1. THIRD CYCLE - DOCTORATE DEGREE
  2. THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
  3. MATHEMATICS DEPARTMENT
General Information Prog. Learning Outcomes Teaching & Learning Methods Course Structure Course & Learning Outcomes LO - NQF-HETR Relation LO - FOE (Academic) LO - FOE (Vocational)

1781 Mathematics PhD

GENERAL INFORMATION
Mathematics Programme offers both theoretical and application-specific courses in various specialized options like Analysis and Theory of Functions, Geometry, Applied Mathematics, Algebra and Number Theory, and Topology.

Objective
A person who graduated from the Mathematics Graduate Program will have expert knowledge one of the topics in analysis and theory of functions, geometry, applied mathematics, algebra and number theory and topology. Person graduated from a scientific point of view the real-world problems are shaped by the ability of scientific research finding necessary information in the literature, making the necessary observations and the information obtained by analyzing, the resulting and writing the information.


Admission Requirements
Standardized graduate examination given by OSYM (ALES), acceptable score on centralized graduate entrance exam, placement through local oral/written exam and certificate of English proficiency.

Graduation Requirements
A student must be complete the required course load (21 PAU credits) with a CGPA of at least 3.30/4.00; and additionally complete two courses for educational evaluation and one course for scientific research techniques; present two research seminars, pass the qualifier exam and successfully prepare and defend a PhD thesis.

Career Opportunties
The mathematics graduates are employed in public and private sector and many areas related to their profession. In addition, our graduates which have completed pedagogical formation courses has been working as a teacher in educational institutions.

Qualification Awarded
Mathematics Phd

Level of Qualification
Third Cycle (Doctorate Degree)

Recognition of Prior Learning
A successful student who has completed at least one semester in another institution / department of the university or another post-graduate program of another higher education institution may be admitted to the post-graduate programs by horizontal transfer. The conditions for acceptance by horizontal transfer are determined by the Senate.

Qualification Requirements and Regulations
A student must be complete the required course load (21 PAU credits) with a CGPA of at least 3.30/4.00; and additionally complete two courses for educational evaluation and one course for scientific research techniques; present two research seminars, pass the qualifier exam and successfully prepare and defend a PhD thesis.

Access to Further Studies
A student graduated with a good PhD Degree may carry on an academic carrier as a lecturer or post doctorate researcher.

Mode of Study
Full Time

Examination Regulations, Assessment and Grading
Measurement and evaluation methods that is applied for each course, is detailed in "Course Structure&ECTS Credits".

Contact (Programme Director or Equivalent)
PositionName SurnamePhoneFaxE-Mail
HEAD OF THE DEPARTMENT OF INSTITUTEProf. Dr. MUSTAFA AŞCI  masci@pau.edu.tr


PROGRAM LEARNING OUTCOMES
1Understands and applies the mathematical proof.
2Reads, understands and uses the basic definitions.
3Has an advanced level of critical thinking skills.
4Solves advanced problems using standard mathematical techniques.
5Uses mathematic as the language of science.
6Writes a software programme for mathematical calculations.
7Gains experiences for the application areas of mathematics and mathematical modelling.
8Has the ability to conduct original research and independent publication.
9His scientific research publications as scientific papers in international journals.
TEACHING & LEARNING METHODS
NameComments
LecturingLecturing is one of the methods that come first, where the teacher is in the center. It is a method where the teacher actively describes topics and the students are passive listeners. With this method, lesson proceeds in the form of report, description and explanation.
DebateDepending on the situation, debate is a tool that allows all students, or a specific portion of the class to participate in the lesson. In this method, members of the group discuss a topic by addressing the various points of view and discuss alternative opinions about problem-solving.
Problem SolvingThe name given to any doubt or ambiguity that arises is, a problem. Problems which usually have a role in human life, that have preventing or annoying aspects are solved by considering the stages of scientific methods. (a) Problems are determined. (b) The problem is identified. 
Cooperative LearningCooperative Learning is; a kind of learning that is based on the students working together for a common purpose. Children with different skills come together in heterogeneous groups to learn by helping each other. Students gain experiences such as becoming aware of the unity
Questions –AnswersThe different types of Questions used (associative, differential, assessment, requesting information, motivating, and brainstorming) although students get in to more active positions during the process; the method is teacher-centered. If possible Questions, that serve a purpose and
Brainstorming Brainstorming is a group work process that has been regulated to reach solutions for a problem without limitations or evaluation. The purpose of brainstorming is to make it easier for students to express themselves and to generate ideas. This technique is used as a high-level discussion

PO - NQF-HETR Relation
NQF-HETR CategoryNQF-HETR Sub-CategoryNQF-HETRLearning Outcomes
INFORMATION  01
INFORMATION  02
SKILLS  01
SKILLS  02
SKILLS  03
SKILLS  04
COMPETENCIESCommunication and Social Competence 01
COMPETENCIESCommunication and Social Competence 02
COMPETENCIESCommunication and Social Competence 03
COMPETENCIESCompetence to Work Independently and Take Responsibility 01
COMPETENCIESCompetence to Work Independently and Take Responsibility 02
COMPETENCIESCompetence to Work Independently and Take Responsibility 03
COMPETENCIESField Specific Competencies 01
COMPETENCIESField Specific Competencies 02
COMPETENCIESField Specific Competencies 03
COMPETENCIESLearning Competence 01
    

PO - FOE (Academic)
FOE CategoryFOE Sub-CategoryFOELearning Outcomes
INFORMATION  01
INFORMATION  02
SKILLS  01
SKILLS  02
SKILLS  03
SKILLS  04
COMPETENCIESCommunication and Social Competence 01
COMPETENCIESCommunication and Social Competence 02
COMPETENCIESCommunication and Social Competence 03
COMPETENCIESCommunication and Social Competence 04
COMPETENCIESCommunication and Social Competence 05
COMPETENCIESCompetence to Work Independently and Take Responsibility 01
COMPETENCIESCompetence to Work Independently and Take Responsibility 02
COMPETENCIESCompetence to Work Independently and Take Responsibility 03
COMPETENCIESField Specific Competencies 01
COMPETENCIESField Specific Competencies 02
COMPETENCIESField Specific Competencies 03
COMPETENCIESLearning Competence 01
    

PO - FOE (Vocational)
No Records to Display

COURS STRUCTURE & ECTS CREDITS
Year :
1st Semester Course Plan
Course CodeCourse TitleL+P HourECTSCourse Type
MAT 611 ANALYTICAL METHODS IN APPLIED MATHEMATICS 3+0 7,5 Compulsory
MAT 540 FUNCTIONAL ANALYSIS I 3+0 7,5 Compulsory
- Mathematics Elective-1 3+0 7,5 Elective
- Mathematics Elective-1 3+0 7,5 Elective
  Total 30  
1st Semester Elective Groups : Mathematics Elective-1

2nd Semester Course Plan
Course CodeCourse TitleL+P HourECTSCourse Type
MAT 698 SEMINAR - I 0+2 7,5 Compulsory
- Mathematics Dr. Elective-2 3+0 7,5 Elective
- Mathematics Dr. Elective-2 3+0 7,5 Elective
- Mathematics Dr. Elective-2 3+0 7,5 Elective
  Total 30  
2nd Semester Elective Groups : Mathematics Dr. Elective-2

3rd Semester Course Plan
Course CodeCourse TitleL+P HourECTSCourse Type
FBE 897 DEVELOPMENT AND LEARNING 3+0 7,5 Compulsory
FBE 896 PLANNING AND ASSESSMENT IN EDUCATION 3+2 7,5 Compulsory
MAT 699 SEMINAR - II 0+2 7,5 Compulsory
FBE 610 METHODS OF RESEARCH AND ETHICS 3+0 7,5 Compulsory
  Total 30  

4th Semester Course Plan
Course CodeCourse TitleL+P HourECTSCourse Type
ENS 600 PROFICIENCY EXAM PREPARATION 0+0 20 Compulsory
ENS 602 THESIS PROPOSAL PREPARATION 0+0 10 Compulsory
  Total 30  

5th Semester Course Plan
Course CodeCourse TitleL+P HourECTSCourse Type
MAT 600 PHD THESIS 0+0 20 Compulsory
MAT 800 PHD EXPERTISE FIELD COURSES 8+0 10 Compulsory
  Total 30  

6th Semester Course Plan
Course CodeCourse TitleL+P HourECTSCourse Type
MAT 600 PHD THESIS 0+0 20 Compulsory
MAT 800 PHD EXPERTISE FIELD COURSES 8+0 10 Compulsory
  Total 30  

7th Semester Course Plan
Course CodeCourse TitleL+P HourECTSCourse Type
MAT 800 PHD EXPERTISE FIELD COURSES 8+0 10 Compulsory
MAT 600 PHD THESIS 0+0 20 Compulsory
  Total 30  

8th Semester Course Plan
Course CodeCourse TitleL+P HourECTSCourse Type
MAT 800 PHD EXPERTISE FIELD COURSES 8+0 10 Compulsory
MAT 600 PHD THESIS 0+0 20 Compulsory
  Total 30  


COURSE & PROGRAM LEARNING OUTCOMES
Year : Compulsory Courses
Course TitleC/EPO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08PO 09
ANALYTICAL METHODS IN APPLIED MATHEMATICSC         
DEVELOPMENT AND LEARNINGC         
FUNCTIONAL ANALYSIS IC         
METHODS OF RESEARCH AND ETHICSC         
PHD EXPERTISE FIELD COURSESC         
PHD THESISC* **     
PLANNING AND ASSESSMENT IN EDUCATIONC         
POSTGRADUATE COUNSELINGC         
PROFICIENCY EXAM PREPARATIONC         
SEMINAR - IC* **     
SEMINAR - IIC* ***    
THESIS PROPOSAL PREPARATIONC         
Click to add elective courses...
Elective Courses
Course TitleC/EPO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08PO 09
ADVANCED ALGEBRAE         
ADVANCED COMPLEX ANALYSIS E         
ADVANCED LINEAR ALGEBRAE         
ADVANCED PROGRAMMINGE         
ADVANCED REGULAR MATRIX MAPPINGS IE         
ADVANCED REGULAR MATRIX MAPPINGS IIE         
ADVANCED RINGS THEORY IIE         
ADVANCED THEORY OF DIFFERENTIAL EQUATIONSE         
ADVANCED TOPOLOGY E         
ALGEBRAIC TOPOLOGY IE         
ALGEBRAIC TOPOLOGY IIE         
AN INTRODUCTION TO NONASSOCIATIVE ALGEBRASE         
ANALYSIS ON TIME SCALES IE         
ANALYSIS ON TIME SCALES IIE         
ANALYTICAL METHODS IN APPLIED MATHEMATICSE         
APPLIED DIFFERENTIAL GEOMETRY IE         
APPLIED DIFFERENTIAL GEOMETRY IIE         
APPLIED DIFFERENTIAL GEOMETRY-IE         
APPLIED DIFFERENTIAL GEOMETRY-IIE         
APPLIED MATHEMATICAL PROGRAMMINGE         
APPROXIMATE METHODS AND MATHEMATICAL MODELINGE         
APPROXIMATION THEORY OF FUNCTIONS IE         
APPROXIMATION THEORY OF FUNCTIONS IIE         
AUTOMORPHIC FUNCTIONSE         
CATEGORY THEORYE         
CLASSICAL AND MODERN METHODS ON SUMMABILITY THEORY IE         
CLASSICAL AND MODERN METHODS ON SUMMABILITY THEORY IIE         
DIFFERENTIABLE MANIFOLDS -IE         
DIFFERENTIABLE MANIFOLDS -IIE         
DIFFERENTIAL GEOMETRIC METHODS IN ANALITIC MECHANICS IE         
DIFFERENTIAL GEOMETRIC METHODS IN ANALITIC MECHANICS IIE         
DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IE         
DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IIE         
ECONOMICS, GEOMETRY, DYNAMICS IE         
ECONOMICS, GEOMETRY, DYNAMICS IIE         
FINITE DIFFERENCE EQUATIONSE         
FINITE DIFFERENCE METHODS FOR PARTIAL DIFFERENTIAL EQUATIONSE         
FRACTIONAL CALCULUSE         
FRACTIONAL DIFFERENTIAL EQUATIONSE         
FUNCTIONAL ANALYSIS IE         
FUNCTIONAL ANALYSIS IIE         
FUNCTIONAL EQUATIONSE         
GENERALISED CLASSICAL MECHANICS AND FIELD THEORY IE         
GENERALISED CLASSICAL MECHANICS AND FIELD THEORY IIE         
GEOMETRIC TOPOLOGYE         
GRAPH AND COMBINATORICS E         
GRAVITATION THEORIES AND COSMOLOGYE         
GROUP THEORY IE         
HIGHER DIFFERENTIAL GEOMETRY-IE         
HIGHER DIFFERENTIAL GEOMETRY-IIE         
HOMOLGY ALGEBRAE         
HYPERBOLIC GEOMETRY E         
INTEGRAL EQUATIONSE         
INTRODUCTION TO LORENTZIAN GEOMETRYE         
INTRODUCTION TO TOPOLOGYE         
JET MANIFOLDS AND JET BUNCHES IE         
JET MANIFOLDS AND JET BUNCHES IIE         
LATEXE         
LORENTZIAN GEOMETRYE         
MATHEMATICAL ANALYSISE         
MATRIX THEORYE         
METHODS OF RESEARCH AND ETHICSE         
MODULE THEORYE         
MÖBIUS TRANSFORMATIONSE         
NON-COMMUTATIVE RINGSE         
NUMERICAL SOLUTIONS OF INTEGRAL EQUATIONSE         
OPERATOR EQUATIONS THEORY IE         
OPERATOR EQUATIONS THEORY IIE         
OPTIMIZATION METHODS IE         
OPTIMIZATION METHODS IIE         
POSITIVE LINEAR OPERATORSE         
POSITIVE SOLUTIONS OF LINEAR OPERATORS IE         
POSITIVE SOLUTIONS OF LINEAR OPERATORS IIE         
RECURRENCE RELATIONS, FIBONACCI AND LUCAS NUMBERSE         
REPRESENTATIONS OF GROUPSE         
RESEARCH PROJECTE         
RING THEORY IE         
SELECTED TOPICS IN NUMERICAL ANALYSISE         
SEMI-RIEMANN MANIFOLDS IE         
SEMI-RIEMANN MANIFOLDS IIE         
SOLUTIONS OF THE EINSTEIN FIELD EQUATIONSE         
SPECIAL FUNCTIONSE         
SPECTRAL THEORY OF LINEAR DIFFERENTIAL OPERATORSE         
STRUCTURAL CHARACTERISTIC OF FUNCTIONS ON COMPLEX PLANE IE         
STRUCTURAL CHARACTERISTIC OF FUNCTIONS ON COMPLEX PLANE IIE         
TENSOR GEOMETRY AND APPLICATIONS IE         
TENSOR GEOMETRY AND APPLICATIONS IIE         
THE GEOMETRY OF DISCRETE GROUPSE         
THE THEORY OF GENERAL RELATIVITY AND INTEGRABLE SYSTEMSE         
THEORY OF ADVANCED DIVERGENT SERIES IE         
THEORY OF ADVANCED DIVERGENT SERIES IIE         
THEORY OF FUNCTIONS OF A REAL VARIABLEE         
THEORY OF GENERALIZED FUNCTIONS AND APPLICATIONSE         
TOPOLOGICAL AND METRIC SPACESE         
TOPOLOGICAL GROUPS E         
TOPOLOGICAL SEQUENCE SPACESE         
UNBOUNDED LINEAR OPERATOR THEORYE         
L+P: Lecture and Practice
C: Compulsory
E: Elective
PO: Program Learning Outcomes
TH [5]: Too High
H [4]: High
M [3]: Medium
L [2]: Low
TL [1]: Too Low
None [0]: None
FOE [0]: Field of Education
NQF-HETR : National Qualifications Framework For Higher Education in Turkey