General Description
Department of Mathematics began to give instructions for bachelor, master and PhD levels in 1983.
Department of Mathematics consists of six main branches of science. These are: Analysis and Function Theory, Geometry, Applied Mathematics, Algebra and Number Theory, Fundamentals of Mathematics and Logic, and Topology.
Third Cycle (Doctorate Degree). This is a third cycle degree program in the science of Mathematics (240 ECTS).
You will be awarded, on successful completion of the programme and gain competencies, a degree of Doctorate in Mathematics.
Third Cycle
4
Specific Admission Requirements
Students, willing to enrol in this graduate programme, must comply with the legal and academic requirements to access the studies in Uludag University according to the process established by the YÖK (Higher Education Council) regulations. The detail information about the application (once or sometimes twice a year) and access requirements are released before academic year starts on its web site (www.uludag.edu.tr). 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 in any courses, running in Turkish. For example, Erasmus students from abroad want to spend one term or two terms in a graduate programme at Uludag University should apply to International Relation Office.
5
Specific arrangements for the recognition of prior learning
The provisions in “Regulation on Transfer among Associate and Undergraduate Degree Programs, Double Major, and Subspecialty and the Principals of Credit Transfer among Institutions in Higher Education Institutions” are applied.
6
Qualification Requirements and Regulations
Doctorate degree in the Mathematics field are given that students: taking at least 24 credits (90 ECTS) from the courses which find in this graduate program or the other graduate programs that are associated with the graduate program, completing succesfully the courses, obtaining at least 75 point of 100 points for the courses, and finally defending successfully the thesis (120 ECTS) related to his/her subject in front of the selected jury.
7
Profile of The Programme
Finding new methods, new applications and also new developments for some known principle and rulers, in the fields of Mathematics.
8
Key Learning Outcomes & Classified & Comparative
1.
evaluates the fundamental notions, teories and data with academic methods, and so solves the encountered problems.

2.
defines a problem and propose a solution for it, and to solve the problem, evaluate the results and apply them if it is necessary in the areas of expertise.

3.
has the ability to conduct original research and independent publication.

4.
writes a software programme for mathematical calculations.

5.
applies the digested knowledge and problem solving ability in the collaborations between different groups.

6.
has an advanced level of critical thinking skills.

7.
solves advanced problems using standard mathematical techniques.

8.
applies problem solving abilities in the interdisciplinary studies and evaluate the results by taking into account the quality process in area of expertise.

9.
uses mathematic as the language of science.

10.
transfers systematically the current developments, studies to other people as verbal or written form confidently.

SKILLS 
Cognitive  Practical 
 uses mathematic as the language of science.
 applies the digested knowledge and problem solving ability in the collaborations between different groups.
 solves advanced problems using standard mathematical techniques.
 defines a problem and propose a solution for it, and to solve the problem, evaluate the results and apply them if it is necessary in the areas of expertise.
 has the ability to conduct original research and independent publication.
 transfers systematically the current developments, studies to other people as verbal or written form confidently.
 evaluates the fundamental notions, teories and data with academic methods, and so solves the encountered problems.
 writes a software programme for mathematical calculations.
 applies problem solving abilities in the interdisciplinary studies and evaluate the results by taking into account the quality process in area of expertise.
 has an advanced level of critical thinking skills.

KNOWLEDGE 
Theoretical  Conceptual 
 defines a problem and propose a solution for it, and to solve the problem, evaluate the results and apply them if it is necessary in the areas of expertise.
 has the ability to conduct original research and independent publication.
 transfers systematically the current developments, studies to other people as verbal or written form confidently.
 evaluates the fundamental notions, teories and data with academic methods, and so solves the encountered problems.
 has an advanced level of critical thinking skills.
 solves advanced problems using standard mathematical techniques.
 applies problem solving abilities in the interdisciplinary studies and evaluate the results by taking into account the quality process in area of expertise.
 writes a software programme for mathematical calculations.
 applies the digested knowledge and problem solving ability in the collaborations between different groups.
 uses mathematic as the language of science.

COMPETENCES 
Field Specific Competence 
 transfers systematically the current developments, studies to other people as verbal or written form confidently.
 uses mathematic as the language of science.
 has the ability to conduct original research and independent publication.
 applies problem solving abilities in the interdisciplinary studies and evaluate the results by taking into account the quality process in area of expertise.
 applies the digested knowledge and problem solving ability in the collaborations between different groups.
 defines a problem and propose a solution for it, and to solve the problem, evaluate the results and apply them if it is necessary in the areas of expertise.
 has an advanced level of critical thinking skills.

COMPETENCES 
Competence to Work Independently and Take Responsibility 
 has an advanced level of critical thinking skills.
 uses mathematic as the language of science.
 solves advanced problems using standard mathematical techniques.
 has the ability to conduct original research and independent publication.
 transfers systematically the current developments, studies to other people as verbal or written form confidently.
 writes a software programme for mathematical calculations.
 defines a problem and propose a solution for it, and to solve the problem, evaluate the results and apply them if it is necessary in the areas of expertise.
 applies the digested knowledge and problem solving ability in the collaborations between different groups.
 applies problem solving abilities in the interdisciplinary studies and evaluate the results by taking into account the quality process in area of expertise.
 evaluates the fundamental notions, teories and data with academic methods, and so solves the encountered problems.

COMPETENCES 
Communication and Social Competence 
 has the ability to conduct original research and independent publication.
 solves advanced problems using standard mathematical techniques.
 has an advanced level of critical thinking skills.
 defines a problem and propose a solution for it, and to solve the problem, evaluate the results and apply them if it is necessary in the areas of expertise.
 writes a software programme for mathematical calculations.
 applies the digested knowledge and problem solving ability in the collaborations between different groups.
 transfers systematically the current developments, studies to other people as verbal or written form confidently.
 uses mathematic as the language of science.

COMPETENCES 
Learning Competence 
 solves advanced problems using standard mathematical techniques.
 defines a problem and propose a solution for it, and to solve the problem, evaluate the results and apply them if it is necessary in the areas of expertise.
 uses mathematic as the language of science.
 has the ability to conduct original research and independent publication.
 evaluates the fundamental notions, teories and data with academic methods, and so solves the encountered problems.
 has an advanced level of critical thinking skills.
 applies the digested knowledge and problem solving ability in the collaborations between different groups.

9
Occupational Profiles of Graduates With Examples
Education field, Researcher in Universities
10
Access to Further Studies
The student who completed succesfully to this program can work in the area of the Mathematics science or in the areas which accept lecturer from this area.
11
Examination Regulations, Assessment and Grading
In Doctorate Program, each student must enroll to the lessons and since he sits for a final examination, he must attend at least 70% of the courses. Students must take at least one exam at the end of the semester. Examination is evaluated on the basis of 100. Students cumulative grade point average has to be at least 75 to be successful from Doctorate Program. Students, who get one of AA, BA, BB, or CB letter marks, are to be succeeding at the available courses.
12
Graduation Requirements
In order to gain the degree, a student is required to take minimum 90 ECTS credits lectures (from the graduate course program) and to complete the courses successfully. In addition, the student should carry out a research under the supervision of a lecturer. Having followed the submission of thesis, the student is required to have a verbal examination on his/her work.
FullTime
14
Address and Contact Details
Program Başkanı: Prof.Dr. İ.Naci CANGÜL
Eposta: cangul@uludag.edu.tr
Tel.: +90 224 2941756
Program Koordinatörü: Doç. Dr. Yeliz KARA ŞEN
Eposta: yelizkara@uludag.edu.tr
Tel.: +90 224 2941775
Adres: Bursa Uludağ Üniversitesi
Fen Edebiyat Fakültesi
Matematik Bölümü
16059 Bursa/TÜRKİYE
Department of Mathematics consists of twelve professors, five associate professors, four assistant professors, three lecturers, and three research assistants.
There are seven classrooms, a computer lab and a graduate classroom in our department.
In addition to undergraduate education, master and doctorate programs are available.
Master´s and PhD programs have been realized under the Institute of Science and Technology.
The students have the chance to make use of the exchange programs: Erasmus and Farabi.
2. Semester 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
ECTS 
MAT6172 
SEMINAR 
Compulsory 
0 
2 
0 
4 
MAT6192 
THESIS CONSULTING II 
Compulsory 
0 
1 
0 
1 

Click to choose optional courses.





25 
Total 

30 
3. Semester 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
ECTS 
MAT6183 
PHD SPECIALISED FIELD COURSE III 
Compulsory 
4 
0 
0 
5 
MAT6193 
THESIS CONSULTING III 
Compulsory 
0 
1 
0 
15 
YET6177 
PHD PROFICIENCY EXAMINATION 
Compulsory 
0 
0 
0 
10 
Total 

30 
4. Semester 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
ECTS 
MAT6184 
PHD SPECIALISED FIELD COURSE IV 
Compulsory 
4 
0 
0 
5 
MAT6194 
THESIS CONSULTING IV 
Compulsory 
0 
1 
0 
25 
Total 

30 
5. Semester 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
ECTS 
MAT6185 
PHD SPECIALISED FIELD COURSE V 
Compulsory 
4 
0 
0 
5 
MAT6195 
THESIS CONSULTING V 
Compulsory 
0 
1 
0 
25 
Total 

30 
6. Semester 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
ECTS 
MAT6186 
PHD SPECIALISED FIELD COURSE VI 
Compulsory 
4 
0 
0 
5 
MAT6196 
THESIS CONSULTING VI 
Compulsory 
0 
1 
0 
25 
Total 

30 
7. Semester 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
ECTS 
MAT6187 
PHD SPECIALISED FIELD COURSE VII 
Compulsory 
4 
0 
0 
5 
MAT6197 
THESIS CONSULTING VII 
Compulsory 
0 
1 
0 
25 
Total 

30 
8. Semester 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
ECTS 
MAT6188 
PHD SPECIALISED FIELD COURSE VIII 
Compulsory 
4 
0 
0 
5 
MAT6198 
THESIS CONSULTING VIII 
Compulsory 
0 
1 
0 
25 
Total 

30 
1. Semester Optional Courses 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
ECTS 
MAT6103 
RIEMANN SURFACES I 
Optional 
3 
0 
0 
5 
MAT6105 
UNIVALENT FUNCTIONS I 
Optional 
3 
0 
0 
5 
MAT6109 
HARMONIC MAPPINGS I 
Optional 
3 
0 
0 
5 
MAT6111 
THEORY OF ELLIPTIC CURVES AND ITS APPLICALTIONS I 
Optional 
3 
0 
0 
5 
MAT6117 
PADIC ANALYSIS I 
Optional 
3 
0 
0 
5 
MAT6181 
PHD SPECIALISED FIELD COURSE I 
Optional 
4 
0 
0 
5 
MAT6201 
ABSTRACT ALGEBRA I 
Optional 
3 
0 
0 
5 
MAT6205 
GEOMETRIC NUMBER THEORY I 
Optional 
3 
0 
0 
5 
MAT6207 
ADVANCED ANALYTIC NUMBER THEORY I 
Optional 
3 
0 
0 
5 
MAT6213 
APPLIED GRAPH THEORI I 
Optional 
3 
0 
0 
5 
MAT6215 
SPECTRAL GRAPH THEORI I 
Optional 
3 
0 
0 
5 
MAT6307 
ALGEBRAIC GEOMETRY I 
Optional 
3 
0 
0 
5 
MAT6307 
ALGEBRAIC GEOMETRY I 
Optional 
3 
0 
0 
6 
MAT6309 
COMBINATORIAL GEOMETRY 
Optional 
3 
0 
0 
5 
MAT6311 
ALGEBRAIC STRUCTURES AND PROJECTIVE GEOMETRIES I 
Optional 
3 
0 
0 
5 
MAT6313 
AFFINE AND PROJECTIVE GEOMETRY 
Optional 
3 
0 
0 
5 
MAT6315 
RIEMANNIAN GEOMETRY I 
Optional 
3 
0 
0 
5 
MAT6317 
SEMIRIEMANN GEOMETRY I 
Optional 
3 
0 
0 
5 
MAT6321 
PROJECTIVE GEOMETRI IN NONASSOCIATIVE ALGEBRAS I 
Optional 
3 
0 
0 
5 
MAT6323 
LOCAL RINGS I 
Optional 
3 
0 
0 
5 
MAT6329 
THEORY OF TANGENT AND COTANGENT BUNDLES 
Optional 
3 
0 
0 
5 
MAT6405 
ADVANCED PARTIAL DIFFERANTIAL EQUATIONS 
Optional 
3 
0 
0 
5 
MAT6407 
GENERAL ANALYTIC FUNCTIONS 
Optional 
3 
0 
0 
5 
MAT6413 
SLECTED TOPICS IN PARTIAL DIFFERANTIAL EQUATIONS 
Optional 
3 
0 
0 
5 
MAT6415 
LIE GROUPS AND CONSEV ATION LAWS I 
Optional 
3 
0 
0 
5 


Optional 




MAT6107 
FUNETIONS OF COMPLEX VARIABLES I 
Optional 
3 
0 
0 
5 
MAT6401 
GENERALIZED ANALYTIC FUNCTIONS I 
Optional 
2 
2 
0 
5 
2. Semester Optional Courses 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
ECTS 
MAT6104 
RIEMANN SURFACES II 
Optional 
3 
0 
0 
5 
MAT6106 
UNIVALENT FUNCTIONS II 
Optional 
3 
0 
0 
5 
MAT6108 
COMPLEX FUNCTIONS II 
Optional 
3 
0 
0 
5 
MAT6110 
HARMONIC MAPPINGS II 
Optional 
3 
0 
0 
5 
MAT6112 
THEORY OF ELLIPTIC CURVES AND ITS APPLICATIONS II 
Optional 
3 
0 
0 
5 
MAT6118 
PADIC ANALYSIS II 
Optional 
3 
0 
0 
5 
MAT6182 
PHD SPECIALISED FIELD COURSE II 
Optional 
4 
0 
0 
5 
MAT6202 
ABSTRACT ALGEBRA II 
Optional 
3 
0 
0 
5 
MAT6202 
ABSTRACT ALGEBRA II 
Optional 
3 
0 
0 
6 
MAT6206 
GEOMETRIC NUMBER THEORY II 
Optional 
3 
0 
0 
5 
MAT6208 
ADVANCED ANALYTIC NUMBER THEORY II 
Optional 
3 
0 
0 
5 
MAT6214 
APPLIED GRAPH THEORI II 
Optional 
3 
0 
0 
5 
MAT6216 
SPECTRAL GRAPH THEORI II 
Optional 
3 
0 
0 
5 
MAT6302 
CONTACT MANIFOLDS 
Optional 
3 
0 
0 
5 
MAT6304 
ADVANCED DIFFERENTIAL GEOMETRY II 
Optional 
3 
0 
0 
5 
MAT6308 
ALGEBRAIC GEOMETRY II 
Optional 
3 
0 
0 
5 
MAT6310 
DIAGRAM GEOMETRIES AND GEOMETRIC STRUCTURES 
Optional 
3 
0 
0 
5 
MAT6312 
ALGEBRAIC STRUCTURES AND PROJECTIVE GEOMETRY II 
Optional 
3 
0 
0 
5 
MAT6316 
RIEMANIAN GEOMETRY II 
Optional 
3 
0 
0 
5 
MAT6318 
SEMIRIEMANIAN GEOMETRY II 
Optional 
3 
0 
0 
5 
MAT6320 
VECTORIAL APPROACH METHODS TO GEOMETRY 
Optional 
3 
0 
0 
5 
MAT6322 
PROJECTIVE GEOMETRI IN NONASSOCIATIVE ALGEBRAS II 
Optional 
3 
0 
0 
5 
MAT6324 
LOCAL RINGS II 
Optional 
3 
0 
0 
5 
MAT6402 
GENERALIZED ANALYTIC FUNCTIONS II 
Optional 
3 
0 
0 
6 
MAT6406 
ADVANCED SPECIAL FUNCTIONS 
Optional 
3 
0 
0 
5 
MAT6416 
LIE GROUPS AND CONSEV ATION LAWS II 
Optional 
3 
0 
0 
5 