Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

INSTITUTE OF SCIENCE / MATHEMATICS (DOCTORATE DEGREE)

History

The PhD program was established in 2011.


Qualification Awarded

The students who successfully complete the program is awarded a PhD.


Level of Qualification

PhD.


Specific Admission Requirements

The candidates which has both undergraduate and graduate degree can apply this programme. Students must comply with the legal and academic requirements to access the studies in Nevşehir Hacı Bektaş Veli University according to the process established by the YÖK (Higher Education Council) regulations. Students who have started studies in other universities within or outside of the country may apply for their recognition. The recognition record is unique for each student and therefore the procedure is carried out accordingly before the start of each academic year. Under an established exchanges program or one approved by the University, exchange students from abroad may be accepted for studies on the courses taught in English. Or, if they are confident in Turkish, they may then enrol any courses, running in Turkish, shown on the Course Structure diagram.


Specific Arrangement For Recognition of Prior Learning

The course \ courses taken at another university in the last three years before to enroll in Doctorate by students of the Mathematics Department at Nevşehir Hacı Bektaş Veli University Institute of Science and Technology is/are examined in terms of equivalent credit, curriculum, etc. and with the approval of related department students may be exempt from course/courses with a proposal from the department finalized by Administration Board of Institute.


Qualification Requirements and Regulations

Graduates must complete all courses available in the program at least 24 credits (a total of 60 ECTS) and have at least 75 on a 100 weighted grade point average . Undergraduates must complete all courses available in the program at least 48 credits (a total of 120 ECTS) and have at least 75 on a 100 weighted grade point average . After passing the qualifying exam, the students who defend the thesis that have been prepared in their subject area, take PhD degree in mathematics.


Profile of The Programme

The purpose of doctorate programs in mathematics is developing their knowledge of theory and applications at master degree depending on the competencies acquired in undergraduate level and master’s level, and producing new solutions with scientific methods mostly based on analysis and synthesis.


Key Learning Outcomes of the Programme

PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues.
PO-2 Students will understand all aspects of mathematics and deepen the knowledge level that can innovate in this field.
PO-3 Students will be dominated by current issues in mathematics.
PO-4 At least one foreign language at an advanced level counterparts in written, oral and visual communicate and participate in academic discussions.
PO-5 Be able to access to information, make research on resources for this purpose and be able to use databases and other information resources.
PO-6 To perform the ethical responsibilities in working life.
PO-7 Ability to learn information about history of science and scientific knowledge production.
PO-8 Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
PO-9 Ability to make individual and team work on issues related to working and social life.
PO-10 Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
PO-11 Ability to use mathematical knowledge in technology.
PO-12 Ability to develop a foreign language in a sufficient level to follow the information in his/her field of interest and to communicate with the colleagues.
PO-13 To apply mathematical principles to real world problems.
PO-14 Ability to use the approaches and knowledge of other disciplines in Mathematics.
PO-15 Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.

NQF-HETR Program Outcomes Matrices
TYYC PÇ-1 PÇ-2 PÇ-3 PÇ-4 PÇ-5 PÇ-6 PÇ-7 PÇ-8 PÇ-9 PÇ-10 PÇ-11 PÇ-12 PÇ-13 PÇ-14 PÇ-15
1- Develop and deepen the current and advanced knowledge in the field with original thought and/or research and come up with innovative definitions based on Master's degree qualifications. X X X X X
2- Conceive the interdisciplinary interaction which the field is related with ; come up with original solutions by using knowledge requiring proficiency on analysis, synthesis and assessment of new and complex ideas. X X X X X X
1- Evaluate and use new information within the field in a systematic approach. X X
2- Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field; research, conceive, design, adapt and implement an original subject. X X X X X X X
3- Critical analysis, synthesis and evaluation of new and complex ideas. X X X
4- Gain advanced level skills in the use of research methods in the field of study. X X X X X X
1- Contribute the progression in the field by producing an innovative idea, skill, design and/or practice or by adapting an already known idea, skill, design, and/or practice to a different field independently. X X X X
2- Broaden the borders of the knowledge in the field by producing or interpreting an original work or publishing at least one scientific paper in the field in national and/or international refereed journals. X X
3- Demonstrate leadership in contexts requiring innovative and interdisciplinary problem solving. X
1- Develop new ideas and methods in the field by using high level mental processes such as creative and critical thinking, problem solving and decision making. X X X
1- Investigate and improve social connections and their conducting norms and manage the actions to change them when necessary. X
2- Defend original views when exchanging ideas in the field with professionals and communicate effectively by showing competence in the field. X X
3- Ability to communicate and discuss orally, in written and visually with peers by using a foreign language at least at a level of European Language Portfolio C1 General Level. X X
1- Contribute to the transition of the community to an information society and its sustainability process by introducing scientific, technological, social or cultural improvements. X
2- Demonstrate functional interaction by using strategic decision making processes in solving problems encountered in the field. X
3- Contribute to the solution finding process regarding social, scientific, cultural and ethical problems in the field and support the development of these values. X
Basic Area Competencies-Program Outcomes Matrix (Academic Weighted)
Açıklama PÇ-1 PÇ-2 PÇ-3 PÇ-4 PÇ-5 PÇ-6 PÇ-7 PÇ-8 PÇ-9 PÇ-10 PÇ-11 PÇ-12 PÇ-13 PÇ-14 PÇ-15
It develops the current and advanced information in the field based on the domestic qualifications, develops in the expertise level with original thinking and / or research, deepens and reach the original definitions to bring innovation in the field. X X X X X
Understands the interdisciplinary interaction of the field; The new and complex ideas reach the original results using the information that requires expertise in analysis, synthesis and evaluation. X X X X X X
Evaluates, uses, and transfers the new information in the field with a systematic approach. X X
It develops innovation in the field, develops a new thought, method, design and / or application or applies a known thought, method, design and / or application to a different area, investigate, comprehend, adheres, and applies. X X X X X X X
It makes the critical analysis, synthesis and evaluation of new and complex thoughts. X X X
In studies related to the field, he has gained high-level skills in using research methods. X X X X X X
Innovation in the field, developing a new thought, method, design and / or developing or developing a known thought, method, design, and / or application to progress in the field of realizing an original study by realizing an original study in a different area. X X X X
Expands the limits of information in the field by publishing at least one scientific article on the field and by publishing at least one scientific article in national and / or international peer-reviewed magazines and / or by producing or interpreting an original artwork. X X
Leads in environments that require analyzing of internal and disciplinary problems. X
Creative and critical thinking improves new thoughts and methods using high-level mental processes such as problem solving and decision making. X X X
Social relations and these relationships examine, develops, develops from a critical perspective, and manages the actions to change when necessary. X
In discussion of the subjects in the field with experts, he defends its original views and establish an effective communication in the field. X X
A foreign language is at least the European Language Portfolio using a general level of C1, and discusses advanced, verbal and visual communication and discusses. X X
By following the developments in the level required by the area of ​​the field, it uses the developments in knowledge and communication technologies effectively in their research to solve their problems. X
It makes scientific research in national and international scientific research groups. X X
By introducing scientific, technological, social or cultural progress in the field, it contributes to the process of knowledge of the community in which the society lived and to continue. X
In the solution of the problems encountered in the field, it establishes functional interactions using strategic decision-making processes. X
It contributes to the solutions of the social, scientific, cultural and ethical problems encountered on the fields related to the field and supports the development of these values. X





Turkey Higher Education Qualifications Framework (TYYC, Level 8,) ) Basic Field Competencies (Academic Weighted) PROGRAM ÇIKTILARI TYYÇ
PÇ-1 PÇ-2 PÇ-3 PÇ-4 PÇ-5 PÇ-6 PÇ-7 PÇ-8 PÇ-9 PÇ-10 PÇ-11 PÇ-12 PÇ-13 PÇ-14 PÇ-15
KNOWLEDGE Theoretical-Conceptual It develops the current and advanced information in the field based on the domestic qualifications, develops in the expertise level with original thinking and / or research, deepens and reach the original definitions to bring innovation in the field. 1 x x x x x x x x x x 1- Develop and deepen the current and advanced knowledge in the field with original thought and/or research and come up with innovative definitions based on Master's degree qualifications. Theoretical-Conceptual KNOWLEDGE
KNOWLEDGE Theoretical-Conceptual Understands the interdisciplinary interaction of the field; The new and complex ideas reach the original results using the information that requires expertise in analysis, synthesis and evaluation. 2 x x x x x x x x x x x x 2- Conceive the interdisciplinary interaction which the field is related with ; come up with original solutions by using knowledge requiring proficiency on analysis, synthesis and assessment of new and complex ideas. Theoretical-Conceptual KNOWLEDGE
SKILLS Cognitive-Practical Evaluates, uses, and transfers the new information in the field with a systematic approach. 1 x x x x 1- Evaluate and use new information within the field in a systematic approach. Cognitive-Practical SKILLS
SKILLS Cognitive-Practical It develops innovation in the field, develops a new thought, method, design and / or application or applies a known thought, method, design and / or application to a different area, investigate, comprehend, adheres, and applies. 2 x x x x x x x x x x x x x x 2- Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field; research, conceive, design, adapt and implement an original subject. Cognitive-Practical SKILLS
SKILLS Cognitive-Practical It makes the critical analysis, synthesis and evaluation of new and complex thoughts. 3 x x x x x x 3- Critical analysis, synthesis and evaluation of new and complex ideas. Cognitive-Practical SKILLS
SKILLS Cognitive-Practical In studies related to the field, he has gained high-level skills in using research methods. 4 x x x x x x x x x x x x 4- Gain advanced level skills in the use of research methods in the field of study. Cognitive-Practical SKILLS
COMPETENCES Creative and critical thinking improves new thoughts and methods using high-level mental processes such as problem solving and decision making. 1 x x x x x x 1- Develop new ideas and methods in the field by using high level mental processes such as creative and critical thinking, problem solving and decision making. Learning Competence COMPETENCES
COMPETENCES Social relations and these relationships examine, develops, develops from a critical perspective, and manages the actions to change when necessary. 1 x x 1- Investigate and improve social connections and their conducting norms and manage the actions to change them when necessary. Communication and Social Competence COMPETENCES
COMPETENCES In discussion of the subjects in the field with experts, he defends its original views and establish an effective communication in the field. 2 x x x x 2- Defend original views when exchanging ideas in the field with professionals and communicate effectively by showing competence in the field. Communication and Social Competence COMPETENCES
COMPETENCES A foreign language is at least the European Language Portfolio using a general level of C1, and discusses advanced, verbal and visual communication and discusses. 3 x x x x 3- Ability to communicate and discuss orally, in written and visually with peers by using a foreign language at least at a level of European Language Portfolio C1 General Level. Communication and Social Competence COMPETENCES
COMPETENCES By following the developments in the level required by the area of ​​the field, it uses the developments in knowledge and communication technologies effectively in their research to solve their problems. 4 x Communication and Social Competence COMPETENCES
COMPETENCES It makes scientific research in national and international scientific research groups. 5 x x Communication and Social Competence COMPETENCES
COMPETENCES By introducing scientific, technological, social or cultural progress in the field, it contributes to the process of knowledge of the community in which the society lived and to continue. 1 x x 1- Contribute to the transition of the community to an information society and its sustainability process by introducing scientific, technological, social or cultural improvements. Field Specific Competence COMPETENCES
COMPETENCES In the solution of the problems encountered in the field, it establishes functional interactions using strategic decision-making processes. 2 x x 2- Demonstrate functional interaction by using strategic decision making processes in solving problems encountered in the field. Field Specific Competence COMPETENCES
COMPETENCES It contributes to the solutions of the social, scientific, cultural and ethical problems encountered on the fields related to the field and supports the development of these values. 3 x x 3- Contribute to the solution finding process regarding social, scientific, cultural and ethical problems in the field and support the development of these values. Field Specific Competence COMPETENCES
COMPETENCES Innovation in the field, developing a new thought, method, design and / or developing or developing a known thought, method, design, and / or application to progress in the field of realizing an original study by realizing an original study in a different area. 1 x x x x x x x x 1- Contribute the progression in the field by producing an innovative idea, skill, design and/or practice or by adapting an already known idea, skill, design, and/or practice to a different field independently. Competence to Work Independently and Take Responsibility COMPETENCES
COMPETENCES Expands the limits of information in the field by publishing at least one scientific article on the field and by publishing at least one scientific article in national and / or international peer-reviewed magazines and / or by producing or interpreting an original artwork. 2 x x x x 2- Broaden the borders of the knowledge in the field by producing or interpreting an original work or publishing at least one scientific paper in the field in national and/or international refereed journals. Competence to Work Independently and Take Responsibility COMPETENCES
COMPETENCES Leads in environments that require analyzing of internal and disciplinary problems. 3 x x 3- Demonstrate leadership in contexts requiring innovative and interdisciplinary problem solving. Competence to Work Independently and Take Responsibility COMPETENCES

Occupational Profiles of Graduates with Examples

Graduates of doctorate programs are strong candidates basically for academic careers and advanced research positions. In addition, they may also be employed by relevant public and private companies for senior positions in R&D departments.


Access to Further Studies

The successfull graduates of this program can apply to a post-doctoral program if they want to.


Course Structure Diagram with Credits

1. Semester Course Plan

Course Code Course Title Theoretical Practice Year Semester of Study Type of Course ECTS
MAT679 SCIENTIFIC RESEARCH AND PUBLICATION ETHICS 3 Hour(s) 0 Hour(s) 1 Fall Semester Compulsory 6
SEC 1 ELECTIVE LESSON POOL 1 - Hour(s) - Hour(s) 1 Fall Semester Optional 24
Total:
30

2. Semester Course Plan

Course Code Course Title Theoretical Practice Year Semester of Study Type of Course ECTS
MAT600 SEMINAR 0 Hour(s) 2 Hour(s) 1 Spring Semester Compulsory 18
SEC 2 ELECTIVE LESSON POOL 2 - Hour(s) - Hour(s) 1 Spring Semester Optional 12
Total:
30

3. Semester Course Plan

Course Code Course Title Theoretical Practice Year Semester of Study Type of Course ECTS
MAT700 PREPARATION FOR PROFICIENCY 0 Hour(s) 0 Hour(s) 2 Fall Semester Compulsory 30
Total:
30

4. Semester Course Plan

Course Code Course Title Theoretical Practice Year Semester of Study Type of Course ECTS
MAT698 THESIS STUDIES 0 Hour(s) 0 Hour(s) 2 Spring Semester Compulsory 24
MAT692 SPECIAL FILED COURSE 4 Hour(s) 0 Hour(s) 2 Spring Semester Compulsory 6
Total:
30

5. Semester Course Plan

Course Code Course Title Theoretical Practice Year Semester of Study Type of Course ECTS
MAT697 THESIS STUDIES 0 Hour(s) 0 Hour(s) 3 Fall Semester Compulsory 24
MAT691 SPECIAL FIELD COURSE 4 Hour(s) 0 Hour(s) 3 Fall Semester Compulsory 6
Total:
30

6. Semester Course Plan

Course Code Course Title Theoretical Practice Year Semester of Study Type of Course ECTS
MAT698 THESIS STUDIES 0 Hour(s) 0 Hour(s) 3 Spring Semester Compulsory 24
MAT692 SPECIAL FIELD COURSE 4 Hour(s) 0 Hour(s) 3 Spring Semester Compulsory 6
Total:
30

7. Semester Course Plan

Course Code Course Title Theoretical Practice Year Semester of Study Type of Course ECTS
MAT697 THESIS STUDIES 0 Hour(s) 0 Hour(s) 4 Fall Semester Compulsory 24
MAT691 SPECIAL FIELD COURSE 4 Hour(s) 0 Hour(s) 4 Fall Semester Compulsory 6
Total:
30

8. Semester Course Plan

Course Code Course Title Theoretical Practice Year Semester of Study Type of Course ECTS
MAT698 THESIS STUDIES 0 Hour(s) 0 Hour(s) 4 Spring Semester Compulsory 24
MAT692 SPECIAL FIELD COURSE 4 Hour(s) 0 Hour(s) 4 Spring Semester Compulsory 6
Total:
30

ELECTIVE LESSON POOL 1

Course Code Course Title Theoretical Practice Year Semester of Study Type of Course ECTS
MAT675 NUMERICAL METHODS FOR ORDINARY AND PARTIAL DIFF. EQ. I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT609 ALGEBRAIC GRAPH THEORY I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT603 THEORY OF FIELD 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT651 BIFURCATION AND CHAOS THEORY I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT621 MATRIX TRANSFORMATION ON SEQUENCE SPACES I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT633 STABILITY THEORY OF DIFFERENCE EQUATIONS 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT649 FRACTAL STRUCTURES AND APPLICATIONS 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT631 THE SEQUENCE SPACES OF FUZZY NUMBERS I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT607 GRAF ENERGY I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT601 THEORY OF RING I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT619 CATEGORICAL TOPOLOGY I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT673 PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT645 COMPLEX MANIFOLDS I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT647 THEORY OF QUATERNIONS I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT641 GEOMETRY OF MANIFOLDS I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT667 BOUNDARY VALUE PROBLEMS I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT661 FINITE DIFFERENCE METHODS I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT605 SPECTRAL GRAPH THEORY I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT617 SELECTED TOPICS IN TOPOLOGY I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6
MAT643 SEMI-RIEMANNIAN MANIFOLDS I 3 Hour(s) 0 Hour(s) 1 Fall Semester Optional 6

ELECTIVE LESSON POOL 2

Course Code Course Title Theoretical Practice Year Semester of Study Type of Course ECTS
MAT676 NUMERICAL METHODS FOR ORDINARY AND PARTIAL DIFF. EQ. II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT610 ALGEBRAIC GRAPH THEORY II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT652 BIFURCATION AND CHAOS THEORY II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT622 MATRIX TRANSFORMATIONS ON SEQUENCE SPACES II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT634 ASIMPOTIC BEHAVIOR OF FARK EQUATIONS 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT632 THE SEQUENCE SPACES OF FUZZY NUMBERS II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT604 GALOIS THEORY 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT608 GRAF ENERGY II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT602 THEORY OF RING II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT620 CATEGORICAL TOPOLOGY II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT674 PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT646 COMPLEX MANIFOLDS II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT648 THEORY OF QUATERNIONS II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT642 GEOMETRY OF MANIFOLDS II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT668 BOUNDARY VALUE PROBLEMS II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT662 FINITE DIFFERENCE METHODS II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT606 SPECTRAL GRAPH THEORY II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT618 SELECTED TOPICS IN TOPOLOGY II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT666 APPLIED FUNCTIONAL ANALYSIS 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6
MAT644 SEMI-RIEMANNIAN MANIFOLDS II 3 Hour(s) 0 Hour(s) 1 Spring Semester Optional 6

Examination Regulations, Assessment and Grading

Students are subjected to midterm and final exam for each course.The contribution of the midterm exam is 40% and final exam is 60%. All examinations are evaluated out of 100 points. On one course students who gets one of the letter grades (AA), (BA), (BB), (CB) and (CC) considered as successful.


Graduation Requirements

To complete the PhD program;the students that have master degree, must complete a total of not less than 24 credits and at least eight of the department seminar course and pass the qualifying examination successfully.


Mode of Study

Full Time


Facilities

The deparment consist of 2 Professors, 4 Associated Professors, 4 Assistant Professors, 1 Lecturer, 3 Research Assistants.


Programme Director or Equivalent

Nevşehir Hacı Bektaş Veli University Faculty of Arts and Sciences Depatment of Mathematics 2000 Evler Mahallesi Zübeyde Hanım Cad. 50300 Nevşehir / Turkey Phone : +90 384 228 10 00 Fax : +90 384 215 39 48