Bölüm Bilgileri - balıkesir üniversitesi matematik bölümü

Transcription

Information about the Department of Mathematics
Goals:
The main aim of graduate education of our department is giving an education based on analytic thought. Our
department is trying to train strong scientists.
Objectives:
Master:
The M. Sc. program supplies an overall and comprehensive outlook on Mathematics issues to the graduate and
gives them an improved knowledge in a selected specific area.
Doctorate:
The main objective of the Ph.D. program is to produce scientists.
Qualification Awarded
The students who successfully complete the program are awarded the degree of Master of Science (M.Sc.) or
Doctor of Philosophy (Ph.D.) in Mathematics.
Admission Requirements
Master:
 Bachelor Degree. (4 years minimum)
 Academic Personnel and Graduate Education Exam (ALES): Minimum score of 55 at quantitative
field.
 Foreign Language: Minimum score of 50 from Interuniversity Board Foreign Language
Examination (ÜDS), or equivalent score from another valid exam (TOEFL, IELTS, etc.), or being
successful at foreign language examination by Balikesir university.
 Successful in the scientific interview.
 For other requirements please visit http://fbe.balikesir.edu.tr .
Doctorate:





Bachelor Degree (4 years minimum) or Master Degree (Applicants to the Ph.D. program with a
bachelor degree must have 85/100 undergraduate grade point average, for applicants with
master degree must have 75/100 graduate grade point average)
Academic Personnel and Graduate Education Exam (ALES): Minimum score of 55 at quantitative
field (Applicants to the Ph.D. program with a bachelor's degree must have 70 at quantitative field).
Foreign Language: Minimum score of 55 from Interuniversity Board Foreign Language
Examination (ÜDS), or equivalent score from other valid exam (TOEFL, IELTS, etc.).
Successful in the scientific interview.
For other requirements please visit http://fbe.balikesir.edu.tr .
Graduation Requirements
Master:
A (The?) student is required to complete at least 7 courses, not being less than 42 ECTS credits, a seminar
course and a thesis. The midterm, if applicable, and the final exams contribute at specified percentages to the
final grade. A student should have a final grade of minimum 65/100 in order to pass a course. Seminar course is
evaluated as “satisfactory” or “unsatisfactory”. After completing the courses, a student have to prepare a thesis.
Doctorate:
Students are required to complete at least 7 courses, not being less than 42 ECTS credits, within at least four
consecutive semesters, maintain a minimum 75/100. Later a student have to be successful at the Doctoral
Qualifying Examination and to prepare a thesis.
Assessment and Grading
Examination assessment guidelines are described in presentation form of each course. For detailed information
on the related course, please look into the detailed course plan.
ECTS Coordinator
Assoc. Prof. Ali GÜVEN
Erasmus Coordinator
Assoc. Prof. Sebahattin İKİKARDEŞ
Program’s Key Learning Outcomes:
1. To be able to understand Mathematical materials in basic and advanced level.
2. To be able to develop research-based solutions for encountered scientific problems.
3. To be able to apply Mathematical principles in real world problems.
4. To be able to use Mathematical knowledge in new technology.
5. To be able to develop new strategic approach and to produce solutions by taking responsibility in unexpected
and complicated situations in his/her area.
6. To be able to develop solution methods for problems in his/her field and to solve them.
7. To be able to approach actual mathematical problems in various viewpoints and to develop solution method
for them.
8. To be able to use Mathematical thought in the whole area of the life, and to apply his/her knowledge in
interdisciplinary studies.
9. To be able to improve the knowledge with scientific methods in his/her field by using limited or missing data.
10. To be able to apply the approach and knowledge of different disciplines in Mathematics.
11. To be able to transfer his/her study and its results to large groups of people in writing or orally.
12. To be able to have a foreign language knowledge in a level for following the developments in mathematics,
and to communicate with colleagues.
13. To be able to have knowledge about basic computer programs used in Mathematics.
14. To be able to teach and check the values, which are scientific and social, under the ethic rules in stage of
collecting, interpreting and announcing the data in his/her field.
Comparison between Program’s Key Learning Outcomes and National Qualifications
Framework for Higher Education in Turkey (NQF-HETR)
KNOWLEDGE - Theoretical, Factual
1. To understand Mathematical materials in basic and advanced level.
SKILLS - Cognitive, Practical
2. To develop research-based solutions for encountered scientific problems.
3.
To apply Mathematical principles in real world problems.
4.
To use Mathematical knowledge in new technology.
COMPETENCIES
Ability to work independently and take responsibility
5. To develop new strategic approach and to produce solutions by taking responsibility in unexpected and
complicated situations in his/her area (of practice?).
6.
To develop solution methods for problems in his/her field and to solve them.
Learning Competence
7. To approach actual mathematical problems in various viewpoints and to develop solution method for them.
8.
To use Mathematical thought in the whole area of the life, and to apply his/her knowledge in interdisciplinary
studies.
9.
To improve the knowledge with scientific methods in his/her field by using limited or missing data.
10. To apply the approach and knowledge of different disciplines in Mathematics.
Communication and Social Competence
11. To transfer his/her study and its results to large groups of people in writing or orally.
12. To have a foreign language knowledge in a level for following the developments in mathematics, and to
communicate with colleagues.
Field-based Competence
13. To have knowledge about basic computer programs used in Mathematics.
14. To teach and check the values, which are scientific and social, under the ethic rules in stage of collecting,
interpreting and announcing the data in his/her field.
T.R.
BALIKESIR UNIVERSITY
THE INSTITUTE OF SCIENCE AND TECHNOLOGY
2012-2013 EDUCATION YEAR
MATHEMATICS DIVISION COURSE PLANS
Fall Semester
COURSE CODE
COURSE NAME
HOURS
CREDIT
T A L Total
ECTS
CREDIT
FMT5101
Topology I
3
3 0 0
3
6
FMT5102
Functional Analysis I
3
3 0 0
3
6
FMT5104
Advanced Group Theory
3
3 0 0
3
6
FMT5106
Module Theory I
3
3 0 0
3
6
FMT5107
Real Analysis I
3
3 0 0
3
6
FMT5108
Quasiconformal Mappings
3
3 0 0
3
6
FMT5109
Advanced Differential Geometry I
3
3 0 0
3
6
FMT5111
N. E. C. Groups
3
3 0 0
3
6
FMT5112
Modular Group and Extended Moduler Group
3
3 0 0
3
6
FMT5114
Approximation Theory I
3
3 0 0
3
6
FMT5115
Riemann Surfaces
3
3 0 0
3
6
FMT5116
Representation Theory On Groups
3
3 0 0
3
6
FMT5119
Riemannian Geometry I
3
3 0 0
3
6
FMT5120
Geometry of Submanifolds I
3
3 0 0
3
6
FMT5125
Advanced Control Theory of Systems I
3
3 0 0
3
6
FMT5126
Convex Functions and Orlicz Spaces I
3
3 0 0
3
6
FMT5128
Contact Manifolds I
3
3 0 0
3
6
FMT5129
Structures on Manifolds I
3
3 0 0
3
6
FMT5130
Commutative Algebra
3
3 0 0
3
6
FMT5131
3
3 0 0
3
6
FMT5132
Introduction to Fractional Calculus
Number Theory I
3
3 0 0
3
6
FMT5133
Function Spaces I
3
3 0 0
3
6
FMT5134
3
3 0 0
3
6
FMT5136
Inversion Theory and Conformal Mappings
Selected Topics in Differential Geometry I
3
3 0 0
3
6
FMT5137
Differentiable Manifolds I
3
3 0 0
3
6
FMT5138
Tensor Geometry I
3
3 0 0
3
6
FMT5139
Seminar
0
0 0 0
0
4
FMT5140
Möbius Transformations I
3
3 0 0
3
6
FMT5141
Averaged Moduli and One Sided Approximation
I
3
3 0 0
3
6
FMT5142
Strong Approximation I
3
3 0 0
3
6
FMT5143
Finite Blascke Products I
3
3 0 0
3
6
FMT5144
Algebra I
3
3 0 0
3
6
FMT5145
Orthogonal Polynomials I
3
3 0 0
3
6
FMT5146
Banach Spaces of Analytic Functions I
3
3 0 0
3
6
FMT5147
Fourier Analysis I
3
3 0 0
3
6
FMT5148
Fourier Series and Approximation I
3
3 0 0
3
6
FMT5149
Applied Mathematics I
3
3 0 0
3
6
FMT5150
Advanced Numerical Analysis I
3
3 0 0
3
6
FMT5151
Differential Geomety of Curves and Surfaces I
3
3 0 0
3
6
FMT5152
Introduction to Fuzzy Topology I
3
3 0 0
3
6
FMT5153
Introduction to Ideal Topological Spaces I
3
3 0 0
3
6
FMT5154
Algebraic Number Theory I
3
3 0 0
3
6
FMT5155
Geometric Theory of Functions I
3
3 0 0
3
6
FMT5156
Numerical Optimization I
3
3 0 0
3
6
FMT5157
Selected Topics in Analysis I
3
3 0 0
3
6
FMT5158
Lorentzian Geometry
3
3 0 0
3
6
FMT5159
Semi-Riemannian Geometry I
3
3 0 0
3
6
FMT5160
Tangent and Cotangent Bundle Theory
3
3 0 0
3
6
5
5 0 0
5
6
FMT6101-6199 Special Topics in Field
2012-2013 EDUCATION YEAR
MATHEMATICS DIVISION LESSON PLANS
Spring Semester
COURSE CODE
COURSE TITLE
HOURS
CREDIT
T A L Total
ECTS
CREDIT
FMT5202
Functional Analysis II
3
3 0 0
3
6
FMT5205
Module Theory II
3
3 0 0
3
6
FMT5206
Fuchsian Groups
3
3 0 0
3
6
FMT5208
Advanced Differential Geometry II
3
3 0 0
3
6
FMT5210
Hyperbolic Geometry
3
3 0 0
3
6
FMT5212
Dynamic System and Applications
3
3 0 0
3
6
FMT5213
Real Analysis II
3
3 0 0
3
6
FMT5215
Discrete Groups
3
3 0 0
3
6
FMT5216
Approximation Theory II
3
3 0 0
3
6
FMT5221
Riemann Geometry II
3
3 0 0
3
6
FMT5222
Geometry of Submanifolds II
3
3 0 0
3
6
FMT5224
Advanced Control Theory of Systems II
3
3 0 0
3
6
FMT5225
Convex Functions and Orlicz Spaces II
3
3 0 0
3
6
FMT5226
Matrices of Semigroups
3
3 0 0
3
6
FMT5227
Contact Manifolds II
3
3 0 0
3
6
FMT5228
Structures on Manifolds II
3
3 0 0
3
6
FMT5230
Algebraic Geometry
3
3 0 0
3
6
FMT5231
Applications of Fractional Calculus
3
3 0 0
3
6
FMT5232
Number Theory II
3
3 0 0
3
6
FMT5233
Seminar
0
0 0 0
0
4
FMT5234
Bergman Spaces
3
3 0 0
3
6
FMT5235
Differentiable Manifods II
3
3 0 0
3
6
FMT5236
Tensor Geometry II
3
3 0 0
3
6
FMT5237
Möbius Transformations II
3
3 0 0
3
6
FMT5238
Averaged Moduli and One Sided Approximation
II
3
3 0 0
3
6
FMT5239
Strong Approximation II
3
3 0 0
3
6
FMT5240
Finite Blaschke Products II
3
3 0 0
3
6
FMT5241
Algebra II
3
3 0 0
3
6
FMT5243
Function Spaces II
3
3 0 0
3
6
FMT5244
Potential Theory
3
3 0 0
3
6
FMT5245
Banach Spaces of Analytic Functions II
3
3 0 0
3
6
FMT5246
Fourier Analysis II
3
3 0 0
3
6
FMT5247
Fourier Series and Approximation II
3
3 0 0
3
6
FMT5248
Applied Mathematics II
3
3 0 0
3
6
FMT5249
Advanced Numerical Analysis II
3
3 0 0
3
6
FMT5250
Numerical Solutions of Partial Differential
Equations
3
3 0 0
3
6
FMT5251
Differential Geometry of Curves and Surfaces II
3
3 0 0
3
6
FMT5252
Topology II
3
3 0 0
3
6
FMT5253
Introduction to Fuzzy Topology II
3
3 0 0
3
6
FMT5254
Introduction to Ideal Topological Spaces II
3
3 0 0
3
6
FMT5255
Orthogonal Polynomials II
3
3 0 0
3
6
FMT5256
Geometric Theory of Functions II
3
3 0 0
3
6
FMT5257
Algebraic Number Theory II
3
3 0 0
3
6
FMT5258
FMT5259
FMT5260
Numerical Optimization II
Selected Topics in Differential Geometry II
Selected Topics in Analysis II
3
3 0 0
3
3
3 0 0
3
3
3 0 0
3
6
6
6
FMT5261
Semi-Riemannian Geometry II
3
3 0 0
3
6
5
5 0 0
5
6
FMT6201-6299 Special Topics in Field
Fall Semester
The Relationship Table between Courses and Program’s Key Learning Outcomes
Courses
PKLO1
PKLO2
PKLO3
PKLO4
PKLO5
PKLO6
PKLO7
PKLO8
Topology I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Advanced Group Theory
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Module Theory I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Real Analysis I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Quasiconformal Mappings
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
N. E. C. Groups
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Modular Group and Extended
Moduler Group
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Approximation Theory I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Riemann Surfaces
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Representation Theory On Groups
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Convex Functions and Orlicz Spaces
I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Contact Manifolds I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Commutative Algebra
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Introduction to Fractional Calculus
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Number Theory I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Function Spaces I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Inversion Theory and Conformal
Mappings
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Selected Topics in Differential
Geometry I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Tensor Geometry I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Advanced
Systems I
Control
Theory
of
PKLO9 PKLO10 PKLO11 PKLO12 PKLO13 PKLO14
X
Seminar
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Averaged Moduli and One Sided
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Approximation I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Finite Blascke Products I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Algebra I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Banach Spaces of Analytic Functions
I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Fourier Analysis I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Applied Mathematics I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Advanced Numerical Analysis I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Differential Geomety of Curves and
Surfaces I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Introduction to Ideal Topological
Spaces I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Algebraic Number Theory I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Numerical Optimization I
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Lorentzian Geometry
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Tangent
Theory
and
Cotangent
Special Topics in Field
Bundle
Spring Semester
The Relationship Table between Courses and Program’s Key Learning Outcomes
Courses
PKLO1
PKLO2
PKLO3
PKLO4
PKLO5
PKLO6
PKLO7
PKLO8
PKLO9 PKLO10 PKLO11 PKLO12 PKLO13 PKLO14
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Module Theory II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Fuchsian Groups
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Hyperbolic Geometry
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Dynamic System and Applications
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Real Analysis II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Discrete Groups
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Approximation Theory II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Riemann Geometry II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Advanced Control Theory of Systems
II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Convex Functions and Orlicz Spaces
II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Matrices of Semigroups
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Algebraic Geometry
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Applications of Fractional Calculus
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Number Theory II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Seminar
Bergman Spaces
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Differentiable Manifods II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Tensor Geometry II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Averaged Moduli and One Sided
Approximation II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Algebra II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Function Spaces II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Potential Theory
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Banach Spaces of Analytic Functions
II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Fourier Analysis II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Applied Mathematics II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Advanced Numerical Analysis II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Numerical Solutions of Partial
Differential Equations
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Differential Geometry of Curves and
Surfaces II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Topology II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Introduction to Ideal Topological
Spaces II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Algebraic Number Theory II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Numerical Optimization II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Selected Topics in Differential
Geometry II
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Special Topics in Field
X
X
X
X
X
X
X
X
X
X
X
X
X
X
GRADUATE COURSE DETAILS
Course Title:
Topology I
Lecture
Code :
FMT5101
Education and Teaching Methods
Laboratuary
Project/
Home
Field Study
work
Application
42
0
0
0
Basic
Scientific
Course
Objectives
To teach fundamental concepts of Topology.
1.
2.
3.
4.
5.
Textbook
and /or
References
Total
198
3
6
Turkish/English
Technical
Elective
Scientific
Credits
Credit
ECTS
T+A+L=Credit
240
Language
Course Type





Other
0
Fall
Semester
Learning
Outcomes
and
Competences
Institute: Instute of Science
Field: Mathematics
Social
Elective
To be able to construct Topological structures by using Topological Construction Methods,
To be able to define the concepts of Normality and Expansion of Functions,
To be able to express the Characterizations related to connectedness,
To be able to express the relations between Connectedness and Derived Spaces,
To be able to express the relations among Components, Local Connectedness, Connectedness and T2Spaces.
Şaziye Yüksel, Genel Topoloji (in Turkish), Eğitim Kitapevi, (2011).
John L.Kelley, General Topology, Springer-Verlag 1955.
K.Kuratowski, Topology, Academic Press 1966.
Michael C.Gemignani, Elementary Topology, Dover publications 1990.
Nicolas Bourbaki, General Topology, Springer-Verlag 1998.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
Project Course and Graduation Study
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
(Projects,reports, ….)
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
% 80
Other (Class
Performance)
X
% 20
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Other
Subjects
Topology Concepts
Topology Construction Methods
Base, Subbase
Open neighborhoods System
First and Second Countable Spaces
Subspaces
Continuity, Homeomorfizm
Part spaces, product spaces
T1-spaces, regular spaces and normal spaces
Normality and Expansion of Functions
The Concept of Connectedness
Characterizations related to connectedness
Connectedness and Derived Spaces
Components, Local Connectedness, Connectedness and T2-Spaces
Instructors
Assoc.Prof. Dr. Ahu Açıkgöz
e-mail
[email protected]
Website
http://matematik.balikesir.edu.tr/
Percent
(%)
Course Title:
Lecture
Code :
FMT5102
Application
42
Home
Laboratuary
Project/
Field Study work
0
0
0
Fall
Semester
Course Type
Course
Objectives
Field: Mathematics
Basic
Scientific
Scientific
Other
Total
198
240
0
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To introduce fundamental concepts and theorems of Functional analysis.




To be able to define the concepts of Banach space and Hilbert space,
To be able to define the concepts of orthogonal set and orthonormal base,
To be able to define the concept of bounded linear operator,
To be able to state the uniform boundedness principle, open mapping theorem and closed graph
theorem,

To be able to state the Hahn-Banach theorem,

To be able to define the concept of quotient space.
1. Barbara D. MacCluer, Elementary Functional Analysis, Springer (2009).
2. J. B. Conway, A Course in Functional Analysis, Springer (1985).
3. W. Rudin, Functional Analysis, McGraw Hill (1991).
Learning
Outcomes
and
Competences
Textbook
and /or
References
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Hilbert Spaces
Normed Spaces
Orthogonality
The Geometry of Hilbert Spaces
Linear Functionals
Orthonormal Bases
Bounded Linear Transformations
Adjoints of Operators on Hilbert Spaces
Dual Spaces
Adjoints of Operators on Banach Spaces
The Hahn-Banach Theorem
Uniform Boundedness Principle
Open Mapping and Closed Graph Theorems
Quotent Spaces
Instructors
Assoc. Prof. Dr. Ali GÜVEN
e-mail
[email protected]
Website
Percent
(%)
Code :
Course Title : Advanced Group Theory
Lecture
Application
42
0
Field: Mathematics
FMT5104
Laboratuary
Project/Field Homework
Study
0
0
0
Semester
Fall
Credits
Other
Total
198
240
Credit
T+A+L=Credit
3
ECTS
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the structure and properties of free groups and some graphs which is very important in group theory.
Learning
Outcomes and
Competences
● to be able to define the free groups,
● to be able to create the presentations of groups,
● to be able to compare the properties of free groups by graphs,
● to be able to express the 1-complexes and their Fundamentals properties,
● to be able to define the Cayley graphs.
Textbook and/or
References
Technical
Elective
Scientific
Social
Elective
D. L. Johnson , Presentatıons of groups, lms student texts 15, Cambrıdge Unıversıty Press, (1997).
R. C. Lyndon, P. E. Schupp, Combınatorıal Group Theory, Sprınger-Verlag, (1977).
G. M. S. Gomes, P. V. Sılva, J. E. Pın, Semıgroups, Algorıthms, automata and languages, World Scıentıfıc, (2002).
W. Magnus, A. Karrass, D. Solıtar, Combınatorıal group theory:Presentatıons of groups ın terms of generators and
relatıons, Dover Publıcatıons, (1975).
5) R. V. Book, F. Otto, Strıng rewrıtıng systems, Sprınger-Verlag, (1993).
1)
2)
3)
4)
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
Percent
(%)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
-
-
Midterm Exams
-
-
Quizzes
-
-
Midterm Controls
-
-
Homeworks
Term Paper
-
-
Term Paper
-
-
-
-
Oral Examination
-
-
Laboratory Work
-
-
Final Exam
-
-
Final Exam
X
100
Other
Other
Week
Subjects
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Instructors
Free groups and theır propertıes
Presentatıons of groups
Graphs and mappıng of graphs
Fundamental group of graph ıs free
Applıcatıons of nıelsen-screıer theorem
To construct the graph groups
Propertıes of free groups by graphs
1-complexes and theır Fundamentals properties
Homomorphısms over 1-complexes
General applıcatıons
2-complexes
Cayley graphs
The fundamental propertıes of cayley graphs
General applıcatıons
e-mail
[email protected]
Website
Assoc.Prof.Dr.Fırat ATEŞ
Code :
Course Title : Module Theory I
Lecture
Application
42
0
Field: Mathematics
FMT5106
Laboratuary
Study
0
0
0
Semester
Fall
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
Course Type
Basic
Scientific
Technical
Elective
Course
Objectives
To teach the module theory with a comprehensive manner.
Learning
Outcomes and
Competences
●
●
●
●
●
Scientific
6
Turkish/English
Language
Social
Elective
To be able to express the concepts of abelian groups and their properties,
To be able to define the concepts of commutator subgroups and their properties,
To be able to create the exact sequences on abelian groups,
To be able to define the concepts of module, submodule and to do their applications,
To be able to define the concepts of Artin and Noether modules.
1) Harmancı, Cebir II, Hacettepe yayınları, (1987).
2) V. P. Snaıth, Groups, rıngs and galoıs theory, World scıentıfıc, (2003).
3) J. J. Rotman, An ıntroductıon to the theory of groups, Sprınger- Verlag, (1995).
Textbook and/or
References
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
Percent
(%)
Midterm Exams
-
-
Quizzes
-
Homeworks
Term Paper
If any,
mark as
(X)
Percent
(%)
Midterm Exams
-
-
-
Midterm Controls
-
-
-
-
Term Paper
-
-
-
-
Oral Examination
-
-
Laboratory Work
-
-
Final Exam
-
-
Final Exam
X
100
Other
Other
Week
Subjects
1
2
3
4
5
6
7
8
9
10
11
12
13
14
İnstructors
Remind the fundamental algebraic structures
Finitely generated Abelian groups and properties
Series of groups and their types (compozıtıon series etc. vs.)
Commutator subgroups
Nilpotent and solvable groups
General applications
Exact sequences on f.g. Abelian groups
Basics of module, submodule and applications
Factor modules and homomorphisms
Direct sum and direct product
Free module and its properties
Injective and projective modules
Artin and noether modules
e-mail
[email protected]
Website
ECTS
Course Title:
Real Analysis I
Lecture
Code :
FMT5107
Application
42
Home
Laboratuary
Project/
Field Study work
0
0
0
Fall
Semester
Course Type
Course
Objectives
Field: Mathematics
Basic
Scientific
Scientific
Other
Total
198
240
0
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach fundamental concepts of Measure and integration theory in advanced level.






1.
2.
3.
Learning
Outcomes
and
Competences
Textbook
and /or
References
To be able to express the concepts of σ- Algebra and measure,
To be able to define the concepts of outer measure and measurable set,
To be able to define the concept of Lebesgue measure,
To be able to express the concept of measurable function,
To be able to the express the Lebesgue integral and its some properties,
To be able to define the product measures.
C. D. Aliprantis, O. Burkinshaw, Principles of Real Analysis, Academic Press, (1998).
W. Rudin, Real and Complex Analysis, McGraw Hill, (1987).
G. B. Folland, Real Analysis, John Wiley & Sons, Inc., (1999).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
σ- Algebras
Measures
Outer measures and measurable sets
Lebesgue measure
Measurable functions
Simple functions
Integration of simple functions
Integration of nonnegative functions
Fatou Lemma and Monotone convergence theorem
İntegrable functions
Lebesgue dominated convergence theorem
Integration of Complex functions
Product measures
Double integrals and Fubini’s theorem
Instructors
Assoc. Prof. Ali GÜVEN
e-mail
[email protected]
Website
Percent
(%)
Course Title: Quasiconformal Mappings
Lecture
Laboratuary
Project/
Home
Field Study
work
Application
42
0
0
Course
Objectives
Learning
Outcomes
and
Competences
Textbook
and /or
References
0
Fall
Semester
Course Type
Field: Mathematics
Code : FMT5108
Basic
Scientific
Scientific
Other
0
Total
198
Credits
Credit
ECTS
T+A+L=Credit
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach some selected topics of Complex Analysis and Quasiconformal mapping theory.
 To be able to define the concept of Conformal mapping,
 To be able to state the concept of normal family and Montel’s theorem,
 To be able to state The Riemann conformal mapping theorem,
 To be able to define the concept of Quasiconformal mappings,
 To be able to explain the relation between conformal and quasiconformal mappings.
1. V. V. Andrievskii, V. I. Beyli, V. K. Dzyadyk, Conformal invariants in constructive theory of functions of
complex variable, World Scientific, (2000).
2. L. Ahlfors, Lectures on Quasiconformal mappings, Mir, Moscow, (1969).
3. O. Lehto, K. I. Virtonen, Quasiconformal mappings in the plane, Springer-Verlag, (1987).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
x
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Conformal mappings
Some simple conformal mappings
Conformal automorphisms and izomorphisms
The normal families
The Montel compactness criterion
The Riemann conformal mapping theorem
Conformal mappings on the boundaries of the domains
Quasiconformal mappings
Different definitions of the quasiconformal mappings
Relation between conformal and quasiconformal mappings
The conformity modulus
Properties of the modulus
The quasiinvariantness of the modulus
Applications of the quasiinvariants in the Approximation theory
Instructors
Prof. Dr. Daniyal Israfilzade
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application.
42
0
Field: Mathematics
Code : FMT 5109
Laboratory. Project/Field Homework
Study
0
0
0
Fall
Semester
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
ECTS
6
Turkish/English
Language
Course Type
Basic
Scientific
Technical
Elective
Course
Objectives
Learning
Outcomes
and
Competences
To teach the general properties of curves and surfaces in three dimensional Euclidean space and
manifolds.
 To be able to express the general properties of curves in 3-dimensional Euclidean space,
 To be able to express the general properties of 1-forms and differential forms,
 To be able to express the fundamental conceptes about surfaces and manifolds,
 To be able to define the concepts of regular surface and oriented surface,
 To be able to define the mappings of surfaces.
Textbook
and /or
References
1) B. O’Neill, Elementary Differential Geometry, Academic Pres, Inc., 1966.
2) H. H. Hacısalihoğlu, Yüksek Diferensiyel Geometri’ ye Giriş, Fırat Ünv. Fen Fak. 1980.
Scientific
Social
Elective
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Curves in 3-dimensional Euclidean space, examples of some curves
1-forms
Differential forms
Frame fields, connection forms
The structural equations
Isometries
Orientation
Surfaces in 3-dimensional Euclidena space
Regular surfaces
Oriented surfaces
Mappings of surfaces
Topological properties of surfaces
Manifolds I
Manifolds II
Instructors
Prof. Dr. Cihan ÖZGÜR
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
N.E.C. Groups
FMT5111
Field: Mathematics
Home
Application Laboratuary
Project/
Field Study work
Lecture
42
0
0
0
Fall
Semester
Other
Total
198
240
0
Credits
Credit
ECTS
T+A+L=Credit
3
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach some fundamental definitions and theorems related with N.E.C. groups.
Learning
Outcomes
and
Competences
Textbook
and /or
References




Scientific
6
Technical
Elective
Social
Elective
To be able to define the concepts of NEC group and Fuchsian group,
To be able to define the concepts of discrete group and fundamental region,
To be able to find the presentation and the signature of NEC groups,
To be able to define the fundamental concepts of Hyperbolic geometry,
To be able to explain the relationships between Fuchsian groups and NEC groups.

1) T. Başkan, Discrete Groups (in Turkish), Hacettepe Üniversitesi Fen Fakültesi Yayınları, (1980).
2) E. Bujalance, J. J. Etayo, J. M. Gamboa, G. Gromadzki , Automorphisms Groups of Compact
Bordered Klein Surfaces. A Combinatorial Approach, Lecture Notes in Mathematics, SpringerVerlag, (1990).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Topological transformation groups
NEC groups
The properties of the NEC groups
Fuchsian groups
The elementary properties of the Fuchsian groups
The relationships between Fuchsian groups and NEC groups
Linear transformations with real coefficients
The elementary properties of the linear transformations with real coefficients
Discrete groups
The properties of discrete groups
Hyperbolic geometry
Fundamental regions
Surface signatures
The presentation of NEC groups
Instructors
Prof. Dr. Recep Şahin
e-mail
[email protected]
Website
Percent
(%)
Course Title: Modular Group and Extended
Code :
Modular Group
FMT5112
Lecture
Application
42
Field: Mathematics
Home
Laboratuary
Project/
Field Study work
0
0
0
Fall
Semester
Other
Total
198
240
0
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To give some fundamental definitions and theorems related with modular group and extended
modular group.


Learning
Outcomes
and
Competences
Textbook
and /or
References


Scientific
Technical
Elective
Social
Elective
To be able to define the fundamental properties of the Modular group,
To be able to define the concepts of Power subgroup, commutator subgroup and congruence
subgroup of the modular group,
To be able to obtain the generators and presentations of these subgroups,
To be able to express the relationships among these subgroups,
To be able to express the fundamental properties of the extended modular group and its subgroups.

1. M. Newman, Integral Matrices, Academic Press, (1972).
2. H.S.M. Coxeter and W.O.J. Moser, Generators and Relations for Discrete Groups, Springer,
(1972).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Percent
(%)
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Modular group and its properties
Generators and abstract presentation of the modular group
Fundamental region of the modular group
Power subgroups of the modular group
Commutator subgroups of the modular group
The relationships between the commutator subgroups and power subgroups of the modular
group
Congruence subgroups of the modular group
Principal congruence subgroups of the modular group
Extended modular group
Generators and abstract presentation of the extended modular group
Power subgroups and commutator subgroups of the extended modular group
The relationships between the commutator subgroups and power subgroups of the extended
modular group
Fundamental region of the extended modular group
The properties of the extended modular group
Instructors
e-mail
[email protected]
Website
Course Title: Theory of Approximation I
Lecture
0
0
Course
Objectives
Learning
Outcomes
and
Competences
Textbook
and /or
References
0
Basic
Scientific
Scientific
Other
0
Fall
Semester
Course Type
Field: Mathematics
Laboratuary
Project/
Home
Field Study
work
Application
42
Code : FMT5114
198
Total
Credits
Credit
ECTS
T+A+L=Credit
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach fundamental concepts and theorems of approximation theory in the real axis.


To be able to express the fundamental concepts of approximation theory,
To be able to express Weierstrass’s theorems for approximation by algebraic and trigonometric
polynomials,
 To be able to express the direct and converse of approximation theory,
 To be able to express the concepts of modulus of continuity,
 To be able to define the local and global estimations of approximation theory.
1.V. K. Dzyadyk, Introduction to the theory of uniform approximation of functions by polynomials (Russian),
Moscow, (1977).
2. R. A. De Vore and G. G. Lorentz, Constructive Approximation, Springer, (1993).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Percent
(%)
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Function Spaces
Fundamental problems of Approximation Theory
Approximation by algebraic polynomials and Weierstrass theorems
Approximation by trigonometric polynomials and Weierstrass theorems
The modulus of continuity and its properties
The direct theorems of polynomial approximation on the real line, Jackson’s theorems
The inverse theorems of polynomial approximation on the real line, Bernstein’s theorems
Local and global estimations of Approximation Theory
Lebesgue spaces
Modulus of smoothness in Lebesgue spaces
Approximation in the Lebesgue spaces
Direct theorems
Inverse theorems
Comparsion of the results
Instructors
e-mail
[email protected]
Website
Course Title:
Code :
Riemann Surfaces
FMT5115
Lecture
Application
42
0
Home
Laboratuary
Project/
work
Field Study
0
0
0
Fall
Semester
Course Type
Course
Objectives
Learning
Outcomes
and
Competences
Textbook
and /or
References
Field: Mathematics
Basic
Scientific
Other
Total
198
240
3
6
Turkish/English
Language
Scientific
Credits
Credit
ECTS
T+A+L=Credit
Technical Elective
Social
Elective
To introduce the basic knowledge about Riemann surfaces.




To be able to express the concepts of analytic and meromorphic continuation,
To be able to define the concepts of Riemann surface and abstract Riemann surface,
To be able to express the Monodromy theorem,
To be able to define the concepts of analytic, meromorphic and holomorphic functions on Riemann
surfaces,

To be able to define the Riemann surface of an algebraic function.
G. A. Jones and D. Singerman, Complex Functions, Cambridge University Press (1987).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
Meromorphic and analytic continuation
Analytic continuation using power series
Regular and singular points
Meromorphic continuation along a path
The Monodromy theorem
The Fundamental group
Riemann surfaces of the functions Log(z) and z1/q
Abstract Riemann surfaces
Analytic, meromorphic and holomorphic functions on Riemann surfaces
The Riemann surface of an algebraic function
Oriantable and non-oriantable surfaces
The genus of a compact Riemann surface
Conformal equivalence and automorphisms of Riemann surfaces
Covering surfaces of Riemann surfaces
Instructors
Prof. Dr. Nihal YILMAZ ÖZGÜR
e-mail
[email protected]
Website
Percent
(%)
Course Title : Representation Theory on
Groups
Lecture
Application
42
0
Field: Mathematics
Code : FMT5116
Laboratuar Project/Field Homework
y
Study
0
Semester
0
Other
Total
198
240
0
Fall
Credits
ECTS
Credit
T+A+L=Credi
t
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Technical
Elective
Course
Objectives
To teach the definitions and theorems of advanced group theory in a comprehensive manner.
Scientific
Social
Elective
● To be able to define the Jacabson radicals of an algebra,
Learning
Outcomes and
Competences
●
●
●
●
To be able to express the exact factorization modules,
To be able to express the Burnside theorem ,
To be able to construct the characters over different algebras,
To be able to define semi simple and simple algebras.
Textbook
and/or
References
1) J. L. Alperin, R. B. Bell, Groups and representations, Springer, (1995).
2) J. J. Rotman, An introduction to the theory of groups, Brown Publ., (1988).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
Midterm Exams
-
-
If any,
Percent
mark as
(%)
(X)
Midterm Exams
-
Percent
(%)
Quizzes
-
-
Midterm Controls
-
-
Homeworks
Term Paper
Laboratory Work
-
-
Term Paper
-
-
-
-
Oral Examination
-
-
-
-
Final Exam
-
-
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Instructors
Subjects
Remind the fundamental algebraic structures
Finitely generated Abelian groups and applications
C-algebras
Modules and homeomorphisms
Jacabson radicals of an algebra
Exact factorization modules
Sem simple and simple algebras
The characters over different algebras
Algebraic integers
Burnside theorem on p^a q^b
Applications of this theorem
e-mail
[email protected]
Website
Course Title:
Lecture
Application.
42
0
Field: Mathematics
Code : FMT 5119
Study
0
0
0
Fall
Semester
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
ECTS
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the general properties of differentiable manifolds, tensors, immersion and imbeddings,
connections and geodesics.




Learning
Outcomes
and
Competences

1)
2)
Textbook
and /or
References
Technical
Elective
Scientific
Social
Elective
To be able to define the notion of a differentiable manifold and to give examples,
To be able to define the general properties of tensors,
To be able to define the notions of affine connections and Riemannian connections,
To be able to define the notions of curvature tensor and sectional curvature,
To be able to define the notion of tensor on Manifolds.
Manfredo Perdigao do Carmo , Riemannian Geometry , Birkhauser, 1992.
W. M. Boothby, An introduction to Differentiable manifolds and Riemannian Geometry, Elsevier,
2003.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Visa examination
Midterm Exams
Quiz
Midterm Controls
Homework
Term Paper
Term project (project,
report, etc)
Oral Examination
Laboratory
Final Exam
Final examination
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Differentiable manifolds
Tangent spaces
Immersions and Imbeddings and some examples
Orientations
Vector fields, Lie brackets
Topology of Manifolds
Riemann metrics
Affine connections and Riemann connections
Geodesics
Convex neighborhoods
Curvature tensor and sectional curvature
Ricci curvature and scalar curvature
Tensors on Manifolds I
Tensors on Manifolds II
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application.
42
0
Field: Mathematics
Code : FMT 5120
Study
0
0
0
Fall
Semester
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
ECTS
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the general properties of differentiable manifolds, tensors, Riemannian and semiRiemannian manifolds and their submanifolds.
 To be able to define the notions of Riemannian and semi-Riemannian manifolds and to
give some examples of them,
 To be able to express general properties of tensors,
 Tobe able to define general properties of submanifolds
 Tobe able to define the notion of second fundamental form and to do its applications,
 Tobe able to define the notion of submanifolds with flat normal connection.
Learning
Outcomes
and
Competences
Technical
Elective
Scientific
Social
Elective
B. Y. Chen , Geometry of Submanifolds, Pure and applied mathematics (Marcel Dekker, Inc.), New York,
1973
Textbook
and /or
References
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Differentiable manifolds
Tensors
Riemannian manifolds
Semi-Riemannian manifolds
Exponential map and normal coordinates
Weyl conformal curvature tensor
Kaehler manifolds
Submersions and Projective spaces
Submanifolds
Induced connections
Second fundamental form and its properties I
Second fundamental form and its properties II
Curvature tensor of submanifolds
Submanifolds with flat normal connection
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title: Advanced Systems Theory I
Lecture
Laboratuary
Project/
Home
Field Study
work
Application
42
0
0
Course
Objectives
Basic
Scientific
Scientific
Other
0
198
Total
Credits
Credit
ECTS
T+A+L=Credit
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the concept of Mathematical control theory.
Learning
Outcomes
and
Competences
Textbook
and /or
References
0
Fall
Semester
Course Type
Field: Mathematics
Code : FMT5125
1.
2.
3.
 To be able to express continuous and discrete time state space systems,
 To be able to express the concepts of Laplace and Z transformations,
 To be able to define the concept of stability analysis,
 To be able to define the concept of Lyapunov stability,
 To be able to define the concepts of controllability and observabilty.
C. T. Chen, Linear System Theory and Design, Oxford University Press, 1999.
E. D. Sontag, Mathematical Control Theory, Springer-Verlag, 1990.
S. Barnett, R. G. Cameron, Introduction to Mathematical Control Theory, Oxford University Press, 1985.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Matrix Algebra
Continuous and discrete time state space systems.
Laplace transform, transfer function.
z transform.
General solutions using with similarity transformations.
Stability Theory and phase portraits.
Stability theory for linear systems
Lyapunov stability method.
Lyapunov stability method for linear systems.
Controllability.
Controllability Canonic Form.
Stabilizability.
Pole placement.
Observability, observers.
Instructors
Assoc. Prof. Dr. Necati ÖZDEMİR
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Convex functions and Orlicz spaces I
Lecture
Laboratuary
Project/
Home
Field Study
work
Application
42
0
0
Course
Objectives
Learning
Outcomes
and
Competences
Textbook
and /or
References
0
Fall
Semester
Course Type
Field: Mathematics
Code : FMT5126
Basic
Scientific
Scientific
Other
0
198
Total
Credits
Credit
ECTS
T+A+L=Credit
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach basic structure of Orlicz spaces.
 To be able to define the fundamental properties of the convex functions,
 To be able to define the notions of N function and complementary N function,
 To be able to define the Notion of Orlicz space,
 To be able to express the relation between Orlicz spaces and Lebesgue spaces,
 To be able to define the quivalent norms on the Orlicz spaces.
1. M. A. Krasnosel’ski and Ya. B. Rutickii, Convex funktions and Orlicz Spaces, Noordhoff, (1961).
2. C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, (1988).
3. M. M. Rao, Z. D. Ren, Applications of Orlicz Spaces, Marcel Dekker, (2002).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
x
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Convex functions and continuous functions
Properties of the convex functions
N function and its properties
Complementary N function and its properties
Young inequality
Some inequalities for the N functions and complementary N functions
Comparsion of the N functions
The fundamental part of the N function
 2 and  ’ conditions
 2 and  ’ conditions for the complementary N functions
Orlicz classes
Relation with Orlicz classes and Lebesgue spaces
Orlicz spaces
Equivalent norms on the Orlicz spaces
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application
42
0
Field: Mathematics
Code : FMT 5128
Contact Manifolds I
Study
0
0
0
Fall
Semester
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
Course Type
Basic
Scientific
Course
Objectives
To teach the general properties of contact structures and contact manifolds.

Learning
Outcomes
and
Competences




Textbook
and /or
References
6
Turkish/English
Language
Technical
Elective
Scientific
Social
Elective
To be able to define the notions of a contact structure and complex structure and to give some
examples of these kinds of structures,
To be able to define the notions of an integral submanifold and a contact transformation,
To be able to define the notions of Legendre curve and CR-submanifold and to give some
applications of them,
To be able to define the curvature of a contact metric manifold,
To be able to define the notions of -sectional curvature and Sasakian space form.
D. Blair , Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, 2002.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
ECTS
Subjects
Symplectic manifolds
Principal S1-bundles
Contact manifolds, examples
Almost complex and contact structures, examples of contact manifolds
Almost contact metric manifolds, examples
Integral submanifolds and contact transformations
Examples of contact integral submanifolds
Legendre curves and Withney spheres
Sasakian and cosymplectic manifolds
CR-manifolds
Product of almost contact manifolds
Curvature of contact metric manifolds
-sectional curvature, Sasakian space form
Examples of Sasakian space forms, locally -symmetric spaces
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application.
42
0
Study
0
0
0
Fall
Semester
Basic
Scientific
Course Type
Field: Mathematics
Code : FMT5129
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
6
Turkish/English
Language
Technical
Elective
Scientific
Social
Elective
To teach the general properties of Riemannian manifolds, tensors, almost complex and complex manifolds,
Hermitian manifolds, Kaehler Manifolds, Nearly Kaehlerian manifolds and Quaternion Kaehlerian
manifolds.

To be able to define the notion of a Riemannian manifold,

To be able to define the notions of tensor, Riemannian curvature tensor, Ricci tensor, sectional
curvature, scalar curvature and to give examples.

To be able to express the Gauss, Codazzi and Ricci equations,

To be able to define the notions of almost complex and complex manifolds,

To be able to define the notions of Hermitian manifold, Kaehler Manifold, Nearly Kaehlerian
manifold and Quaternion Kaehlerian manifolds.
Course
Objectives
Learning
Outcomes
and
Competences
Textbook
and /or
References
Kentaro Yano and Mashiro Kon , Structures On Manifolds, World Sci. 1984.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Percent
(%)
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
ECTS
Subjects
Riemannian manifolds
Tensors
Connections and covariant derivatives
Riemannian curvature tensor, Ricci tensor, sectional curvature, scalar curvature
Fibre bundles and covering spaces
Induced connection and second fundamental form
Gauss, Codazzi and Ricci equations
The Laplacian of the second fundamental form, submanifolds of space forms
Minimal submanifolds
Almost complex and complex manifolds
Hermitian manifolds
Kaehlerian Manifolds
Nearly Kaehlerian manifolds
Quaternion Kaehlerian manifolds
Instructors
e-mail
[email protected]
Website
Course Title:
Commutative Algebra
Lecture
Application
42
0
Lab.
Project/
Homework
Field Study
0
0
100
Fall
Semester
Basic
Scientific
Course Type
Course
Objectives
Institute: Graduate School of Natural and Applied
Sciences
Field
: Mathematics
Code :
FMT5130
Other
Total
98
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Scientific
Social
Elective
To teach the commutative rings including algebraic geometry, number theory and invariant theory.




To be able to define the concepts of ring, ideal and module,
To be able to express the Hilbert basis theorem,
To be able to define the integral extensions,
To be able to define the concept of an irreducible variete,
 To be able to define the concept of Artinian ring.
1. D. Eisenbud , Commutative Algebra with a View Toward Algebraic Geometry, Springer 1995.
2. M.F Atiyah and I.G. MacDonald, Introduction to Commutative Algebra, Perseus Books 1994.
3. E. Kunz , Introduction to Algebra and Algebraic Geometry, Birkhäuser Boston 1984.
Learning
Outcomes
and
Competencies
Textbooks
and /or
References
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as (X)
Percent
(%)
If any,
mark as (X)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homework
X
60
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
40
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Rings and Ideals
Radicals
Modules
The determinant trick
Noetherian rings
The Hilbert Basis Theorem
Integral Extensions
Noether Normalization
The Nullstellensatz
Irreducible Varieties
Ring of Fractions and Localization
Primary Decomposition
Artinian Rings
Discrete Valuation Rings
Instructor/s
Asst.Prof.Dr. Pınar Mete
e-mail
[email protected]
Website
http://matematik.balikesir.edu.tr
Percent
(%)
Course Title: Introduction to Fractional Calculus
Lecture
Laboratuary
Project/
Home
Field Study
work
Application
42
0
0
Course
Objectives
Basic
Scientific
Scientific
Other
0
198
Total
Credits
Credit
ECTS
T+A+L=Credit
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the concept of fractional derivative and fractional integral.
Learning
Outcomes
and
Competences
Textbook
and /or
References
0
Fall
Semester
Course Type
Field: Mathematics
Code : FMT5131
1.
2.
3.
 To be able to define special functions of fractional analysis,
 To be able to express the concepts of Riemann-Liouville fractional integral and derivative,
 To be able to express Grünwald-Letnikov fractional derivative and its properties,
 To be able to express Caputo fractional derivative and its properties,
 To be able to calculate the Laplace transforms of fractional derivatives,
 To be able to express solution methods of fractional-order differential equations.
I. Podlubny, Fractional Differential Equations, Academic Pres, 1999.
K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, 1974.
K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations,
John Wiley & Sons, Inc., 1993.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Percent
(%)
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
The origin of the fractional calculus.
Special functions of the fractional calculus.
Riemann-Liouville fractional integral and derivative.
Grünwald-Letnikov fractional derivative and its properties.
Caputo fractional derivative and its properties
Comparison of fractional derivative approaches.
Laplace transforms of fractional derivatives
Fractional-order differential equations.
Fractional Green functions.
Solution methods of fractional-order differential equations.
Numerical evaluation of fractional derivatives.
Comparison the analytical and numerical solutions of fractional-order differential equations.
Physical problems defined by fractional-order differential equations
MATLAB applications of problem solutions.
Instructors
e-mail
[email protected]
Website
Course Title:
Code :
Number Theory I
FMT5132
Lecture
Application
42
Field: Mathematics
Home
Laboratuary
Project/
Field Study work
0
0
0
Fall
Semester
Other
Total
198
240
0
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To give some fundamental definitions and theorems related with the number theory.
Scientific
Technical
Elective
Social
Elective




To be able to solve the linear Diophantine equations,
To be able to express Euler’s and Fermat’s Theorems,
To be able to solve systems of linear equations and congruence systems,
To be able to define the fundamental notions related to Fermat and Mersenne primes, Gauss and
Jacobi sums,
 To be able to apply division and Euclid’s algorithms.
1. K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer, (1990).
2. İ.N.Cangül, B. Çelik, Sayılar Teorisi Problemleri, Nobel Yayınları, (2004).
3.G. A.Jones and J.M. Jones, Elementary Number Theory, Springer, (2004).
Learning
Outcomes
and
Competences
Textbook
and /or
References
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Divisibility and Euclid’s Algorithm
Linear Diophantine Equations
Euler’s Function
Congruences and The Chinese Remainder Theorem
Euler’s Theorem and Fermat’s Theorem
Congruences Systems
Fermat prime and Mersenne prime
The ring Z[i] and Z[w]
Primitive Roots
The Group Structure of Un
Sums of Squares
Gauss Sums
Jacobi Sums
Divisibility and Euclid’s Algorithm
Instructors
Assist. Prof. Dr. Dilek Namlı
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
Function Spaces I
FMT5133
Field: Mathematics
Home
Project/
Field Study work
Lecture
42
0
0
Course
Objectives
Basic
Scientific
Total
198
240
0
Fall
Semester
Course Type
0
Other
Credits
Credit
ECTS
T+A+L=Credit
3
Turkish/English
Language
Technical
Elective
Scientific
6
Social
Elective
To teach several function spaces and relations among them.




Learning
Outcomes
and
Competences

1)
2)
Textbook
and /or
References
3)
To be able to define the notion of Lebesgue space,
To be able to define the notion of Orlicz space,
To be able to Express the relation between Orlicz and Lebesgue spaces,
To be able to define the concept of Rearrangement invariant Banach function space,
To be able to Express the relation between Orlicz and Rearrangement invariant Banach function
spaces.
C. Bennet and R. Sharpley, Interpolation of operators, Academic Pres, 1987.
M. A. Krasnosel’ski and Ya. B. Rutickii, Convex funktions and Orlicz Spaces, Noordhoff, (1961).
L. Grafakos, Classical Fourier Analysis, Springer, 2008.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Lebesgue spaces
Lebesgue spaces
Lebesgue spaces
Inequalities in Lebesgue spaces
Inequalities in Lebesgue spaces
Orlicz spaces
Orlicz spaces
Structure properties of Orlicz spaces
Rearrangement invariant Banach function spaces
Rearrangement invariant Banach function spaces
Main inequalities in Rearrangement invariant Banach function spaces
Main inequalities in Rearrangement invariant Banach function spaces
Particular cases of Rearrangement invariant Banach function spaces
Particular cases Rearrangement invariant Banach function spaces
Instructors
Assoc.Prof.Dr. Ramazan AKGÜN
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
Inversion Theory and Conformal Mappings
FMT5134
Field: Mathematics
Home
Project/
work
Field Study
0
0
0
0
Lecture
42
Fall
Semester
Course Type
Course
Objectives
Basic
Scientific
Total
198
240
6
Turkish/English
Language
Scientific
3
Technical Elective
Social
Elective
To introduce the basic knowledge about inversion theory and conformal mapping.


Learning
Outcomes
and
Competences
Textbook
and /or
References
Other
Credits
Credit
ECTS
T+A+L=Credit



1)
2)
To be able to define and to apply the concept of cross ratio,
To be able to express the definition and fundamnetal properties of fractional linear transformations
and to apply them,
To be able to define the concept of conformal mapping and to apply it,
To be able to define the Poincaré model of Hyperbolic geometry,
To be able to define the concept of inversion.
D. E. Blair, Inversion Theory and Conformal Mapping, AMS, Providence, RI, (2000).
G. A. Jones and D. Singerman, Complex Functions, Cambridge University Press, (1987).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
Classical inversion theory in the plane
Cross ratio
Applications: Miquel’s Theorem
Applications: Feuerbach’s Theorem
The extended complex plane and stereographic projection
Linear fractional transformations
Some special linear fractional transformations
Extended Möbius transformations
The Poincaré models of hyperbolic geometry
Conformal maps in the plane
Inversion in spheres, conformal maps in Euclidean space
Sphere preserving transformations
Surface theory, the classical proof of Liouville’s theorem
Curve theory and convexity
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title: Selected Topics in Differential
Geometry I
Lecture
Application
42
Lab.
Project/
Homework
Field Study
0
0
Basic
Scientific
Course
Objectives
0
Field: Mathematics
Other
Total
198
240
0
Fall
Semester
Course Type
Code : FMT5136
Scientific
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach fundamental concepts of Riemannian geometry and finite-type submanifolds.




Learning
Outcomes
and
Competencies
Textbooks
and /or
References

To be able to define the concept of differentiable manifold and to give examples,
To be able to define the concept of tangent space,
To be able to define the topology of manifolds,
To be able to define the concepts of Riemannian metric, affine and Riemannian connection and to
give examples,
To be able to define the concept of geodesic.
1)
2)
M.P. do Carmo, Riemannian Geometry, Birkhauser Boston 1992.
Bang-yen Chen, Total Mean Curvature and Submanifolds of Finite Type, World Scientific 1984.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as (X)
Percent
(%)
If any,
mark as (X)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Differentiable manifolds,
Differentiable manifolds,
Tangent space
Tangent space
Immersions and Embeddings
Immersions and Embeddings
Orientation
Vector fields,
Riemannian metrics, affine and Riemannian connections
Riemannian metrics, affine and Riemannian connections
Geodesics
Geodesics
Instructor/s
Assoc.Prof.Dr.BENGÜ BAYRAM
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application.
42
0
Field: Mathematics
Code : FMT5137
Study
0
0
0
Fall
Semester
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the general properties of differentiable manifolds, vector fields and Lie groups.





Learning
Outcomes
and
Competences
Textbook
and /or
References
Technical
Elective
Scientific
Social
Elective
To be able to define the concept of a differentiable manifold and to give some examples,
To be able to define the concept of submanifold,
To be able to express the fundamental geometrical structures of Lie groups,
To be able to define the concept of vector field on manifolds,
To be able to define one parameter subgroups of Lie groups.
Boothby, William M. An introduction to differentiable manifolds and Riemannian geometry. Second
edition. Academic Press, Inc., Orlando, FL, 1986.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
ECTS
Subjects
An introduction to manifolds
Multi variables functions and mappings
Vector fields and inverse function theorem
The rank of a mapping
Differentiable manifolds and examples
Differentiable functions and mappings
Applications
Submanifolds
Lie groups
Applications
Vector fields on manifolds
One parameter subgroups of Lie groups
Frobenius Theorem
Applications
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application.
42
0
Field: Mathematics
Code : FMT5138
Tensor Geometry I
Study
0
0
0
Fall
Semester
Basic
Scientific
Course
Objectives
To teach the fundamental knowledge about tensors.

Textbook
and /or
References
Total
Credit
T+A+L=Credit
198
240
3
Technical
Elective
Scientific
6
Social
Elective




To be able to define the notions of tensors, covariant and contravariant tensors and to
give their examples,
To be able to use tensors on Riemannian manifolds,
To be able to define and calculate the derivative of a tensor,
To be able to define the Christoffel symbols,
To be able to define the notions of Riemannian curvature tensor and sectional curvature.
1)
2)
3)
H. Hilmi Hacısalihoğlu , Tensör Geometri, Ankara Ünv. Fen-Fakültesi, 2003.
D. C. Kay, , Schaum’s outline of theory and problems, McGraw-Hill, 1988.
C. T. J. Dodson, T. Poston, Tensor geometry, Springer-Verlag, Berlin, 1991.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
ECTS
Turkish/English
Language
Course Type
Learning
Outcomes
and
Competences
Credits
Other
Subjects
Tensors, covariant and contravariant tensors
Applications
Tensor products of two tensors
Applications
Metric tensor
Applications
The derivative of a tensor
Applications
Tensors on Riemannian manifolds
Applications
Christoffel symbols
Applications
Riemannian curvature tensor, sectional curvature
Applications
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
FMT5140
Field: Mathematics
Home
Project/
work
Field Study
0
0
0
0
Lecture
42
Fall
Semester
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To introduce the basic knowledge about Möbius transformations and their elementary properties.

Learning
Outcomes
and
Competences




1)
2)
3)
Textbook
and /or
References
Scientific
Technical Elective
Social
Elective
To be able to define and apply basic properties of Möbius transformations on the extended complex
plane,
To be able to explain the relations between Möbius transformations and circles,
To be able to explain fundamental properties of the inversion in a circle,
To be able to define types of transformations and to give examples,
To be able to define the notion of isometric circle.
L. R. Ford, Automorphic Functions, Chelsea Pub. Co., 1951.
G. A. Jones and D. Singerman,Complex Functions, Cambridge University Press, 1987.
A. F. Beardon, Algebra and geometry, Cambridge University Press, Cambridge, 2005.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Percent
(%)
Other
Subjects
The Riemann sphere and behaviour of functions at infinity
The definition and basic properties of Möbius transformations (linear fractional transformations)
The connection between Möbius transformations and matrices, and the group PGL(2,C)
Fixed points of the Möbius transformations
Transitivity and cross-ratios
Möbius transformations and circles
Inversion in a circle
The Multiplier, K
Hyperbolic transformations
Elliptic transformations
Loxodromic transformations
Parabolic transformations
The isometric circle
The unit circle
Instructors
e-mail
[email protected]
Website
Course Title:
Averaged moduli and one sided approximation I
Lecture
Application
42
0
Course
Objectives
Fall
Basic
Scientific
Other
Total
198
240
3
6
Turkish/English
Language
Scientific
Credits
Credit
ECTS
T+A+L=Credit
Technical Elective
Social
Elective
To teach the averaged moduli and their applications.



Learning
Outcomes
and
Competences
Textbook
and /or
References
Field: Mathematics
Home
Laboratuary
Project/
work
Field Study
0
0
0
Semester
Course Type
Code :
FMT5141


To be able to define the notions of integral moduli and averaged moduli,
To be able to express Whitney type inequalities,
To be able to express interpolation theorems,
To be able to express the quadrature formulas for periodic functions,
To be able to define the notions of Bernstein and Szasz-Mirakian operators.
Bl. Sendov and V. A. Popov, The avaraged moduli of smoothness, 1988.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
% 100
Other
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Preliminaries
Integral moduli and averaged moduli
Interrelations of two moduli
Whitney type inequalities
Intermediate approximation
Intermediate approximation
Interpolation theorems
Quadrature formulas for periodic functions
Quadrature formulas for periodic functions
Bernstein operators, Szasz-Mirakian operators
Bernstein operators, Szasz-Mirakian operators
Korovkin theorems in Lp
Interpolation splines
Interpolation splines
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Code :
FMT5142
Application
42
0
Home
Laboratuary
Project/
work
Field Study
0
0
0
Fall
Semester
Course Type
Course
Objectives
Basic
Scientific
Other
Total
198
Credits
Credit
ECTS
T+A+L=Credit
240
6
Turkish/English
Language
Scientific
3
Technical Elective
Social
Elective
To teach the fundemantal properties of strong approximation.



Learning
Outcomes
and
Competences


Textbook
and /or
References
Field: Mathematics
To be able to define the order of strong approximation in Lipschitz class,
To be able to define the order of strong approximation in WrHw class,
To be able to express the basic theorems of strong approximation by (C,alpha) means of negative
order,
To be able to define the strong approximation by matrix means,
To be able to apply these concepts
Laszlo Leindler, Strong approximation by Fourier series, Akademiai Kiado., 1985.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
% 100
Other
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Preliminaries
Order of strong approximation in Lipschitz class
Order of strong approximation in WrHw class
Strong approximation by (C,alpha) means of negative order
Some applications
Some applications
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
FMT5143
Finite Blaschke Products I
Field: Mathematics
Home
Project/
work
Field Study
0
0
0
0
Lecture
42
Fall
Semester
Course Type
Course
Objectives
Basic
Scientific
Other
Total
198
240
3
6
Turkish/English
Language
Scientific
Credits
Credit
ECTS
T+A+L=Credit
Technical Elective
Social
Elective
To introduce the basic knowledge about Finite Blaschke Products and their elementary properties.





1)
2)
Learning
Outcomes
and
Competences
3)
Textbook
and /or
References
4)
5)
To be able to define the concepts of Möbius transformation and finite Blaschke product,
To be able to prove the basic theorems about finite Blaschke products,
To be able to define and apply geometric properties of finite Blaschke products,
To be able to express the uniqueness theorem for monic Blaschke products,
To be able to express the relations between ellipses and finite Blaschke products.
L. R. Ford, Automorphic Functions, Chelsea Pub. Co., 1951.
R. L. Craighead and F. W. Carroll, A decomposition of finite Blaschke products. Complex Variables
Theory Appl. 26 (1995), no. 4, 333-341.
A. L. Horwitz and A. L. Rubel, A uniqueness theorem for monic Blaschke products. Proc. Amer.
Math. Soc. 96 (1986), no. 1, 180-182.
J. Mashreghi, Expanding a finite Blaschke product. Complex Var. Theory Appl. 47 (2002), no. 3,
255-258.
U. Daepp, P. Gorkin and R. Mortini, Ellipses and finite Blaschke products. Amer. Math. Monthly
109 (2002), no.9, 785-795.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
Möbius transformations
Basic properties of Möbius transformations
The Multiplier, K
The isometric circle
The unit circle
The definition and basic properties of finite Blaschke products
A decomposition of finite Blaschke products I
A decomposition of finite Blaschke products II
A uniqueness theorem for monic Blaschke products
Expanding a finite Blaschke product I
Expanding a finite Blaschke product II
Basic geometric properties of finite Blaschke products
Ellipses and finite Blaschke products I
Ellipses and finite Blaschke products II
Instructors
e-mail
[email protected]
Website
Percent
(%)
Lecture
Sciences
Field
: Mathematics
Code :
Course Title:
Algebra I
FMT5144
Application
42
0
Lab.
Project/
Homework
Field Study
0
0
100
Fall
Semester
Basic
Scientific
Course Type
Course
Objectives
Other
Total
98
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Scientific
Technical
Elective
Social
Elective
To teach the basic concepts of algebra in graduate level.
 To be able to state and prove some of the classical theorems of finite group theory,
 To be able to determine whether or not there can be a simple group of a given order,
 To be able to present the facts in the theory of rings,
 To be able to construct a factor ring from an ideal in a ring,
 To be able to define the ideal structure of Euclidean domains.
1. T. W. Hungerford, Algebra, Springer 1996.
2. D.S. Dummit and R.M.Foote, Abstract Algebra, Wiley 2nd edition ,1999.
3. N. Jacobson, Basic Algebra I-II, Dover Publications, 2009.
4. H.İ. Karakaş, Cebir Dersleri, TUBA 2008.
Learning
Outcomes
and
Competencies
Textbooks
and /or
References
ASSESSMENT CRITERIA
Theoretical Courses
Midterm Exam
If any,
mark as (X)
Percent
(%)
X
30
Quizzes
If any,
mark as (X)
Midterm Exams
Midterm Controls
Homework
X
40
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
30
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Groups: Review basic group theory
Isomorphisms theorems
Symmetric, Alternating and Dihedral Groups
Direct Products and Direct Sums
Free groups, Free Abelian groups, Group actions
The Sylow Theorems
Classification of Finite Groups
Nilpotent and Solvable Groups
Normal and Subnormal Series
Introduction to Rings: Homomorphisms, Ideals
Factorization in Commutative Rings
Rings of Quotients and Localization
Ring of Polynomials and Formal Power Series
Factorization in Polynomial Rings
Instructor/s
Asst. Prof.Dr. Pınar Mete
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
FMT5145
Lecture
Application
42
0
Course
Objectives
Credits
Laboratuary
Project/
Hw.
Field Study
0
0
0
Fall
Semester
Course Type
Institute: Institute of Science
Field: Mathematics
Basic
Scientific
Other
Total
T+A+L=
Credit
ECTS
198
240
3
6
Turkish/English
Language
Technical
Elective
Scientific
Social
Elective
To introduce properties of orthogonal polynomials and expansions on complex plane.




Learning
Outcomes
and
Competences
1)
2)
Textbook
and /or
References
3)
4)
To be able to express the fundamental properties of orthogonal polynomials,
To be able to define the properties of orthogonal polynomials on an interval,
To be able to define the properties of orthogonal polynomials over a region,
To be able to express the general properties of the polynomials which are expressed with the help of
orthogonal polynomials,

To be able to define the approximation properties of the polynomials which are expressed with the
help of orthogonal polynomials.
P. K. Suetin, Fundamental Properties of Polynomials Orthogonal on a Contour, Russ. Math. Surv., 1966.
P. K .Suetin, Polynomials Orthogonal over a region and Bieberbach Polynomials, Proceedings of the
Steklov Institute of Mathematics, AMS, 1974.
D.Gaier, Lectures on Complex Approximation,1985.
V.V. Andrievskii, H. P. Blatt, Discrepancy of Signed Measures and Polynomial Approximation,
Springer, 2001.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
The fundamental properties of orthogonal polynomials
The construction of orthogonal polynomials by Gram-Schmidt method
The construction of orthogonal polynomials by moments
Orthogonal polynomials on an interval
Orthogonal polynomials over a region
Orthogonal polynomials on the boundary of a region
Estimation of the leading coefficient
The polynomials which are expressed orthogonal polynomials: Bieberbach polynomials
Approximation of Bieberbach polynomials
The zeros of orthogonal polynomials
Estimations the rate of approximation of zeros
Erdös-Turan type theorems
Asymptotic behavior of zeros of Bieberbach polynomials
Relations with potential theory
Instructors
Assist. Prof. Dr. Burcin OKTAY
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Banach Spaces of Analytic Functions I
Lecture
Application
42
0
Code :
FMT5146
Course
Objectives
Credits
Laboratuary
Project/
Hw.
Field Study
0
0
0
Fall
Semester
Course Type
Field: Mathematics
Basic
Scientific
Scientific
Other
Total
T+A+L=
Credit
ECTS
198
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To introduce fundamental properties of Hp and hp Spaces.






1)
2)
Learning
Outcomes
and
Competences
Textbook
and /or
References
3)
To be able to express some properties of harmonic functions,
To be able to define the Poisson integral of a function,
To be able to express the fundamental properties of hp Spaces,
To be able to define the Blaschke products,
To be able to express the fundamental properties of Hp Spaces,
To be able to define the concepts iner and outer functions.
P. Koosis, Introduction to Hp Spaces, Cambridge University Press (1998).
P. L. Duren, Teory of Hp spaces, Academic Press (1970).
J. B. Garnett, Bounded Analytic Functions, Academic Press (1981).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Harmonic functions in the unit disk
Poisson kernel and the Poisson integral
Boundary behaviour of harmonic functions
Subharmonic functions
The spaces hp and Hp
The Nevanlinna class N
Boundary behaviour of analytic functions
Blaschke products
Inner and outer functions
Mean convergence to boundary values
The class N+
Harmonik majorants
The space H1 and Cauchy integral
Description of boundary values
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Fourier Analysis I
Code :
FMT5147
Lecture
Application
42
0
Course
Objectives
Fall
Basic
Scientific
Other
Total
T+A+L=
Credit
ECTS
198
240
3
6
Turkish/English
Language
Technical
Elective
Scientific
Social
Elective
To introduce fundamental concepts and theorems related to Fourier analysis.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Credits
Laboratuary
Project/
Hw.
Field Study
0
0
0
Semester
Course Type
Field: Mathematics
1)
2)
3)

To be able to define the concept of distribution function,

To be able to express the approximate identities,

To be able to express the Marcinkiewicz interpolation theorem,

To be able to express the Riesz-Thorin interpolation theorem,

To be able to define the Hardy-Littlewood maximal function,

To be able to define the Fourier and inverse Fourier transforms.
L. Grafakos, Classical Fourier Analysis, Springer (2008).
J. Duoandikoetxea, Fourier Analysis, American Math. Soc. (2001).
E.M.Stein, G.Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press (1971).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Lp and weak Lp spaces
The distribution function
Topological groups
Convolution
Approximate identities
Marcinkiewicz interpolation theorem
Riesz-Thorin interpolation theorem
Decreasing rearrangements
Lorentz spaces
Duals of Lorentz spaces
The Hardy-Littlewood maximal function
The class of Schwartz functions
Fourier transforms of Schwartz functions
The Inverse Fourier transform
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application
42
0
Code :
FMT5148
Course
Objectives
Credits
Laboratuary
Project/
Hw.
Field Study
0
0
0
Fall
Semester
Course Type
Field: Mathematics
Basic
Scientific
Scientific
Other
Total
T+A+L=
Credit
ECTS
198
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To introduce Fundamental properties of Trigonometric Fourier series.






1.
2.
To able to define Fourier series,
To able to define the notions of Dirichlet, Fejer and Poisson kernels,
To able to express summability of Fourier series by Cesaro method,
To able to express summability of Fourier series by Abel’s method,
To able to define the concept of conjugate function and M. Riesz’s theorem,
To able to define the norm convergence of Fourier series.
A. Zygmund, Trigonometric Series, Cambridge Univ. Press (1959).
Y. Katznelson, An Introduction to Harmonic Analysis, Cambridge Univ. Press (2004)
3. R.A. DeVore, G.G.Lorentz, Constructive Approximation, Springer-Verlag (1993).
Learning
Outcomes
and
Competences
Textbook
and /or
References
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
The spaces C and Lp
Best approximation
Weierstrass approximation theorems
Trigonometric series and conjugate series
Fourier series
Partial sums and the Dirichlet kernel
Fejer kernel and ve Fejer means
Convergence of the Fejer mean, Fejer’s theorem
Pointwise convergence of Fourier series
Almost everywhere convergence of Fourier series, the Carleson-Hunt theorem
Poisson kernel and Abel-Poisson means
Conjugate functions and theorem of M. Riesz
Convergence of Fourier series in the norm
Marcinkiewicz multiplier theorem and Littlewood-Paley theorem
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title: Applied Mathematics I
Lecture
Lab.
Project/
Homework
Field Study
0
0
0
Application
42
0
Spring
Semester
Course Type
Course
Objectives
Learning
Outcomes
and
Competencies
Textbooks
and /or
References
Basic
Scientific
Field: Mathematics
Code : FMT5149
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish
Language
Scientific
Technical
Elective
Social
Elective
To teach the methods which are usually used in applied mathematics and give their Maple applications.





To be able to express the class of first order ordinary differential equation,
To be able to solve first order linear differential equation and do MAPLE applications,
To be able to express high order ordinary differential equations and do MAPLE
applications,
To be able to apply Laplace, inverse Lapalce and Fourier transformation in MAPLE,
To be able to express the concept of Legendre equations and polynomials.
1. E. Hasanov, G. Uzgören, A. Büyükaksoy, Diferansiyel Denklemler Teorisi, Papatya, 2002.
2. B. Karaoğlu, Fizikte ve Mühendislikte Matematik Yöntemler, Seyir, 2004.
3. C. T. J. Dodson, E. A. Gonzalez, Experiments in Mathematics Using Maple, Springer, 1991.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as (X)
Percent
(%)
If any,
mark as (X)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Classes of first order ordinary differential equations.
Classes of first order ordinary differential equations., Bernoulli, Riccati etc.
Higher order differential equations.
Laplace transformations.
Inverse Laplace transformations.
Solving differential equations with Laplace Transformations.
Fourier transformations.
Legendre equations and polynomials.
Introduction to maple.
Plotting with Maple.
Solving first order differential equations with Maple.
Solving higher order differential equations with Maple.
Laplace applications with Maple.
Fourier applications with Maple.
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title: Advanced Numerical Analysis I
Lecture
Application
42
0
Lab.
Project/
Homework
Field Study
0
0
0
Spring
Semester
Course Type
Course
Objectives
Learning
Outcomes
and
Competencies
Textbooks
and /or
References
Basic
Scientific
Field: Mathematics
Code : FMT5150
Scientific
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish
Language
Technical
Elective
Social
Elective
To teach advanced techniques of methods which are used while make numerical calculation.
 To be able to solve nonlinear equations by applying numerical analysis methods,
 To be able to do approximation by using polynomials,
 To be able to apply numerical derivation and integration operations,
 To be able to solve the problems of eigenvalues and eigenvectors,
 To be able to find inverse with Sequential Iteration Methods.
1) G. Amirali, H. Duru, Nümerik Analiz, Pegem A Yayınları, 2002,
2) A. Ralston, A First Course in Numerical Analysis, McGraw-Hill,1978,
3) S.C. Chapra, R.P. Canale, Numerical Methods for Engineers, McGraw-Hill, 1990.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as (X)
Percent
(%)
If any,
mark as (X)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Percent
(%)
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Nonlinear Equations, Existence Theorems
Newton and semi-Newton Methods, Optimization,
Local and Maximum Notions, Methods of Foundation of True,
The Method of Foundation of Maximum Variable, Conjugate Gradient Method,
Minimization of Quadratic Function,
Conjugate Direction Methods,
Lagrange Multipliers, Kuhn-Tucker Conditions,
Approximation Method of Polynomials,
Orthogonal Polynomials,
Approximation in Maximum Norm,
Numerical Differentiable, Richardson Extrapolation,
Numerical Integration, Gaussian Integration Formulas, Calculation of Generalized Integrals,
Eigenvalues and Eigenvectors Problem,
Foundation of Inverse with Sequential Iteration Methods
Instructors
Assist. Prof. Dr. Figen KİRAZ
e-mail
[email protected]
Website
Course Title: Differential Geometry of Curves
and Surfaces I
Lecture
Application
42
Lab.
Project/
Homework
Field Study
0
0
0
Basic
Scientific
Field: Mathematics
Other
Total
198
240
0
Fall
Semester
Course Type
Code : FMT5151
Scientific
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
Course
Objectives
To teach the differential geometry of curves and surfaces both in local and global aspects.
Learning
Outcomes
and
Competencies





Textbooks
and /or
References
Manfredo P. do Carmo, Differential Geometry of Curves and Surfaces, 1976.
To able to define the concepts of parametrized curves and regular curves,
To able to express the local Canonical form,
To able to express the global properties of plane curves,
To able to express the notions of the tangent plane, the differential of a map, the first fundamental form,
To able to characterize the compact orientable surfaces.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as (X)
Percent
(%)
If any,
mark as (X)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Parametrized curves, Regular curves,
Parametrized curves, Regular curves,
The vector product in R^3, The local theory of curves parametrized by arc length,
The vector product in R^3, The local theory of curves parametrized by arc length,
The local Canonical form, Global properties of plane curves.
The local Canonical form, Global properties of plane curves.
Regular surfaces, Inverse images of regular values ,
Regular surfaces, Inverse images of regular values ,
Change of parameters, Differential functions on surfaces ,
Change of parameters, Differential functions on surfaces
The tangent plane, The differential of a map, The first fundamental form ,
The tangent plane, The differential of a map, The first fundamental form
Orientation of surfaces, A characterization of compact orientable surfaces,
Orientation of surfaces, A characterization of compact orientable surfaces,
Instructor/s
Assoc. Prof. Dr. Bengü Bayram
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
FMT5152
Field: Mathematics
Home
Project/
Field Study work
Lecture
42
0
0
0
Fall
Semester
Course Type
Course
Objectives
Basic
Scientific
Scientific
Other
Total
198
240
0
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the fundamental concepts and theorems of Fuzzy topological spaces.




Learning
Outcomes
and
Competences

1.
2.
3.
4.
Textbook
and /or
References
5.
To be able to define the basic concepts about Fuzzy sets and to state theorems,
To be able to do algebraic operations on Fuzzy sets,
To be able to define the concept of convexity in Fuzzy sets,
To be able to do Cartesian Product of Fuzzy sets,
To be able to find the image and reverse image of Fuzzy Sets under a function.
Şaziye Yüksel, Genel Topoloji, Eğitim Kitapevi, 2011.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
Fuzzy Sets
Fuzzy Set Concept
Fuzzy sets Transactions
Algebraic Operations on Fuzzy sets
Problem solving
Convexity of fuzzy sets
The Concept of Fuzzy Relation,
Cartesian Product of Fuzzy sets
Family of Fuzzy Sets
The image of Fuzzy Sets under a function
The reverse image of Fuzzy Sets Under a function
Problem solving
The concept of fuzzy point.
General review of the issues.
Instructors
Assoc. Prof. Dr. Ahu Açıkgöz
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
Introduction to Ideal Topological Spaces I
FMT5153
Field: Mathematics
Home
Project/
Field Study work
Lecture
42
0
0
0
Fall
Semester
Course Type
Basic
Scientific
Course
Objectives
Scientific
Other
Total
198
240
0
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach properties and several examples of Ideal topological spaces.





1.
2.
3.
4.
Learning
Outcomes
and
Competences
Textbook
and /or
References
5.
To be able to define the basic concepts and the seperation properties of Ideal topological spaces,
To be able to construct topologies by using maximal and minimal Ideals,
To be able to express several Ideal examples and their properties,
To be able to define the seperation axioms in Ideal topological spaces,
To be able to define the concept of compactness in Ideal topological spaces.
Şaziye Yüksel, Genel Topoloji, Eğitim Kitapevi, (2011).
Osman Mucuk, Topoloji, Nobel Kitapevi, (2009).
Mahmut Koçak, Genel Topoloji I ve II, Gülen Ofset Yayınevi, (2006).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
The concept of Ideally
Maximal ideal
Minimal ideal
Comparisons
Local function
*- topology, and generalized open sets
The ideal characteristics and a variety of the ideal samples
Problem solving
Ideal topological spaces and separation axioms
*- topological features
Compactness in ideal topological spaces
Various sets in ideal topological spaces.
Some properties of the sets
General review of the issues
Instructors
e-mail
[email protected]
Website
Percent
(%)
Code :
Course Title: Algebraic number theory I
Field: Mathematics
FMT5154
Home
Project/
Field Study work
Lecture
42
0
0
Course
Objectives
Learning
Outcomes
and
Competences
Textbook
and /or
References
Basic
Scientific
Total
198
240
0
Fall
Semester
Course Type
0
Other
3
6
Turkish/English
Language
Technical
Elective
Scientific
Credits
Credit
ECTS
T+A+L=Credit
Social
Elective
To give fundamental concepts and theorems related with the algebraic number theory.




To be able to define the concepts of ring, field and algebraic field extensions,
To be able to define the Dedekind domains,
To be able to define the norms of ideals,
To be able to define the prime factors in a number field,
 To be able to find units in quadratic fields.
1) E. Weiss, Algebraic Number Theory, Dover publications, 1998.
2) I. Stewart, D. Tall, Algebraic Number Theory and Fermat’s Last Theorem, A K Peters Ltd., 2002.
3) M.R. Murty, J. Esmonde, Problems in Algebraic Number Theory, Springer,2005.
4) Ş. Alaca, K. S. Williams, Introductory Algebraic Number Theory, Cambridge Univ. Press, 2004.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Rings
Fields
Algebraic Extensions of a Field
Algebraic Extensions of a Field
Algebraic Number Fields
Algebraic Number Fields
Conjugates
Dedekind Domains
Dedekind Domains
Norms of Ideals
Norms of Ideals
Prime factoring in a number field
Units in Real Quadratic Fields
Units in Real Quadratic Fields
Instructors
Assoc. Prof. Dr. Sebahattin İkikardes
e-mail
[email protected]
Website
http://w3.balikesir.edu.tr/~skardes/
Percent
(%)
Course Title:
Lecture
Application
42
0
Code :
FMT5155
Field: Mathematics
Credits
Laboratuary
Project/
Hw.
Field Study
0
0
0
Fall
Semester
Other
Total
T+A+L=
Credit
ECTS
198
240
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the one-to-one correspondence between analytic properties of the functions and geometric properties
of the domains.

To be able to define the concepts of curve, domain, simply connected domain and multiply connected
domain,

To be able to express the fundamental properties of conformal mappings,

To be able to define the boundary behavior of derivatives,

To be able to define the modulus of continuity and its properties,

To be able to express the fundamental properties of Smirnov Lavrentiev domains.
1. Ch. Pommerenke, Boundary Behaviour of Conformal Maps,1992
2. Zeev Nehari, Conformal Mapping, 1952.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Scientific
Technical
Elective
Social
Elective
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Curve, Domain, Simply connected domain, Multiply connected domain
Conformal mappings
Analytic curves
Smooth Jordan curves
Domains by bounded boundary rotation
The analytic characterization of smoothness
The boundary behavior of derivatives
Modulus of continuity
Quasidisks
John Domains
Quasiconformal extension
Rectifiable curves
Smirnov Domains
Lavrentiev domains
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title: Numerical Optimization I
Lecture
Laboratuary
Project/
Home
Field Study
work
Application
42
Field: Mathematics
Code : FMT 5156
0
0
0
Fall
Semester
Other
0
198
Total
Credits
Credit
ECTS
T+A+L=Credit
240
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the fundamental concepts of linear programming and unconstrained optimization problems with
solution methods.
 To be able to express the fundamental concept of optimization problems,
 To be able to define linear programming problems,
 To be able to solve LP problems by Simplex method,
 To be able to express optimality conditions for unconstrained optimization problems,
 To be able to express line search method,
 To be able to apply basic descent, conjugate gradient and quasi newton methods.
Learning
Outcomes
and
Competences
1)
Textbook
and /or
References
2)
3)
4)
5)
6)
Scientific
Technical
Elective
Social
Elective
Bazaraa M.S., Sherali H.D. and Shetty S.M., Nonlinear programming: Theory and Applications, 3rd edition,
Chong E.K. and Zak S.H., An introduction to optimization, 2nd edition, John Wiley & Sons, Inc., 2001.
Griva I., Nash S.G. and Sofer A., Linear and nonlinear optimization, 2nd edition, SIAM, 2008.
Luenberger D.G. and Ye Y., Linear and nonlinear programming, 3rd edition, Springer, 2008.
Nocedal J. and Wright S.J., Numerical optimization, Springer, 1999.
Sun W. and Yuan Y-X, Optimization Theory and Method: Nonlinear Programming, Springer, 2006.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Mathematical review and background
Fundamentals of optimization
Basic properties of linear programming
The simplex method
The simplex method and analysis
Duality
İnterior-point method
Unconstrained optimization
Optimality conditions and basic properties
Line search methods
Basic descent methods
Conjugate direction method
Quasi-newton method
Trust-region method
Instructors
Assist. Prof. Dr. Fırat EVİRGEN
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
FMT5157
Field: Mathematics
Home
Project/
work
Field Study
0
0
0
0
Lecture
42
Fall
Semester
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To introduce the basic knowledge about Fibonacci, Lucas and generalized Fibonacci polynomials and their
elementary properties.
 To be able to define the concepts of Fibonacci, Lucas and generalized Fibonacci polynomials and
their basic properties,
 To be able to use and apply these basic properties in some analysis problems,
 To be able to find the generating functions,
 To be able to find the zeros of Fibonacci and Lucas polynomials,
 To be able to define the Jacobsthal polynomials.
1) T. Koshy, Fibonacci and Lucas numbers with applications, Wiley, 2001.
2) V. E. Hoggatt and M. Bicknell, Generalized Fibonacci polynomials, Fibonacci Quart. 11(5), 457-465,
1973.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Scientific
Technical Elective
Social
Elective
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
Fibonacci and Lucas numbers
Generalized Fibonacci numbers
Generating functions
Fibonacci and Lucas series I
Fibonacci and Lucas series II
Fibonacci polynomials
Byrd’s Fibonacci polynomials
Applications
Lucas polynomials
Jacobsthal polynomials
Applications
Zeros of Fibonacci and Lucas polynomials I
Zeros of Fibonacci and Lucas polynomials II
Applications
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lorentzian Geometry
Lecture
Application
42
0
Lab.
Project/
Homework
Field Study
0
0
0
Fall
Semester
Basic
Scientific
Course Type
Course
Objectives
Field: Mathematics
Code : FMT5158
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Scientific
Technical
Elective
Social
Elective
To teach general properties of Lorentzian manifolds.





Learning
Outcomes
and
Competencies
Textbooks
and /or
References
To be able to define the concepts of Lorentzian metric and Lorentzian space,
To be able to express the fundamental properties of Lorentzian manifolds,
To be able to define the concepts of Minkowski space time and Robertson-Walker space time,
To be able to express the fundamental properties of the Schwarzschild and Kerr space time,
To be able to define bi-linear Lorentzian metrics on Lie groups.
J. K. Beem, P. E. Ehrlich and K. L. Easley, Global Lorentzian Geometry, Second Edition, Pure and Applied
Mathematics, Marcel Dekker, Inc., 1996.
ASSESSMENT CRITERIA
Theoretical Courses
Midterm Exams
If any,
mark as (X)
Percent
(%)
X
40
If any,
mark as (X)
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
60
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Lorentzian metric and Lorentzian space
Lorentzian manifolds
Convex normal neighborhoods
Curves and topology on curves
Two dimensional space times
The second fundamental form
Warped products
Homothetic maps
Minkowski space time
Schwarzschild-Kerr space times
Spaces of constant curvature
Robertson-Walker space times
Bi-linear Lorentzian metrics on Lie groups
Lorentzian sectional curvature
Instructor/s
Assist. Prof. Dr. Sibel SULAR
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application
42
0
Lab.
Project/
Homework
Field Study
0
0
0
Fall
Semester
Basic
Scientific
Course Type
Course
Objectives
Field: Mathematics
Code : FMT5159
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Scientific
Technical
Elective
Social
Elective
To teach general properties of Semi-Riemannian manifolds.





1)
2)
Learning
Outcomes
and
Competencies
Textbooks
and /or
References
To be able to express the fundamental properties of Semi-Riemannian manifolds,
To be able to define the concepts of type changing and metric contraction,
To be able to define the geometrical structure of warped product manifolds,
To be able to express the fundamental properties of Lightlike manifolds,
To be able to define Non-Degenerate and Null curves in Semi-Riemannian manifolds.
B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, Inc., 1983.
K. L. Duggal D. H. Jin, Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Sci.,
2007.
ASSESSMENT CRITERIA
Theoretical Courses
Midterm Exams
If any,
mark as (X)
Percent
(%)
X
40
If any,
mark as (X)
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
60
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Symmetric bilinear forms
Isometries
The Levi-Civita connection
Parallel translation
Geodesics
Curvatures
Semi-Riemannian surfaces
Type changing and metric contraction
Frame fields
Some differential operators
Semi-Riemannian manifolds
Warped product manifolds and curvatures of warped product manifolds
Lightlike manifolds
Non-Degenerate and Null curves in Semi-Riemannian manifolds
Instructor/s
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Tangent and Cotangent Bundle Theory
Lecture
Application
42
0
Lab.
Project/
Homework
Field Study
0
0
0
Fall
Semester
Basic
Scientific
Course Type
Course
Objectives
Field: Mathematics
Code : FMT5160
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Scientific
Technical
Elective
Social
Elective
To teach fundamnetal properties of tangent and cotangent bundles.





Learning
Outcomes
and
Competencies
Textbooks
and /or
References
To be able to express the general properties of tangent bundles,
To be able to define tangent bundles of Riemannian manifolds,
To be able to define Non-linear connections of tangent bundles
To be able to express the general properties of cotangent bundles,
To be able to express the fundamental properties of tangent and cotangent bundles of order 2.
K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker, Inc., New York, 1973.
ASSESSMENT CRITERIA
Theoretical Courses
Midterm Exams
If any,
mark as (X)
Percent
(%)
X
40
If any,
mark as (X)
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
60
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Tangent bundles
Vertical and complete lifts from a manifold to its tangent bundle
Metrics on tangent bundle
Complete lifts of vector fields to the tangent bundle
Complete lifts of affine connections to the tangent bundle
Horizontal lifts from a manifold to its tangent bundle
Tangent bundles of Riemannian manifolds
Non-linear connections of tangent bundles
Cotangent bundles
Vertical and complete lifts from a manifold to its cotangent bundle
Horizontal and complete lifts from a manifold to its cotangent bundle
Complete lifts of affine connections to the cotangent bundle
Tangent bundles of order 2
Cotangent bundles of order 2
Instructor/s
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Code :
FMT5202
Application
42
0
Home
Laboratuary
Project/
Field Study work
0
0
0
Spring
Semester
Course Type
Course
Objectives
Field: Mathematics
Basic
Scientific
Scientific
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach some advanced topics of functional analysis.






1.
2.
3.
Learning
Outcomes
and
Competences
Textbook
and /or
References
To be able to define the concept of compact operator,
To be able to define the concept of Banach algebra,
To able to define the spectrum of an operator,
To be able to define the concept of C* Algebra,
To be able to define the concept of weak topology
To be able to define the concept of Fredholm operator.
Barbara D. MacCluer, Elementary Functional Analysis, Springer, (2009).
J. B. Conway, A Course in Functional Analysis, Springer, (1985).
W. Rudin, Functional Analysis, McGraw Hill, (1991).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Finite Dimensional Spaces
Compact Operators
The Invariant Subspace Problem
Banach Algebras
Spectrum
Analytic Functions in Banach Spaces
Ideals and Homomorphisms
Commutative Banach Algebras
C* Algebras
Weak Topologies
Fredholm Operators
Lp Spaces
Stone-Weierstrass Theorem
Positive Linear Functionals on C(X)
Instructors
e-mail
[email protected]
Website
Other
Percent
(%)
Code :
Course Title : Module Theory II
Lecture
Application
42
0
Field: Mathematics
FMT5205
Laboratuary
Study
0
0
0
Semester
Spring
Credits
Other
Total
198
240
Basic
Scientific
Course
Objectives
To teach fundamental concepts of the module theory .
Learning
Outcomes and
Competences
Textbook and/or
References
Technical
Elective
Scientific
3
Social
Elective
● to be able to define the Noetherian and Artinian modules,
● to be able to express the semi simple modules,
● to be able to express the Goldie theorem for rings,
● to be able to define the modules on Goldie rings,
● to be able to express the bimodules and Noetherian bimodules.
1. A. Harmancı, Cebir II, Hacettepe yayınları, (1987).
2. V. P. Snaith, Groups, rings and Galois theory, World Scientıfıc, (2003).
3. J. J. Rotman, An introductıon to the theory of groups, Springer- Verlag, (1995).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
Percent
(%)
Midterm Exams
-
-
Quizzes
-
Homeworks
If any,
mark as
(X)
Percent
(%)
Midterm Exams
-
-
-
Midterm Controls
-
-
-
-
Term Paper
-
-
Term Paper
-
-
Oral Examination
-
-
Laboratory Work
-
-
Final Exam
-
-
Final Exam
X
100
Other
Other
Week
Subjects
1
2
3
4
5
6
7
8
9
10
11
12
13
14
İnstructors
Remind some material over abelıan groups
Remind some material over module theory ı
The classical ring definition and applications
Noetherian and artinian modules
Semı simple modules
Injective hull
The Goldie theorem for rıngs
Modules defined on goldie rıngs
Bimodüles, noetherian bimodüles
Modules of factors
Submodules of factors
e-mail
[email protected]
Website
ECTS
6
Turkish/English
Language
Course Type
Credit
T+A+L=Credit
Course Title:
Code :
Fuchsian Groups
FMT5206
Lecture
Application
42
0
Home
Laboratuary
Project/
work
Field Study
0
0
0
Spring
Semester
Course Type
Course
Objectives
Field: Mathematics
Basic
Scientific
Other
Total
198
240
3
6
Turkish/English
Language
Scientific
Credits
Credit
ECTS
T+A+L=Credit
Technical Elective
Social
Elective
To teach Fuchsian groups and their elementary algebraic properties.


Learning
Outcomes
and
Competences



1.
2.
3.
Textbook
and /or
References
To be able to state and apply the basic properties of the group PGL(2,C),
To be able to express the definition and basic properties of Möbius transformations on the extended
complex plane,
To be able to express the definition and basic properties of the group PSL(2,R) and its
transformations,
To be able to define the concepts of Elliptic function and topological group,
To be able to express the automorphisms of compact Riemann surfaces.
G. A. Jones and D. Singerman,Complex Functions, Cambridge University Press, (1987).
A. F. Beardon, The Geometry of Discrete Groups, Springer-Verlag, New York, (1983).
B. Iversen, Hyperbolic Geometry, , Cambridge University Press, (1992).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
The Riemann sphere
Möbius transformations
Generators for PGL(2,C)
Transitivity and cross-ratios
Conjugacy classes in PGL(2,C)
Geometric classification of Möbius transformations
The area of a spherical triangle
Elliptic functions, topological groups
Lattices and fundamental regions
PSL(2,R) and its discrete subgroups
The hyperbolic metric
Hyperbolic area and the Gauss-Bonnet formula
Fuchsian groups and elementary algebraic properties of Fuchsian groups
Automorphisms of compact Riemann surfaces
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application.
42
0
Study
0
0
0
Spring
Semester
Basic
Scientific
Course Type
Course
Objectives
Field: Mathematics
Code : FMT 5208
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
6
Turkish/English
Language
Technical
Elective
Scientific
Social
Elective
To teach fundamantel concepts of Differential Geometry.

Learning
Outcomes
and
Competences




Textbook
and /or
References
To be able to find the shape operator, Gaussian curvature and the mean curvature of a
surface,
To be able to define the orientatiability of a surface,
To be able to calculate the Euler-Poincare charactersitic of a surface,
To be able to state and prove the Gauss-Bonnet theorem,
To be able to define the congruence of surfaces.
1) B. O’Neill, Elementary Differential Geometry, Academic Pres, Inc., 1966.
2) H. H. Hacısalihoğlu, Yüksek Diferensiyel Geometri’ ye Giriş, Fırat Ünv. Fen Fak. 1980.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
ECTS
Subjects
Shape operator
Normal curvature, Gaussian curvature
Gauss map, minimal surfaces
Computational techniques
Special curves on a surface
Surfaces of revolution
Form computations
Isometries and local isometries
Integration and Orientation
Congruence of surfaces
Geodesics
Mappings that preserve inner products
Euler-Poincare characteristic of a surface
Gauss-Bonnet Theorem
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
Hyperbolic Geometry
FMT5210
Field: Mathematics
Home
Project/
Field Study work
Lecture
42
0
0
0
Spring
Semester
Other
Total
198
240
0
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the fundamental definitions and theorems related with Hyperbolic geometry.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Scientific
Technical
Elective
Social
Elective
 To be able to define define the concepts of hyperbolic metric and hyperbolic area,
 To be able to state the fundamental teorems related with hyperbolic geometry,
 To be able to state the Gauss-Bonnet thorem,
 To be able to define the fundamental concepts of Hyperbolic trigonometry,
 To be able express the relations in a Hyperbolic triangle.
1) G. A. Jones and D. Singerman,Complex functions, Cambridge University Press, (1987).
2) A.F. Beardon, The geometry of Discrete Groups, Springer, (1983).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Hyperbolic geometry
The isometry of the hyperbolic plane
Hyperbolic metric
The properties of the hyperbolic metric
Hyperbolic metric in the upper half plane
Hyperbolic metric in the unit disk
Topology induced by hyperbolic metric
Hyperbolic disk and its presentation
Hyperbolic area
The theorem of Gauss-Bonnet
Hyperbolic polygons
Hyperbolic trygonometry
The relations on hyperbolic triangle
Some theorems of hyperbolic trigonometry
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title: Dynamic Systems and Applications
Lecture
Laboratuary
Project/
Home
Field Study
work
Application
42
0
0
Course
Objectives
Basic
Scientific
Scientific
Other
0
198
Total
Credits
Credit
ECTS
T+A+L=Credit
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the fundamental concepts of dynamic system theory.
Learning
Outcomes
and
Competences
Textbook
and /or
References
0
Spring
Semester
Course Type
Field: Mathematics
Code : FMT5212
1.
2.
3.
4.
5.
 To be able to define Laplace and invere Laplace transformations,
 To be able to express the concept of state space and transfer function,
 To be able to express the fundamental concepts of stability theory,
 To be able to define Routh-Hurwitz stability criteria and to do MATLAB application,
 To be able to define Nyquist criteria and to do MATLAB application.
R. S. Burns, Advanced Control Engineering, Butterworth Heinemann, 2001.
B. C. Kuo, Otomatik Kontrol Sistemleri, Literatür Yayınları,2002.
J.Wilkie, M. Johnson, R. Katebi, Control Engineering Introductory Course, Palgrave Macmillan,2002.
E.P. Erander, A. Sjöberg, The Matlab Handbook 5, Addison-Wesleys,1999.
İ. Yüksel, Matlab ile Mühendislik sistemlerin Analizi, Vipaş A.Ş.,2000.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Fundamental Matrix Theory.
S-plane and Laplace transformations
Inverse Laplace transformations.
State space and Transfer functions.
Time domain input functions and time domain. Response of systems.
Step response and Performance identification.
Stability analysis.
Routh-Hurwitz Stability criterion.
Routh-Hurwitz criterion and MATLAB application.
Root Locus methods.
Root Locus methods MATLAB application.
Nyquist criterion.
Nyquist criterion MATLAB application.
Bode diagram and its MATLAB application.
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Real Analysis II
Lecture
Code :
FMT5213
Application
42
0
Home
Laboratuary
Project/
Field Study work
0
0
0
Spring
Semester
Course Type
Course
Objectives
Field: Mathematics
Basic
Scientific
Scientific
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach fundamental theorems of Real analysis.
Learning
Outcomes
and
Competences





To be able to define Lp Spaces and state their fundamental properties,
To be able to express the duals of Lp Spaces,
To be able to state the Radon-Nikodym Theorem,
To be able to state the Riesz Representation Theorem,
To be able to define the concepts of function of bounded variation and absolutely continuous
function,
Textbook
and /or
References
1.
2.
3.
C.D. Aliprantis, O. Burkinshaw, Principles of Real Analysis, Academic Pres (1998).
W. Rudin, Real and Complex Analysis, McGraw Hill (1987).
G. B. Folland, Real Analysis, John Wiley & Sons, Inc. (1999).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Normed Linear Spaces and Banach Spaces
Bounded Linear Transformations
Linear Functionals and Dual Spaces
Lp Spaces (1 ≤p<∞)
The space L∞
Linear Functionals on Lp Spaces
Signed Measures
Comparison of Measures
Decomposition of Measures
Radon-Nikodym Theorem
Riesz Representation Theorem
Functions of Bounded Variation
Absolutely Continuous Functions
Lebesgue differentiation theorem
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
Discrete Groups
FMT5215
Lecture
Application
42
0
Home
Laboratuary
Project/
work
Field Study
0
0
0
Spring
Semester
Course Type
Course
Objectives
Field: Mathematics.
Basic
Scientific
Othe
r
198
Total
240
3
6
Turkish/English
Language
Scientific
Credits
Credit
ECTS
T+A+L=Credit
Technical Elective
Social
Elective
To teach the discrete group theory at the basic level.


Learning
Outcomes
and
Competences



1)
2)
3)
Textbook
and /or
References
To be able to express the definition and basic properties of Möbius transformations on Rn,
To be able to express the definition and basic properties of some discontinuous groups of Möbius
transformations,
To be able to express the Discrete groups of isometries,
To be able to define the function groups,
To be able to define the concept of Schottky groups.
A. F. Beardon, The Geometry of Discrete Groups, Springer-Verlag, New York, (1983).
B. Maskit, Kleinian Groups, Springer-Verlag, Berlin, (1988).
B. Fine and G. Rosenberger, Algebraic Generalizations of Discrete Groups, Marcel Dekker, (1999).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
% 80
Other (Class
Performance)
X
% 20
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Other
Subjects
Basic Properties of Möbius transformations on Rn
Complex Möbius transformations
Discontinuous groups
Jorgensen’s inequality
Fundamental Domains
The Dirichlet Polygon
Covering spaces
Groups of isometries
Discrete groups of isometries
The geometric basic groups
Geometrically finite groups
Function groups
Signatures
Schottky groups
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title: Theory of Approximation II
Lecture
Laboratuary
Project/
Home
Field Study
work
Application
42
0
0
Course
Objectives
Learning
Outcomes
and
Competences
Textbook
and /or
References
0
Spring
Semester
Course Type
Field: Mathematics
Code : FMT5216
Basic
Scientific
Scientific
Other
0
198
Total
Credits
Credit
ECTS
T+A+L=Credit
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the fundamental principles of approximation theory in the complex plane.
 To be able to define function spaces in the complex plane,
 To be able to construct the approximating polynomials in the complex plane,
 To be able to state the Walsh, Keldysh, Lavrentiev and Mergelyan theorems,
 To be able to express the asymptotic properties of Faber polynomials,
 To be able to state the theorems of rational approximation on the curves.
1. V. K. Dzyadyk, Introduction to the theory of uniform approximation of functions by polynomials
(Russian). Moscow, (1977).
2. J. L. Walsh. Approximation and interpolation of the domains of the complex plane
3. V. V. Andrievskii, V. I. Beyli, V. K. Dzyadyk, Conformal invariants in constructive theory of functions of
complex variable, Atalanta, (1995).
4. P. S. Suetin, Series of Faber Polynomials, Moscow, (1984).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
x
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Function spaces in the complex plane
Modulus of smoothness on the complex plane
Polynomials of the best approximation on the complex plane
Construction of the approximation polynomials
Theorems of Walsh, Keldysh, Lavrentiev and Mergelyan
Faber polynomials and their’s properties
Generalized Faber polynomials
The asymptotical properties of Faber polynomials
Approximation by Faber polynomials
Approximation by rational functions on the curves
Approximation on the domains
Direct theorems
Inverse theorems
Comparsion of the results
Instructors
Prof. Dr. Daniyal İsrafilzade
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application.
42
0
Field: Mathematics
Code : FMT 5221
Riemannian Geometry II
Study
0
0
0
Spring
Semester
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
ECTS
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the general properties of Einstein manifolds, submanifolds, surfaces, hypersurfaces and space
forms.

To be able to define the notions of Einstein manifold and submanifold and to give examples,

To be able to express the general properties of total geodesic , totally umbilical and pseudoumbilical submanifolds,

To be able to define and apply the notion of space form,

To be able to state and prove Cartan’s theorem and its corollaries,

To be able to Express the isometries of Hyperbolical space and Liouville’s theorem.
1) Manfredo Perdigao do Carmo , Riemannian Geometry , Birkhauser, 1992.
2) W. M. Boothby, An introduction to Differentiable manifolds and Riemannian Geometry, Elsevier,
2003.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Technical
Elective
Scientific
Social
Elective
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Visa examination
Midterm Exams
Quiz
Midterm Controls
Homework
Term Paper
Term project (project,
report, etc)
Oral Examination
Laboratory
Final Exam
Final examination
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Ricci curvature tensor, definition and geometric meaning of Ricci curvature tensor
Some theorems about Ricci curvature tensor
Einstein manifolds
Submanifolds, definition and basic notions
Isometric Immersions
Fundamental forms
Totally geodesic , totally umbilic and pseudo umbilic submanifolds
Curvature of submanifolds
Surfaces
Hypersurfaces
Space forms
Cartan Theorem and its results
Hyperbolical space
Isometries of Hyperbolical space, Liouville Theorem
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application.
42
0
Field: Mathematics
Code : FMT 5222
Study
0
0
0
Spring
Semester
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
ECTS
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the notions of totally umbilical submanifolds, minimal submanifolds, invariant and totally real
submanifolds , quaternionic submanifolds, submanifolds of Kahler manifolds, surfaces in a real space form.

To be able to define the concepts of totally umbilical submanifold and minimal submanifold, and
to give examples,

To be able to express the concepts of invariant and totally real submanifold,

To be able to define the concepts of quaternionic submanifold and submanifold of a Kahler
manifold,

To be able to define the concept of surfaces in a real space form and to give examples,

To be able to prove the Gauss-Bonnet theorem.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Technical
Elective
Scientific
Social
Elective
B. Y. Chen , Geometry of Submanifolds, Pure and applied mathematics (Marcel Dekker, Inc.), New York,
1973
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Totally umbilical submanifolds
Minimal submanifolds
The first Standard imbeddings of Projective Spaces I
The first Standard imbeddings of Projective Spaces II
Invariant and totally real submanifolds I
Invariant and totally real submanifolds II
Quaternionic submanifolds
Riemann submersions
Submanifolds of Kahler manifolds, basic definitions and notions I
Submanifolds of Kahler manifolds, basic definitions and notions II
Surfaces in 3-dimensional Eucliden space and related results
Surfaces in a Real space form I
Surfaces in a Real space form II
Gauss-Bonnet Theorem
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title: Advanced Control Systems II
Lecture
Laboratuary
Project/
Home
Field Study
work
Application
42
0
0
0
Course
Objectives
Basic
Scientific
Other
0
Spring
Semester
Course Type
Field: Mathematics
Code : FMT5224
Total
198
240
3
6
Turkish/English
Language
Technical
Elective
Scientific
Credits
Credit
ECTS
T+A+L=Credit
Social
Elective
To teach controllability of nonlinear systems and optimal control theory in advanced level.
Learning
Outcomes
and
Competences





To be able to express controllability of nonlinear systems,
To be able to define unconstrained optimization problems,
To be able to define problems of optimal control theory,
To be able to state Pontryagin maximum principle,
To be able to express sufficient conditions for optimal control.
Textbook
and /or
References
1.
2.
E. R. Pinch, Optimal Control And The Calculus Of Variations, Oxford University Press, 1995.
J. Macki, A. Strauss, Introduction to Optimal Control Theory, Springer-Verlag, 1982.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Controllability for nonlinear systems.
Controllability for nonlinear systems.
Optimization: functions of one variable, critical points, end points, discontinuity points.
Optimization with constraint, geometrical interpretation.
Calculus of variation, fixed end points problems, minimization curves.
Isometric problems, sufficient problems, extreme fields.
Optimal control theory problems.
Pontryagin maximum principle.
Optimal control to objective curve.
Time optimal control problems of linear systems.
Linear systems and quadratic costs.
Steady State Riccati equations.
n
Convex sets in
Sufficient conditions for optimal control.
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Convex Functions and Orlicz Spaces II
Lecture
Laboratuary
Project/
Home
Field Study
work
Application
42
0
0
Course
Objectives
Learning
Outcomes
and
Competences
Textbook
and /or
References
0
Spring
Semester
Course Type
Field: Mathematics
Code : FMT5225
Basic
Scientific
Scientific
Other
0
198
Total
Credits
Credit
ECTS
T+A+L=Credit
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the completeness and separability concepts and compactness criteria in Orlicz spaces.
 To be able to define the concept of completeness in Orlicz spaces,
 To be able to Express the Notion of absolute continuity of the norm in Orlicz spaces,
 To be able to Express the Kolmogorov compactness criter in Orlicz spaces,
 To be able to Express the approximation theorems in Orlicz spaces,
 To be able to define the notion of weighted Orlicz space.
1) M. A. Krasnosel’ski and Ya. B. Rutickii, Convex funktions and Orlicz Spaces, Noordhoff, 1961.
2) C. Bennett and R. Sharpley, Interpolation of Operators, Academic Pres, 1988.
3) M. M. Rao, Z. D. Ren, Applications of Orlicz Spaces, New York, 2002.
4) R. A. De Vore and G. G. Lorentz, Constructive Approximation, Springer, 1993.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
x
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Completeness in the Orlics spaces
Norm of the characteristic functions, Hölder’s inequality
Mean convergence
Separability in the Orlicz spaces, necessary conditions
The absolute continuity of the norm
Compactness criteria
Kolmogorov’s compactness criterion for the Orlics spaces
Riesz’s compactness criterion for the Orlics spaces
Basis in the Orlisz spaces
Comparsion of spaces
An inequality for norms
Approximation in the Orlicz spaces
Direct and inverse theorems
Weighted Orlicz spaces
Instructors
Prof. Dr. Daniyal İsrafilzade
e-mail
[email protected]
Website
Percent
(%)
Code :
Course Title : Matrices of Semigroups
Lecture
Application
42
0
Field: Mathematics
FMT5226
Laboratuary
Study
0
0
0
Semester
Spring
Credits
Other
Total
198
240
Course Type
Basic
Scientific
Course
Objectives
To introduce semigroups of matrices and to teach the rewriting system.
Learning
Outcomes and
Competences
Textbook and/or
References
3
Technical
Elective
Social
Elective
● to be able to express the definitions of semıgroup and monoıd,
● to be able to understand the construction of lineer semigroup,
● to be able to create the monoids with lie type,
● to be able to express the non-factorization semigroups,
● to be able to create the rewriting systems
1) J. Okninski, Semigroups of matrices, World Scientific, (1988).
2) C. Kart, Matris metodları ve lineer dönüşümler, Ank. Üniv. , (1985).
3) J. Almedia, Fınıte semigroups and universal algebra, World Scientific, (1994).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
Percent
(%)
Midterm Exams
-
-
Quizzes
-
Homeworks
Term Paper
If any,
mark as
(X)
Percent
(%)
Midterm Exams
-
-
-
Midterm Controls
-
-
-
-
Term Paper
-
-
-
-
Oral Examination
-
-
Laboratory Work
-
-
Final Exam
-
-
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Remind the basics on fundamental algebraic structures
Definitions of semigroup and monoid, and applications
To extend the usegace of definitions
General tecnics
Exact linear monoid
Construction of linear semigroup
Non factorization semigroups
Identities of semigroups
Monoids with lie type
Rewriting systems
Rewriting systems-cont.
Instructors
Assoc. Prof. Dr. Fırat ATEŞ
e-mail
[email protected]
Website
ECTS
6
Turkish/English
Language
Scientific
Credit
T+A+L=Credit
Course Title:
Lecture
Application.
42
0
Study
0
0
0
Spring
Semester
Basic
Scientific
Course Type
Field: Mathematics
Code : FMT 5227
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
6
Turkish/English
Language
Technical
Elective
Scientific
Social
Elective
To teach submanifolds Kaehler and Sasakian manifolds, Invariant and anti-invariant
submanifolds, Lagrangian and integral submanifolds and general properties of tangent sphere
bundles.
 To be able to understand the notions of Kaehler and Sasakian manifolds and to give some
examples of them,
 To be able to understand the notions of invaryant ve anti-invariant submanifolds,
Lagrangian and integral submanifolds and to do their applications,
 To be able to express some general properties of Complex contact manifolds and 3-Sasakian
manifolds,
 To be able to express the geometry of tangent sphere bundles and vector bundles,
 To be able to define integral submanifolds of 3-Sasakian manifolds.
Course
Objectives
Learning
Outcomes
and
Competences
Textbook
and /or
References
D. Blair , Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, 2002.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
ECTS
Subjects
Submanifolds of Kaehler and Sasakian manifolds
Invariant and anti-invariant submanifolds
Lagrangian and integral submanifolds
Legendre curves
Tangent bundles
Tangent sphere bundles, geometry of vector bundles
The *-scalar curvature
The integral of Ric(), the Webster scalar curvature
Complex contact manifolds and associated metrics
Examples of complex contact manifolds
Normality of complex contact manifolds
Holomorphic Legendre curves
3-Sasakian manifolds
Integral submanifolds of 3-Sasakian manifolds
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application.
42
0
Study
0
0
0
Spring
Semester
Basic
Scientific
Course Type
Field: Mathematics
Code : FMT5228
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
6
Turkish/English
Language
Technical
Elective
Scientific
Social
Elective
To teach the general properties of submanifolds of Kaehlerian manifolds, Almost contact manifolds, contact
manifolds, contact manifolds, locally product manifolds, submanifolds of product manifolds, submersions
and submanifolds.
 To be able define the submanifolds of Kaehlerian manifolds,
 To be able to define the almost contact manifolds and contact manifolds, and to give examples of them,
 To be able to define the locally product manifolds and submanifolds of product manifolds,
 To be able to define the concept of submersions and to give examples,
 To be able to define the concept of CR-submanifod and to give examples.
Course
Objectives
Learning
Outcomes
and
Competences
Textbook
and /or
References
Kentaro Yano and Mashiro Kon , Structures On Manifolds, World Sci. 1984.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
ECTS
Subjects
Submanifolds of Kaehlerian manifolds
Anti-invariant submanifolds of Kaehlerian manifolds
CR submanifolds of Kaehlerian manifolds
Almost contact manifolds, contact manifolds
Sasakian manifolds
Invariant submanifolds of Sasakian manifolds
Anti-invariant submanifolds of Sasakian manifolds
Contact CR-submanifolds
Locally product manifolds
Submanifolds of product manifolds
Submanifolds of Kaehlerian product manifolds
Fundamental equations of Submersions
Almost Hermitian submersions
Submersions and submanifolds
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Algebraic Geometry
Lecture
Application
42
0
Lab.
Project/
Homework
Field Study
0
0
100
Spring
Semester
Basic
Scientific
Course Type
Course
Objectives
Sciences
Field
: Mathematics
Code :
FMT5230
Other
Total
98
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Scientific
Social
Elective
To teach the algebraic varieties which are the zero sets of polynomials in several variables.





1.
2.
3.
4.
Learning
Outcomes
and
Competencies
Textbooks
and /or
References
To be able to define the concept of Affine Algebraic Variete,
To be able to state Hilbert basis theorem,
To be able to define the concept of projective variete,
To be able to express the Veronese Maps and Product of Varieties,
To be able to define the concept of Hilbert function.
Huishi Li - F. Van Oystaeyen, A Primer of Algebraic Geometry, Marcel Dekker 2000.
Kenji Ueno, An Introduction to Algebraic Geometry, American Mathematical Society 1997.
Karen E. Smith et al, An Invitation to Algebraic Geometry, Springer 2000.
J. Harris , Algebraic Geometry, Springer 1992.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as (X)
Percent
(%)
If any,
mark as (X)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homework
X
60
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
40
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Plane curves, conics and cubics
Affine Algebraic Varieties
Hilbert Basis Theorem
The Zariski Topology
Hilbert Nullstellensatz
The Coordinate Ring
Morphisms of Affine Varieties
Projective Varieties
Quasi-Projective Varieties
Veronese Maps and Product of Varieties
Grassmannians, The Hilbert Function
Smoothness, Bertini’s Theorem
Resolution of Singularities
Blowing Up
Instructor/s
Assist. Prof.Dr. Pınar Mete
e-mail
[email protected]
Website
Percent
(%)
Course Title: Applications of Fractional Calculus
Lecture
Laboratuary
Project/
Home
Field Study
work
Application
42
Field: Mathematics
Code : FMT5231
0
0
0
Spring
Semester
Other
0
Total
198
Credits
Credit
ECTS
T+A+L=Credit
240
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach fractional-order systems and controllers, fractional optimal control problems and applications of
fractional.
 To be able to define the concept of the fractional order controllers,
Learning
Outcomes
and
Competences
Technical
Elective
Social
Elective

1.
Textbook
and /or
References
Scientific
2.
3.

 To be able to make comparison between fractional PI D and classic PID controllers,
 To be able to define Hamiltonian and Euler-Lagrange Equations,
 To be able to construct mathematical modeling of fractional diffusion-wave equations,
 To be able to construct Fractional mathematical modeling of viscoelastic materials.
S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives-Theory and Applications,
CRC Press, 1993.
R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, 2000.
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations,
Elsevier Science, 2006.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Fractional-order systems.
Fractional-order controllers.
Fractional-order transfer functions.


Comparison of classic PID and fractional PI D controllers.
Responses of open-loop and closed-loop fractional-order systems.
Stochastic analysis of fractional dynamic systems
Hamiltonian and Euler-Lagrange Equations.
Definition and examples of optimal control problems.
Fractional optimal control problems.
Mathematical modeling of fractional diffusion-wave equations.
Fractional mathematical modeling of viscoelastic materials.
Other applications of fractional calculus in physics.
Applications of fractional calculus in chemistry.
Applications of fractional calculus in biology.
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
Number Theory II
FMT 5232
Lecture
Application
42
Field: Mathematics
Home
Laboratuary
Project/
Field Study work
0
0
0
Spring
Semester
Other
Total
198
240
0
Basic
Scientific
Course
Objectives
To teach the concepts of quadratic and cubic residue.





1.
2.
3.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Scientific
3
6
Turkish/English
Language
Course Type
Credits
Credit
ECTS
T+A+L=Credit
Technical
Elective
Social
Elective
To be able to define the reduction rule of second degree and to apply it,
To be able to apply the quadratic residues,
To be able to define the concept of cubic residue,
To be able to solve the cubic equations,
To be able to express the primes in Z[w].
K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer, (1990).
D. Namlı, Kübik Rezidüler, Doktora Tezi, Balıkesir, (2001).
G. A.Jones and J.M. Jones, Elementary Number Theory, Springer, (2004).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
The ring of congruence class
Quadratic Residues and The Legendre Symbol
The group of quadratic residues
Quadratic Reciprocity
Algebraic Numbers
The quadratic character of 2
Quadratic Gauss Sums
An application to quadratic residues
Cubic Residue Character
The cubic character of 2
Primes of Z[w]
Index Rules
Cubic Equations
Cubic Residues
Instructors
Assist. Prof. Dr. Dilek Namlı
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
Bergman Spaces
FMT5234
Lecture
Application
42
0
Home
Laboratuary
Project/
work
Field Study
0
0
0
Spring
Semester
Course Type
Course
Objectives
Field: Mathematics
Basic
Scientific
Other
Total
198
240
3
6
Turkish/English
Language
Scientific
Credits
Credit
ECTS
T+A+L=Credit
Technical Elective
Social
Elective
To teach the structure of Bergman spaces.





1)
2)
3)
Learning
Outcomes
and
Competences
Textbook
and /or
References
To be able to define the Bergman space,
To be able to express the relations between Bergman spaces and other function spaces,
To be able to interpret the density of polynomials,
To be able to express the Hilbert space structure of the Bergman space A2,
To be able to state the appraximation theorems in the Bergman space A2.
P. L. Duren and Schuster, Bergman Spaces.
P. L. Duren, Introduction to Hp spaces, Academic Press, 1970.
D. Gaier, Lectures on complex approximation, Birkhauser, 1987.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
Bergman Kernel function
Orthonormal bases, conformal invariants
Hardy spaces, strict and uniform convexity
Bergman projection, Harmonic conjugate
Linear isometries, Function multipliers
Growth properties of functions
Coefficients multipliers
Approximation in Bergman space A2
Bergman space A2 as a Hilbert space
Orthonormal systems
Density of polynomials
Domains with PA property
Domains with PA property
Expansions with respect to ON systems
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Differentiable Manifolds II
Lecture
Application.
42
0
Field: Mathematics
Code : FMT 5235
Study
0
0
0
Spring
Semester
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
ECTS
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the notions of a tensor on a manifold, integration on a manifold and the general properties of
Riemannian manifolds.

To be able to define the notion of a tensor on a manifold and to give some examples,
 To be able to define the notion of a Riemannian manifold and to give some examples,
 To be able to define the concept of orientiability of manifolds,

To be able to express the concept of integration on manifods,

To be able to define the concept of Manifold of constant curvature nad to give examples.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Technical
Elective
Scientific
Social
Elective
Boothby, William M. An introduction to differentiable manifolds and Riemannian geometry. Second
edition. Pure and Applied Mathematics, 120. Academic Press, Inc., Orlando, FL, 1986.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Tensors on manifolds
2-lineer forms, Riemann metrics
Riemannian manifolds a metric spaces
Tensor fields on manifolds
Tensor products
Orientation on manifolds
Exterior differentiation
Applications
Integration on Manifolds
Differential forms
Differentiation on Riemannian manifolds
Geodesics on Riemannian manifolds
Manifolds of constant curvature
Applications
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application.
42
0
Study
0
0
0
Spring
Semester
Basic
Scientific
Course Type
Course
Objectives
Field: Mathematics
Code : FMT5236
Tensor Geometry II
Credits
Other
Total
Credit
T+A+L=Credit
198
240
3
6
Turkish/English
Language
Technical
Elective
Scientific
Social
Elective
To teach fundamental knowledge about tensors.





1.
2.
3.
Learning
Outcomes
and
Competences
Textbook
and /or
References
To be able to define and to apply the notions of Ricci tensor, scalar curvature,
To be able to apply the concept of tensor in classical mechanics,
To be able to apply the concept of tensor in special relativity,
To be able to define the concept of Einstein Manifold and to give examples,
To be able to define the concept of Quasi-Einstein Manifold and to give examples.
H. Hilmi Hacısalihoğlu , Tensör Geometri, Ankara Ünv. Fen-Fakültesi, 2003.
D. C. Kay, Tensor Calculus, McGraw-Hill, 1988.
C. T. J. Dodson, T. Poston, Tensor geometry, Graduate Texts in Mathematics, 130. SpringerVerlag, Berlin, 1991.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
ECTS
Subjects
Ricci tensor, scalar curvature
Applications
Spaces of constant curvature
Applications
Einstein manifolds
Applications
Quasi-Einstein manifolds
Applications
Tensors in classical mechanics I
Tensors in classical mechanics II
Applications
Tensors in special relativity I
Tensors in special relativity II
Applications
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
FMT5237
Lecture
Application
42
0
Field: Mathematics
Home
Laboratuary
Project/
work
Field Study
0
0
0
Spring
Semester
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the the fundamental algebraic and geometric properties of Möbius transformations.

Learning
Outcomes
and
Competences




1)
2)
Textbook
and /or
References
3)
Scientific
6
Technical Elective
Social
Elective
To be able to define and to apply the algebraic properties of Möbius transformations on the extended
complex plane,
To be able to define and to apply the geometric properties of Möbius transformations on the
extended complex plane,
To be able to express the finite groups of Möbius tranfromation,
To be able to define the group of rotations of the shpere,
To be able to express a geormetric definition of the infinity.
A. F. Beardon, Algebra and geometry, Cambridge University Press, Cambridge, 2005.
T. Needham, Visual complex analysis, The Calerendon Press, Oxford University Press, New York,
1997.
C. Caratheodory, The most general transformations of plane regions which transform circles into
circles. Bull. Amer. Math. Soc. 43 (1937), no. 8, 573-579.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
The stabilisers of a circle and a disc
Conformality
Complex lines
Fixed points and eigenvectors
A geometric view of infinity
Rotations of the sphere I
Rotations of the sphere II
Finite groups of Möbius transformations I
Finite groups of Möbius transformations II
The most general transformations of plane regions which transform circles into circles
The most general planar transformations that map hyperbolas to hypaerbolas I
The most general planar transformations that map hyperbolas to hypaerbolas II
The most general planar transformations that map parabolas into parabolas I
The most general planar transformations that map parabolas into parabolas II
Instructors
e-mail
[email protected]
Website
Percent
(%)
Code :
Course Title:
Averaged moduli and one sided approximation II
Field: Mathematics
FMT5238
Home
Project/
work
Field Study
0
0
0
0
Lecture
42
Spring
Semester
Course Type
Course
Objectives
Basic
Scientific
Total
198
240
6
Turkish/English
Language
Scientific
3
Technical Elective
Social
Elective
To teach the theorems of one sided approximation in the space Lp, 0<p<infinity.





Learning
Outcomes
and
Competences
Textbook
and /or
References
Other
Credits
Credit
ECTS
T+A+L=Credit
To be able to state the direct theorem of one sided approximation in the space Lp, p>1,
To be able to state the converse theorem of one sided approximation in the space Lp, p>1,
To be able to state the direct theorem of one sided approximation in the space Lp, p<1,
To be able to state the converse theorem of one sided approximation in the space Lp, p<1,
To be able to explain the concepts of modulus of smoothness with real order and one sided
approximation.
Bl. Sendov and V. A. Popov, The avaraged moduli of smoothness, 1988.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
% 100
Other
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Preliminaries
In short, the main trigonometric approximation theorems
The direct theorem of one sided approximation in Lp, p>1
The direct theorem of one sided approximation in Lp, p>1
The inverse theorem of one sided approximation in Lp, p>1
The inverse theorem of one sided approximation in Lp, p>1
The direct theorem of one sided approximation in Lp, p<1
The direct theorem of one sided approximation in Lp, p<1
The inverse theorem of one sided approximation in Lp, p<1
The inverse theorem of one sided approximation in Lp, p<1
Fractional order moduli of smoothness an done sided approximation
Fractional order moduli of smoothness an done sided approximation
Some exact inequalities
Some applications
Instructors
e-mail
[email protected]
Website
Percent
(%)
Code :
Course Title:
Lecture
Application
42
0
Home
Laboratuary
Project/
work
Field Study
0
0
0
Spring
Semester
Course Type
Course
Objectives
Basic
Scientific
Other
Total
198
240
3
6
Turkish/English
Language
Scientific
Credits
Credit
ECTS
T+A+L=Credit
Technical Elective
Social
Elective
To teach the strong approximation and the embedding theorems.





Learning
Outcomes
and
Competences
Textbook
and /or
References
Field: Mathematics
FMT5239
To be able to explain the relation between strong approximation and structural properties,
To be able to define the concept of generalized strong de la Vallee Poussin means,
To be able to explain the relation between the order of strong approximation and structural properties,
To be able to the concept of generalized strong approximation,
To be able to state the embedding theorems
Laszlo Leindler, Strong approximation by Fourier series, Akademiai Kiado, 1985.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
% 100
Other
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Preliminaries
Generalized strong de la Vallee Poussin means
Order of strong approximation and structural properties
structural properties function derivatives
structural properties function derivatives
Generalized strong approximation
Generalized strong approximation
Imbedding theorems
WrH1 class
WrH1 class
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
FMT5240
Lecture
Application
42
0
Field: Mathematics
Home
Laboratuary
Project/
work
Field Study
0
0
0
Spring
Semester
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach fundamental definitions and theorems about the notions of centralizers of finite Blaschke products and
commuting finite Blaschke products.
 To be able to define the concept of centralizer of a finite Blaschke product,
 To be able to express the theorems about the concept of centralizer of a finite Blaschke product,
 To be able define the concept of commuting finite Blaschke products,

To be able to express the theorems about the concept of commuting finite Blaschke products,
 To be able to give examples about these topics.
1. C. Artega, Centralizers of finite Blaschke products. Bol. Soc. Brasil Mat. (N.S.) 31 (2000), no. 2,
163-173.
2. C. Artega, Commuting finite Blaschke products. Ergodic Theory Dynam. Systems 19 (1999), no. 3,
549-552.
3. I. Chalender and R. Mortini, When do finite Blaschke products commute? Bull. Austral. Math. Soc.
64 (2001), no. 2, 189-200.
4. C. Artega, On a theorem of Ritt for commuting finite Blaschke products. Complex Var. Theory Appl.
48 (2003), no.8, 671-679.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Scientific
Technical Elective
Social
Elective
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
Centralizers of finite Blaschke products I
Centralizers of finite Blaschke products II
Centralizers of finite Blaschke products III
Examples
Commuting finite Blaschke products
Commuting finite Blaschke products with a fixed point in the unit disc I
Commuting finite Blaschke products with a fixed point in the unit disc II
Counterexamples to C. C. Cowen’s Conjectures
Commuting finite Blaschke products with no fixed point in the unit disc I
Commuting finite Blaschke products with no fixed point in the unit disc II
Examples
Commuting finite Blaschke products with no fixed point in the unit disc III
Commuting finite Blaschke products with no fixed point in the unit disc IV
Applications
Instructors
e-mail
[email protected]
Website
Percent
(%)
Lecture
Sciences
Field : Mathematics
Code :
Course Title:
Algebra II
FMT5241
Application
42
0
Lab.
Project/
Homework
Field Study
0
0
100
Spring
Semester
Basic
Scientific
Course Type
Course
Objectives
Scientific
Other
Total
98
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the fundamental properties of module and field theories.
 To be able to classify free modules over a ring and finitely generated module over PID,
 To be able to demonstrate various constructions involving modules,
 To be able to express the fundamental facts about field extensions,
 To be able to state the main theorems,
 To be able to classify finite fields.
1. T. W. Hungerford, Algebra, Springer 1996.
2. D.S. Dummit and R. M. Foote, Abstract Algebra, Wiley 2nd edition ,1999.
3. N. Jacobson, Basic Algebra I-II, Dover Publications, 2009.
4. H.İ. Karakaş, Cebir Dersleri, TUBA 2008.
Learning
Outcomes
and
Competencies
Textbooks
and /or
References
ASSESSMENT CRITERIA
Theoretical Courses
Midterm Exam
If any,
mark as (X)
Percent
(%)
X
30
Quizzes
If any,
mark as (X)
Midterm Exams
Midterm Controls
Homework
X
40
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
30
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Modules, Homomorphisms and Exact Sequences
Projective and Injective Modules
Free Modules, Vector Spaces
Hom and Duality
Tensor Products
Modules over a Principal Ideal Domain
Basic properties of Fields
Algebraic and transcendental extensions of fields
Fundamental theorem of Galois theory
Splitting fields and Normal extensions
The Galois Group of a Polynomial
Finite Fields
Separability
Cyclic Extensions
Instructor/s
Assist. Prof.Dr. Pınar Mete
e-mail
[email protected]
Website
Percent
(%)
Code :
Course Title:
Function Spaces II
Field: Mathematics
FMT5243
Home
Project/
work
Field Study
0
0
0
0
Lecture
42
Spring
Semester
Course Type
Course
Objectives
Basic
Scientific
Other
Total
198
240
3
6
Turkish/English
Language
Scientific
Credits
Credit
ECTS
T+A+L=Credit
Technical Elective
Social
Elective
To teach several function spaces and relations among them.





Learning
Outcomes
and
Competences
1)
2)
Textbook
and /or
References
To able to define the concept of Modular space,
To able to define the concept of Musielak Orlicz space,
To be able express the relations between modular spaces and Musielak Orlicz spaces,
To be able to define the Lebesgue spaces with variable exponent,
To be able to express the relation between Musielak Orlicz space and Lebesgue space with variable
exponent.
J. Musielak, Orlicz spaces and Modular Spaces, Springer, 1982.
L. Diening, P. Harjulehto, P. Hästö, M. Růžička Lebesgue and Sobolev spaces with variable
exponents , Springer, 2011.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
% 100
Other
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Modular space
Modular space
Modular space
Modular space
Musielak Orlicz space
Variable exponent Lebesgue space
Variable exponent Lebesgue space
Inequalities in Variable exponent Lebesgue space
Inequalities Variable exponent Lebesgue space
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Potential Theory
Code :
FMT5244
Field: Mathematics
Credits
Project/
Hw.
Field Study
0
0
0
0
Lecture
42
Spring
Semester
Course Type
Course
Objectives
Basic
Scientific
Other
Total
T+A+L=
Credit
198
240
3
6
Turkish/English
Language
Technical
Elective
Scientific
ECTS
Social
Elective
To teach the concepts and tecniques in potential theory.





1.
2.
3.
4.
Learning
Outcomes
and
Competences
Textbook
and /or
References
To be able to define the concept of subharmonic function,
To be able to state the maximum principle for potantials,
To be able to define the concepts of potantial equilibrium measure and capacity,
To be able to apply the techniques of potantial theory in analysis of orthogonal polynomials,
To be able to define the concept of Green function.
E. B. Saff, Orthogonal Polynomials From a Complex Perspective, Kluwer Academic Publisher, 1990.
E. B. Saff, V. Totik, Logaritmic Potentials with External Fields, Springer, 1997.
H. Stahl, V. Totik, General Orthogonal Polynomials, Cambridge University Press, 1992.
T. Ransford, Potential Theory in the Complex Plane, London Math. Soc.Student Texts. Cambridge
Press. 1995.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Harmonic functions
Dirichlet problem
Subharmonic functions
Potentials
Maximum principle,for potentials
Equilibrium measure
Logarithmic capacity
Energy
Relations with orthogonal polynomials
Relations with potential theory
Geometric convergence
Fejer theorem
Green functions
Relations with approximation theory
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Banach Spaces of Analytic Functions II
Lecture
Application
42
0
Code :
FMT5245
Course
Objectives
Credits
Laboratuary
Project/
Hw.
Field Study
0
0
0
Spring
Semester
Course Type
Field: Mathematics
Basic
Scientific
Scientific
Other
Total
T+A+L=
Credit
ECTS
198
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach fundamental properties of Smirnov and Bergman spaces.





Learning
Outcomes
and
Competences
1)
2)
Textbook
and /or
References
3)
To be able to express the linear space structure of Hp spaces,
To be able to define the dual spaces of Hp spaces,
To be able to express the fundamental properties of Smirnov spaces,
To be able to express the fundamental properties of Bergman spaces,
To be able to express the domains with the PA property and the domains does not have the PA
property.
P. Koosis, Introduction to Hp Spaces, Cambridge University Press (1998).
P. L. Duren, Teory of Hp spaces, Academic Press (1970).
D. Gaier, Lectures on Complex Approximation, Birkhauser (1987).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Conjugate functions
Theorems of Riesz and Kolmogorov
Zygmund’s theorem
Hp as a linear space
Duals of Hp spaces
Hp spaces over general domains
The Smirnov spaces Ep (G)
The space E1 (G) and Cauchy integral
Smirnov domains
The Bergman space A2(G)
A2(G) as a Hilbert space
Orthonormal systems in A2(G)
Polynomials in A2(G)
Domains with the PA property and domains not having the PA property
Instructors
e-mail
[email protected]
Website
http://w3.balikesir.edu.tr/~aguven/
Percent
(%)
Course Title:
Fourier Analysis II
Code :
FMT5246
Lecture
Application
42
0
Course
Objectives
Spring
Basic
Scientific
Scientific
Other
Total
T+A+L=
Credit
ECTS
198
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach convergence properties and summability methods of multiple Fourier series.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Credits
Laboratuary
Project/
Hw.
Field Study
0
0
0
Semester
Course Type
Field: Mathematics
1)
2)
3)

To be able to define the square and circular Dirichlet and Fejer kernels,

To be able to state the poisson summation Formula,

To be able to express the convergence propeties of Fejer means,

To be able to express the convergence and divergence of multiple Fourier series,

To be able to express the Bochner-Riesz summability method.
L. Grafakos, Classical Fourier Analysis, Springer (2008).
J. Duoandikoetxea, Fourier Analysis, American Math. Soc. (2001).
E.M.Stein, G.Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press (1971).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
The n-torus Tn
Multiple Fourier series
The square and circular Dirichlet and Fejer kernels
The Poisson summation formula
Decay of Fourier coefficients
Pointwise convergence of the Fejer means
Almost everywhere convergence of the Fejer means
Pointwise divergence of multiple Fourier series
Pointwise convergence of multiple Fourier series
Bochner-Riesz summability
Divergence of Bochner-Riesz means of Integrable functions
Boundedness of the conjugate function in Lp spaces
Convergence of multiple Fourier series in the norm
Almost everywhere convergence of multiple Fourier series
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application
42
0
Code :
FMT5247
Course
Objectives
Credits
Laboratuary
Project/
Hw.
Field Study
0
0
0
Spring
Semester
Course Type
Field: Mathematics
Basic
Scientific
Scientific
Other
Total
T+A+L=
Credit
ECTS
198
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the fundamental theorems of trigonometric approximation theory.





1.
2.
To be able to define the concepts of modulus of smoothness and modulus of continuity,
To be able to state the direct theorems of trigonometric approximation in the spaces C and Lp,
To be able to state the converse theorems of trigonometric approximation in the spaces C and Lp,
To be able to define the Muckenhoupt (Ap) weights,
To be able to state the fundamental theorems of trigonometric approximation in weighted Lp spaces.
R.A. DeVore, G.G.Lorentz, Constructive Approximation, Springer-Verlag (1993).
G. Mastroianni, G.V.Milovanovic, Interpolation Processes, Springer (2008).
3. J. Garcia Cuerva, J. L. Rubio De Francia, Weighted Norm Inequalities and Related Topics, North
Holland (1985)
Learning
Outcomes
and
Competences
Textbook
and /or
References
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Percent
(%)
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Modulus of continuity and modulus of smoothness
Lipschitz and generalized Lipschitz classes
Direct theorems of trigonometric approximation in the spaces C and Lp
Bernstein inequality and inverse theorems of trigonometric approximation
Characterization of Lipschitz and gemneralized Lipschitz classes in terms of best approximation
Improvement of direct and inverse theorems
The Hardy-Littlewood maximal function
The Hilbert transform
Weighted Lp spaces and Ap weights
Weighted norm inequalities for the Hilbert transform and conjugate function
Convergence of Fourier series in weighted Lp spaces
Modulus of smoothness and K-functionals in weighted Lp spaces
Trigonometric approximation in weighted Lp spaces
Analogues of Marcinkiewicz multiplier and Littlewood-Paley theorems in weighted Lp spaces
Instructors
e-mail
[email protected]
Website
Course Title: Applied Mathematics II
Lecture
Lab.
Project/
Homework
Field Study
0
0
0
Application
42
0
Spring
Semester
Course Type
Course
Objectives
Learning
Outcomes
and
Competencies
Textbooks
and /or
References
Basic
Scientific
Field: Mathematics
Code : FMT5248
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish
Language
Scientific
Technical
Elective
Social
Elective
To teach the concepts of feedback linearization of nonlinear systems, Lyapunov stablity.





To be able to state existence and uniqueness theorems of nonlinear systems,
To be able to express and apply Lyapunov stability theorem,
To be able to express the concept of Input-Output stability,
To be able to express the concept of Stability with linearization
To be able to express Input-output Linearization.
1- H. K. Khalil, Nonlineer Systems, Prenice-Hall,1996.
2- F. Verhulst, Nonlineer Differential Equations and Dynamics Systems, Springer-Verlag, 1989.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as (X)
Percent
(%)
If any,
mark as (X)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Introduction to nonlinear systems. (Existence and uniqueness theorems).
Autonomous systems , Phase space, orbits,
Class of Critical points,
Periodic of solutions,
Stability Theory,
Lyapunov Stability Method,
Input-Output stability,
Stability with linearization,
Feedback systems,
Feedback control,
Feedback linearizable systems,
Feedback linearization,
Input-output Linearization,
State feedback control.
Instructors
Assoc Prof. Dr. Necati ÖZDEMİR
e-mail
[email protected]
Website
Percent
(%)
Course Title: Advanced Numerical Analysis II
Lecture
Lab.
Project/
Homework
Field Study
0
0
0
Application
42
0
Spring
Semester
Course Type
Course
Objectives
Learning
Outcomes
and
Competencies
Textbooks
and /or
References
Basic
Scientific
Field: Mathematics
Code : FMT5249
Scientific
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish
Language
Technical
Elective
Social
Elective
To teach numerical solution methods for ordinary differential equartions.



To be able to solve first order differential equations with sequential iterative method,
To be able to get numerical solutions of initial value problems for ordinary differential equations,
To be able to express Euler and Runge-Kutta one Step methods for first order ordinary differential
equations,
 To be able to use Nystom method for high order ordinary differential equations,
 To be able to express stability of numerical methods.
1) G. Amirali, H. Duru, Nümerik Analiz, Pegem A Yayınları, 2002,
2) A. Ralston, A First Course in Numerical Analysis, McGraw-Hill,1978,
3) S.C. Chapra, R.P. Canale, Numerical Methods for Engineers, McGraw-Hill, 1990.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as (X)
Percent
(%)
If any,
mark as (X)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Percent
(%)
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Difference Equations,
Solution of First Order Differential Equations with Sequential Iterative Method,
Numerical Solutions of Initial Value Problems for Ordinary Differential Equations,
One Step Methods for Ordinary Equations: Euler and Runge-Kutta,
Multi Step Methods,
Trial and Correction Formulas,
Runge-Kutta Method for Systems of First Order Equations,
Hamming Method,
Solutions of Higher Order Equations, Nystöm Method,
Numerical Solution of Ordinary Differential Equations for Boundary Value Problems,
Ignition Method,
Finite Difference Method,
Variational Difference Methods,
Stability of Numerical Methods.
Instructors
Assist Prof. Dr..Figen KİRAZ
e-mail
[email protected]
Website
Course Title: Numerical Solution of Partial
Lecture
Application
42
0
Lab.
Project/
Homework
Field Study
0
0
0
Spring
Semester
Course Type
Course
Objectives
Basic
Scientific
Field: Mathematics
Code : FMT5250
Differential Equations
Scientific
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish
Language
Technical
Elective
Social
Elective
To teach Numerical Methods for Solutions of Partial Differential Equations.
Learning
Outcomes
and
Competencies
1.
Textbooks
and /or
References
2.
3.
4.
 To be able to express convergence and stability of Parabolic Equations,
 To be able to apply Crank-Nicolson Closed Method,
 To be able to apply Finite-Difference Methods,
 To be able to solve Hyperbolic equations,
 To be able to solve Eliptic Equations.
K. W. Morton, D.F. Mayers, Numerical solution of partial differential equations, Cambridge University
Press, 1994
G.D. Smith, Numerical solution of partial differential equations, Oxford University Press, 1985.
J.Strickwerda, Finite difference schemes and partial differential equations, Wadsworth&Brooks/Cole,
1989.
E. Godlewski, P-a. Raviart, Numerical approximation of hyperbolic systems of conservation laws,
Springer, 1996.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as (X)
Percent
(%)
If any,
mark as (X)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Percent
(%)
Other
Other
Week
1
2
3
4
5
6
7
8
Subjects
Instructors
Introduction and Finite-Difference Formula,
Parabolic Equations: Finite Difference Methods, Convergence and Stability,
Explicit Method,
Crank-Nicolson Implicit Method,
Fourier Analysis of Eror,
Descriptive Treatment, Convergence, Stability
Gerschgorin’s theorems, Neumann’s Methods, Lax’s equivalence Theorem,
Hyperbolic equations and Characteristics: Analytical Solution of First Order Quasi-Linear
equations,
Numerical Integration Along a Characteristic,
Finite-Difference Methods, Lax-Wendroff Explicit Metod,
The Counrant –Friedrichs-Lewy Condition,
Wendroff’s Implicit Appoximation,
Elliptic Equations and Systematic Iterative Methods,
Systematic Iterative Methods for Large Linear Systems.
Assist Prof. Dr. Figen KİRAZ
e-mail
[email protected]
Website
9
10
11
12
13
14
Course Title: Differential Geometry of Curves
and Surfaces II
Lecture
Application
42
Lab.
Project/
Homework
Field Study
0
0
Basic
Scientific
Course
Objectives
0
Field: Mathematics
Other
Total
198
240
0
Spring
Semester
Course Type
Code : FMT5251
Scientific
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the differential geometry of curves and surfaces both in local and global aspects.





Learning
Outcomes
and
Competencies
Textbooks
and /or
References
To be able to define the Gauss map,
To be able to state the Gauss theorem,
To be able to define the concept of parallel transport,
To be able to express the properties of geodesics,
To be able to define the geodesic polar coordinates.
Manfredo P. do Carmo, Differential Geometry of Curves and Surfaces, 1976.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as (X)
Percent
(%)
If any,
mark as (X)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
A geometric definition of area.
A geometric definition of area.
The definition of Gauss map and its fundamental properties,
The definition of Gauss map and its fundamental properties,
The Gauss map in local coordinates, Vector fields.
The Gauss map in local coordinates, Vector fields.
Isometries , conformal maps ,
Isometries , conformal maps ,
The Gauss theorem, Parallel transport ,
The Gauss theorem, Parallel transport ,
The exponential map, Geodesic polar coordinates,
The exponential map, Geodesic polar coordinates,
Further properties of geodesics, Convex neighborhoods
Further properties of geodesics, Convex neighborhoods.
Instructor/s
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
Topology II
FMT5252
Field: Mathematics
Home
Project/
Field Study work
Lecture
42
0
0
Spring
Semester
Course Type
Course
Objectives
0
Basic
Scientific
Scientific
Other
Total
198
240
0
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the concepts of general topology in advanced level.





Learning
Outcomes
and
Competences
1.
2.
3.
4.
Textbook
and /or
References
To be able to construct topological structures by convergence of nets and filters,
To be able to express the countability properties,
To be able to define the concepts of compactness and local compactness,
To be able to express the metrizability properties of topological spaces,
To be able to define the concepts of Cauchy sequence, complete metric space, Baire category
theorem, paracompactness, totally regularity.
Osman Mucuk, Topoloji , Nobel Kitapevi, 2009.
Mahmut Koçak, Genel Topoloji I ve II, Gülen Ofset Yayınevi, 2006.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Instructors
e-mail
Website
X
% 80
X
% 20
Percent
(%)
Other
Subjects
Convergence
Networks, Convergence of networks
Limit Point
Continuity and Convergence
Countability Features
Compactness, Derived Spaces and Compactness
Compactness in Rn Compactness, local compactness
Kompaktifikasyon, Sequential Compactness and Countable Compactness
Metric Space Concept
Neighborhoods, Open Sets, Closed Sets
Convergence of Sequences
Continuity
Metrizability
Cauchy Sequences, Complete Metric Spaces, Baire Category Theorem, paracompactness,
totally Regularity
[email protected]
Course Title:
Code :
FMT5253
Lecture
Application
42
Field: Mathematics
Home
Laboratuary
Project/
Field Study work
0
0
0
Spring
Semester
Other
Total
198
240
0
Credits
Credit
ECTS
T+A+L=Credit
3
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the corresponding concepts of general topology in fuzzy topological spaces.





1.
2.
3.
4.
5.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Scientific
6
Technical
Elective
Social
Elective
To be able to give examples of interior, closure and boundary of a set in fuzz topological spaces,
To be able to define the concepts of fuzzy regular open set and fuzzy regular closed set,
To be able to define the concepts of fuzzy topology base and subbase,
To be able to define the fuzzy product spaces,
To be able to express the fuzzy separation axioms.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
The Concept of Fuzzy Topology
Fuzzy Topological Spaces
Fuzzy Neighborhoods Family
Within the cluster is a fuzzy
Closing and Limitation of a fuzzy cluster
On Fuzzy Regular Regular Closed Sets and Fuzzy
Accumulation Points of a fuzzy cluster
Fuzzy Topology Base and Subbase
Fuzzy First Countable Space
Fuzzy Second Countable Space
Fuzzy Subspaces
Fuzzy Product Spaces
Fuzzy Continuity
Fuzzy Separation Axioms
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
Introduction to Ideal Topological Spaces II
FMT5254
Lecture
Application
42
Home
Laboratuary
Project/
Field Study work
0
0
0
Fall
Semester
Course Type
Course
Objectives
Field: Mathematics
Basic
Scientific
Scientific
Other
Total
198
240
0
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the concept of delta-I-continuous function and to compare with the other types of functions.

Learning
Outcomes
and
Competences




1.
2.
3.
4.
5.
Textbook
and /or
References
To be able to define a type of continuous function in Ideal topological spaces and to prove related
theorems,
To be able to express the properties of Delta-I-closure point,
To be able to prove the characterization of Delta-I-continuous function,
To be able to compare the functions,
To be able to express the properties of functions in SI-R and AI-R spaces.
Şaziye Yüksel, Genel Topoloji, Eğitim Kitapevi, (2011).
Osman Mucuk, Topoloji, Nobel Kitapevi, (2009).
Mahmut Koçak, Genel Topoloji I ve II, Gülen Ofset Yayınevi, (2006).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
Delta-I-sets
Delta-I-Cluster Point
Properties of Delta-I-Cluster Point
R-I-open set
Comparison of the Sets
Delta-I-continuous function
Characterization of Delta-I-continuous function
Strongly theta-I-continuous function
Almost-I-continuous function
Comparison Functions
All the reverse examples studies
SI-R space
AI-R space
Investigation of the functions in these spaces
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application
42
0
Code :
FMT5255
Course
Objectives
Credits
Laboratuary
Project/
Hw.
Field Study
0
0
0
Fall
Semester
Course Type
Field: Mathematics
Basic
Scientific
Scientific
Other
Total
T+A+L=
Credit
ECTS
198
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach the approximation properties of orthogonal polynomials in the complex plane.




Learning
Outcomes
and
Competences

1)
2)
Textbook
and /or
References
3)
4)
To be able to express the asymptotic representations of orthogonal polynomials,
To be able to express the Bernstein-Walsh maximal convergence theorem,
To be able to express the asymptotic properties of orthogonal polynomials,
To be able to express the approximation properties of Fourier series of orthogonal polynomials on
closed domains,
To be able to define the distribution of zeros of kernel functions.
V.I.Smirnov and N. A. Lebedev, Functions on a Complex Variable, MIT pres, 1968.
P. K. Suetin, Fundamental Properties of Polynomials Orthogonal on a Contour, Russ. Math. Surv.,
1966.
P. K .Suetin, Polynomials Orthogonal over a region and Bieberbach Polynomials, Proceedings of the
Steklov Institute of Mathematics, AMS, 1974.
D.Gaier, Lectures on Complex Approximation,Birkhauser, 1987.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Percent
(%)
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
The representation of asymptotic s of othogonal polynomials , Carleman Theorem
The rate of approximation of analytic functions on closure of the domain
Bernstein-Walsh Lemma
The convergence of Fourier Series of orthogonal polynomials on closed domains
In the case of weight function, the convergence of Fourier Series of orthogonal polynomials
Orthogonal polynomials on unit circle
The convergence of Fourier Series of orthogonal polynomials on closed domains on the boundary of the
domain
Ortogonal polynomials from potential theory perspective
Asymptotics of ortogonal polynomials over domains bounded with analytic Jordan curves,
Zeros of ortogonal polynomials over domains bounded with analytic Jordan curves
Asymptotics of Bergman polynomials
Zero distribution of Bergman polynomials
Asymptotics of Kernel polynomials,
Zero distribution of Kernel polynomials
Instructors
e-mail
[email protected]
Website
Course Title:
Lecture
Application
42
0
Code :
FMT5256
Fall
Basic
Scientific
Course
Objectives
Scientific
Other
Total
T+A+L=
Credit
ECTS
198
240
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To introduce the problems of convergence in the geometric theory of functions.





Learning
Outcomes
and
Competences
Textbook
and /or
References
Credits
Laboratuary
Project/
Hw.
Field Study
0
0
0
Semester
Course Type
Field: Mathematics
To be able to define the convergence of the sequences of analytic and harmonic functions,
To be able to expressthe boundary value problems for analytic functions defined on a disk,
To be able to express the boundary value problems for functions analytic inside a rectifiable contour,
To be able to define the conformal mappings of multiply connected domains,
To be able to make representations of harmonic functions by aim of Poisson integral.
G. M. Goluzin, Geometric Theory of Functions of a complex variable, 1969.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Fundamental properties of analytic functions
Fundamental properties of harmonic functions
The convergence of sequence of analytic functions
The convergence of sequence of harmonic functions
Conformal mappings of simply connected domains
Riemann conformal theorem
Conformal mappings of multiply connected domains
Dirichlet problem; Green function
Limiting values of Poisson’s integral
The representation of harmonic functions by means of Poisson integral
Boundary properties of analyic functions in Hardy class
The limiting values of Cauchy integrals
Applications of conformal mappings
Applications of conformal mapping
Instructors
e-mail
[email protected]
Website
Percent
(%)
Code :
Course Title: Algebraic Number Theory II
Field: Mathematics
FMT5257
Home
Project/
Field Study work
Lecture
42
0
0
0
Total
198
240
0
Fall
Semester
Other
Credits
Credit
ECTS
T+A+L=Credit
3
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach fundamental concepts and theorems related with the algebraic number theory.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Technical
Elective
Scientific
6
Social
Elective
 To be able to define the ideal class group,
 To be able to apply the algorithms for the ideal class group,
 To be able to state the Dirichlet’s unit theorem,
 To be able to determine the fundamental units of cubic fields,
 To be able to apply the diophantine equations.
1) E. Weiss, Algebraic Number Theory, Dover publications, 1998.
2) I. Stewart, D. Tall, Algebraic Number Theory and Fermat’s Last Theorem, A K Peters Ltd., 2002.
3) M.R. Murty, J. Esmonde, Problems in Algebraic Number Theory, Springer,2005.
4) Ş. Alaca, K. S. Williams, Introductory Algebraic Number Theory, Cambridge Univ. Press, 2004 .
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
The Fundamental Unit
Calculating the Fundamental Unit
The Ideal Class Group
The Ideal Class Group
Algorithm to Determine the Ideal Class Group
Applications to Binary Quadratic Forms
Dirichlet’s Unit Theorem
Valuations of an Element of a Number Field
Valuations of an Element of a Number Field
Fundamental System of Units
Fundamental Units in Cubic Fields
Fundamental Units in Cubic Fields
Applications to Diophantine Equations
Applications to Diophantine Equations
Instructors
Assoc. Prof. Dr. Sebahattin İkikardes
e-mail
[email protected]
Website
http://w3.balikesir.edu.tr/~skardes/
Percent
(%)
Course Title: Numerical Optimization II
Lecture
Laboratuary
Project/
Home
Field Study
work
Application
42
Field: Mathematics
Code : FMT 5258
0
0
0
Spring
Semester
Other
0
198
Total
Credits
Credit
ECTS
T+A+L=Credit
240
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach optimality conditions of unconstrained and constrained nonlinear optimization problems with
fundamental solution methods.
 To be able to express optimality conditions for unconstrained and constrained optimization problems,
 To be able to express the concept of Lagrange function and multiplier,
 To be able to define Karush-Kuhn-Tucker conditions,
 To be able to express optimality conditions for quadratic programming,
 To be able to apply penalty, barrier and feasible direction methods.
Learning
Outcomes
and
Competences
1)
Textbook
and /or
References
2)
3)
4)
5)
Scientific
Technical
Elective
Social
Elective
Bazaraa M.S., Sherali H.D. and Shetty S.M., Nonlinear programming: Theory and Applications, 3rd edition,
Chong E.K. and Zak S.H., An introduction to optimization, 2nd edition, John Wiley & Sons, Inc., 2001.
Griva I., Nash S.G. and Sofer A., Linear and nonlinear optimization, 2nd edition, SIAM, 2008.
Luenberger D.G. and Ye Y., Linear and nonlinear programming, 3rd edition, Springer, 2008.
Sun W. and Yuan Y-X, Optimization Theory and Method: Nonlinear Programming, Springer, 2006.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Nonlinear programming and problem formulations
Optimality conditions for equality constraints
Optimality conditions for inequality constraints
Constraint qualifications
The Lagrange multipliers and the Lagrangian functions
Karush-Kuhn-Tucker conditions
Optimality for Quadratic Programming
Methods for quadratic Programming
Penalty an Barrier Methods
Feasible Direction Methods
Sequential Quadratic Programming
Nonsmooth optimization and problems
Generalized gradients
The sub-gradient method
Instructors
Assist. Prof. Dr. Fırat EVİRGEN
e-mail
[email protected]
Website
Percent
(%)
Course Title: Selected Topics in Differential
Geometry II
Lecture
Application
42
Lab.
Project/
Homework
Field Study
0
0
Basic
Scientific
Course
Objectives
0
Field: Mathematics
Other
Total
198
240
0
Spring
Semester
Course Type
Code : FMT5259
Scientific
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Technical
Elective
Social
Elective
To teach fundamental concepts of Riemannian Geometry and the concept of submanifold of finite type.
Learning
Outcomes
and
Competencies





To be able to define the concepts of Sectional , Ricci and scalar curvature,
To be able to define the concept of tensor in Riemann manifolds,
To be able to define the concept of submanifold of finite type and to give examples,
To be able to define closed curves of finite type and to give examples,
To be able to define the concept of isometric immersion.
Textbooks
and /or
References
1)
2)
M.P. do Carmo, Riemannian Geometry, Birkhauser Boston 1992.
Bang-yen Chen, Total Mean Curvature and Submanifolds of Finite Type, World Scientific 1984.
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as (X)
Percent
(%)
If any,
mark as (X)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Curvature; Sectional , Ricci and scalar curvature
Curvature; Sectional , Ricci and scalar curvature
Jacobi fields
Isometric immersions
Submanifolds
Submanifolds
Submanifolds of finite type
Submanifolds of finite type
Characterizations of 2-type submanifolds
Characterizations of 2-type submanifolds
Closed curves of finite type
Closed curves of finite type
Instructor/s
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Code :
FMT5260
Field: Mathematics
Home
Project/
work
Field Study
0
0
0
0
Lecture
42
Spring
Semester
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Course Type
Basic
Scientific
Course
Objectives
To teach the basic knowledge about r-bonacci polynomials and generalized complex Fibonacci and Lucas
functions.

To be able to define and apply basic properties of tribonacci, quadranacci polynomials,

To be able to define and apply basic properties of r-bonacci polynomials,
 To be able to define and apply basic properties of generalized complex Fibonacci functions,
 To be able to define and apply basic properties of Lucas functions,
 To be able to express the continuous functions for the Fibonacci and Lucas p-numbers.
1) N. D. Cahill, J. R. D’Ericco and J. P. Spence, Complex factorizations of the Fibonacci and Lucas
numbers, Fibonacci Quart., 41(1), 13-19, 2003.
2) A. Stakhov and B. Rozin, Theory of Binet formulas for Fibonacci and Lucas p-numbers, Chaos,
Solitons Fractals, 27(5), 1162-1177, 2006.
3) A. Stakhov and B. Rozin, The continuous functions for the Fibonacci and Lucas p-numbers, Chaos,
Solitons Fractals, 28(4), 1014-1025, 2006.
Learning
Outcomes
and
Competences
Textbook
and /or
References
Scientific
Technical Elective
Social
Elective
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
Oral Examination
Laboratory Work
Final Exam
Final Exam
Other (Class
Performance)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X
% 80
X
% 20
Other
Subjects
Tribonacci numbers
Tribonacci polynomials
Factoring Fibonacci and Lucas polynomials I
Factoring Fibonacci and Lucas polynomials II
Applications
Quadranacci and r-bonacci polynomials I
Quadranacci and r-bonacci polynomials II
Complex factorizations of the Fibonacci numbers I
Complex factorizations of the Fibonacci numbers II
Applications
Generalized complex Fibonacci and Lucas functions
Fibonacci and Lucas p-numbers
The continuous functions for the Fibonacci and Lucas p-numbers
Applications
Instructors
e-mail
[email protected]
Website
Percent
(%)
Course Title:
Lecture
Application
42
0
Lab.
Project/
Homework
Field Study
0
0
0
Spring
Semester
Basic
Scientific
Course Type
Course
Objectives
Field: Mathematics
Code : FMT5261
Other
Total
198
240
Credits
Credit
ECTS
T+A+L=Credit
3
6
Turkish/English
Language
Scientific
Technical
Elective
Social
Elective
To teach the general properties of hypersurfaces and submanifolds of Semi-Riemannian manifolds.





3)
4)
Learning
Outcomes
and
Competencies
Textbooks
and /or
References
To be able to express the general properties of submanifolds of Semi-Riemannian manifolds,
To be able to define the Non-Degenerate hypersurfaces of Semi-Riemannian manifolds,
To be able to define the Lightlike hypersurfaces of Semi-Riemannian manifolds,
To be able to define the concept of totally umbilical hypersurface,
To be able to define the concept of normal connection.
B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, Inc., 1983.
K. L. Duggal D. H. Jin, Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Sci.,
2007.
ASSESSMENT CRITERIA
Theoretical Courses
Midterm Exams
If any,
mark as (X)
Percent
(%)
X
40
If any,
mark as (X)
Midterm Exams
Quizzes
Midterm Controls
Homework
Term Paper
Term Paper, Project
Reports, etc.
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
60
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Tangents and normal
Induced connections
Geodesic submanifolds
Non-Degenerate hypersurfaces of a Semi-Riemannian manifold
Lightlike hypersurfaces of a Semi-Riemannian manifold
Lightlike submanifolds
Lightlike surfaces in R14
Hyperquadrics
Codazzi equation
Totally umbilical hypersurfaces
The normal connection
A Congruence Theorem
Isometric immersions
Two-parameter maps
Instructor/s
e-mail
[email protected]
Website
Percent
(%)

Bölüm Bilgileri - balıkesir üniversitesi matematik bölümü

Transcription

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