the capability of fields of application of Functional Analysis
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics

Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results

Design and conduct research projects independently
Method of assessment

Written exam

Oral exam

Homework assignment


Contents


Week 1: 
Introduction to Metric Spaces 
Week 2: 
Connectedness and Comleteness 
Week 3: 
Compactness and Connectedness in Metric Spaces

Week 4: 
Normed Vector Spaces and Banach Spaces 
Week 5: 
Linear Functionals, HahnBanach Theorem 
Week 6: 
Inner Product spaces and Hilbert Spaces 
Week 7: 
Ortogonal Expansions and Riesz Representation Theorem 
Week 8: 
Bounded Linear Transformations, Invertible Operators and Banach Theorem for Bounded Inverse 
Week 9: 
Midterm exam. Linear Transformations on Hilbert Spaces 
Week 10: 
Compact Operators and Examples in Integral Operators 
Week 11: 
Selfadjoint, Unitar and Normal Operators 
Week 12: 
The main theorems in Normed and Banach spaces, Baire category and BanachSteinhaus Theorems 
Week 13: 
The Open Mapping and Glosed Graph Theorems 
Week 14: 
Spectrum of a Linear Operators and Hilbert  Schmidt Theorem 
Week 15*: 
 
Week 16*: 
Final Exam 
Textbooks and materials: 

Recommended readings: 
Introductory functional analysis with applications (Erwin Kreyszig) Elements of the theory of functions and functional analysis ( A. N. Kolmogorov and S. V. Fomin) Functional analysis (Walter Rudin) Elements of Functional Analysis ( L. A. Lusternik and V. J. Sobolev) 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
9 
40 
Other interm studies: 

0 
Project: 

0 
Homework: 
2, 4, 6, 8, 10, 12 
10 
Quiz: 

0 
Final exam: 
16 
50 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
3 
14 

Own studies outside class: 
4 
14 

Practice, Recitation: 
0 
0 

Homework: 
7 
6 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
0 
0 

Own study for midterm exam: 
20 
1 

Midterm: 
3 
1 

Personal studies for final exam: 
20 
1 

Final exam: 
3 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



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