Mathematics

General Description

1

Brief History

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.

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.

2

Qualification Awarded

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.

3

Level of Qualification

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. |

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.

13

Mode of Study

Full-Time

14

Address and Contact Details

Program Başkanı: Prof.Dr. İ.Naci CANGÜL

E-posta: cangul@uludag.edu.tr

Tel.: +90 224 2941756

Program Koordinatörü: Doç. Dr. Yeliz KARA ŞEN

E-posta: yelizkara@uludag.edu.tr

Tel.: +90 224 2941775

Adres: Bursa Uludağ Üniversitesi

Fen Edebiyat Fakültesi

Matematik Bölümü

16059 Bursa/TÜRKİYE

E-posta: cangul@uludag.edu.tr

Tel.: +90 224 2941756

Program Koordinatörü: Doç. Dr. Yeliz KARA ŞEN

E-posta: yelizkara@uludag.edu.tr

Tel.: +90 224 2941775

Adres: Bursa Uludağ Üniversitesi

Fen Edebiyat Fakültesi

Matematik Bölümü

16059 Bursa/TÜRKİYE

15

Facilities

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.

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.

16

Curriculum

1. Semester | |||||||

Course Code | Course Title | Type of Course | T^{1} |
U^{2} |
L^{3} |
ECTS | |

MAT6181 | ADVANCED TOPICS IN PHD THESIS I | Compulsory | 4 | 0 | 0 | 5 | |

MAT6191 | THESIS CONSULTING I | Compulsory | 0 | 1 | 0 | 1 | |

Click to choose optional courses. | 24 | ||||||

Total | 30 |

2. Semester | |||||||

Course Code | Course Title | Type of Course | T^{1} |
U^{2} |
L^{3} |
ECTS | |

FEN6002 | TECHNOLOGY TRANSFER, R-D AND INNOVATION | Compulsory | 2 | 0 | 0 | 2 | |

MAT6172 | SEMINAR | Compulsory | 0 | 2 | 0 | 4 | |

MAT6182 | ADVANCED TOPICS IN PHD THESIS II | Compulsory | 4 | 0 | 0 | 5 | |

MAT6192 | THESIS CONSULTING II | Compulsory | 0 | 1 | 0 | 1 | |

Click to choose optional courses. | 18 | ||||||

Total | 30 |

3. Semester | |||||||

Course Code | Course Title | Type of Course | T^{1} |
U^{2} |
L^{3} |
ECTS | |

MAT6183 | ADVANCED TOPICS IN PHD THESIS 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 | ADVANCED TOPICS IN PHD THESIS IV | Compulsory | 4 | 0 | 0 | 5 | |

MAT6194 | THESIS CONSULTANTS 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 | ADVANCED TOPICS IN PHD THESIS 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 | ADVANCED TOPICS IN PHD THESIS 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 | 6 | |

MAT6105 | UNIVALENT FUNCTIONS I | Optional | 3 | 0 | 0 | 6 | |

MAT6107 | FUNCTIONS OF COMPLEX VARIABLES I | Optional | 3 | 0 | 0 | 6 | |

MAT6109 | HARMONIC MAPPINGS I | Optional | 3 | 0 | 0 | 6 | |

MAT6111 | THEORY OF ELLIPTIC CURVES AND ITS APPLICALTIONS I | Optional | 3 | 0 | 0 | 6 | |

MAT6117 | P-ADIC ANALYSIS I | Optional | 3 | 0 | 0 | 6 | |

MAT6201 | ABSTRACT ALGEBRA I | Optional | 3 | 0 | 0 | 6 | |

MAT6205 | GEOMETRIC NUMBER THEORY I | Optional | 3 | 0 | 0 | 6 | |

MAT6207 | ADVANCED ANALYTIC NUMBER THEORY I | Optional | 3 | 0 | 0 | 6 | |

MAT6213 | APPLIED GRAPH THEORY I | Optional | 3 | 0 | 0 | 6 | |

MAT6215 | SPECTRAL GRAPH THEORI I | Optional | 3 | 0 | 0 | 6 | |

MAT6303 | ADVENCED DIFFERANTIAL GEOMETRY | Optional | 3 | 0 | 0 | 6 | |

MAT6307 | ALGEBRAIC GEOMETRY I | Optional | 3 | 0 | 0 | 6 | |

MAT6309 | COMBINATORIAL GEOMETRY | Optional | 3 | 0 | 0 | 6 | |

MAT6311 | ALGEBRAIC STRUCTURES AND PROJECTIVE GEOMETRY I | Optional | 3 | 0 | 0 | 6 | |

MAT6313 | AFFINE AND PROJECTIVE GEOMETRY | Optional | 3 | 0 | 0 | 6 | |

MAT6315 | RIEMANNIAN GEOMETRY I | Optional | 3 | 0 | 0 | 6 | |

MAT6317 | SEMI-RIEMANN GEOMETRY I | Optional | 3 | 0 | 0 | 6 | |

MAT6321 | PROJECTIVE GEOMETRI IN NONASSOCIATIVE ALGEBRAS I | Optional | 3 | 0 | 0 | 6 | |

MAT6323 | LOCAL RINGS I | Optional | 3 | 0 | 0 | 6 | |

MAT6329 | THEORY OF TANGENT AND COTANGENT BUNDLES | Optional | 3 | 0 | 0 | 6 | |

MAT6401 | GENERALIZED ANALYTIC FUNCTIONS I | Optional | 2 | 2 | 0 | 6 | |

MAT6405 | ADVANCED PARTIAL DIFFERANTIAL EQUATIONS | Optional | 3 | 0 | 0 | 6 | |

MAT6407 | GENERAL ANALYTIC FUNCTIONS | Optional | 3 | 0 | 0 | 6 | |

MAT6413 | SELECTED TOPICS IN PARTIAL DIFFERANTIAL EQUATIONS | Optional | 3 | 0 | 0 | 6 | |

MAT6415 | LIE GROUPS AND CONSEVATION LAWS I | Optional | 3 | 0 | 0 | 6 | |

MAT6417 | GRAFS AND TOPOLOGY | Optional | 3 | 0 | 0 | 6 | |

MAT6419 | GRAPH INDICES RESPECT TO VERTEX DEGREE | Optional | 3 | 0 | 0 | 6 | |

MAT6421 | METRIC STRUCTURES IN DIFFERENTIAL GEOMETRY | Optional | 3 | 0 | 0 | 6 | |

MAT6423 | GEOMETRIC MODELING IN PROBABILITY AND STATISTICS | Optional | 3 | 0 | 0 | 6 | |

MAT6425 | P-ADIC NUMBER THEORY I | Optional | 3 | 0 | 0 | 6 | |

MAT6427 | COMPUTATIONAL ALGEBRAIC NUMBER THEORY I | Optional | 3 | 0 | 0 | 6 | |

MAT6429 | ANALYTIC THEORY OF POLYNOMIALS | Optional | 3 | 0 | 0 | 6 |

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 | 6 | |

MAT6106 | UNIVALENT FUNCTIONS II | Optional | 3 | 0 | 0 | 6 | |

MAT6108 | COMPLEX FUNCTIONS II | Optional | 3 | 0 | 0 | 6 | |

MAT6110 | HARMONIC MAPPINGS II | Optional | 3 | 0 | 0 | 6 | |

MAT6112 | THEORY OF ELLIPTIC CURVES AND ITS APPLICATIONS II | Optional | 3 | 0 | 0 | 6 | |

MAT6118 | P-ADIC ANALYSIS II | Optional | 3 | 0 | 0 | 6 | |

MAT6202 | ABSTRACT ALGEBRA II | Optional | 3 | 0 | 0 | 6 | |

MAT6206 | GEOMETRIC NUMBER THEORY II | Optional | 3 | 0 | 0 | 6 | |

MAT6208 | ADVANCED ANALYTIC NUMBER THEORY II | Optional | 3 | 0 | 0 | 6 | |

MAT6214 | APPLIED GRAPH THEORY II | Optional | 3 | 0 | 0 | 6 | |

MAT6216 | SPECTRAL GRAPH THEORI II | Optional | 3 | 0 | 0 | 6 | |

MAT6302 | CONTACT MANIFOLDS | Optional | 3 | 0 | 0 | 6 | |

MAT6304 | ADVANCED DIFFERENTIAL GEOMETRY II | Optional | 3 | 0 | 0 | 6 | |

MAT6308 | ALGEBRAIC GEOMETRY II | Optional | 3 | 0 | 0 | 6 | |

MAT6310 | DIAGRAM GEOMETRIES AND GEOMETRIC STRUCTURES | Optional | 3 | 0 | 0 | 6 | |

MAT6312 | ALGEBRAIC STRUCTURES AND PROJECTIVE GEOMETRY II | Optional | 3 | 0 | 0 | 6 | |

MAT6316 | RIEMANIAN GEOMETRY II | Optional | 3 | 0 | 0 | 6 | |

MAT6318 | SEMI-RIEMANIAN GEOMETRY II | Optional | 3 | 0 | 0 | 6 | |

MAT6320 | VECTORIAL APPROACH METHODS TO GEOMETRY | Optional | 3 | 0 | 0 | 6 | |

MAT6322 | PROJECTIVE GEOMETRI IN NONASSOCIATIVE ALGEBRAS II | Optional | 3 | 0 | 0 | 6 | |

MAT6324 | LOCAL RINGS II | Optional | 3 | 0 | 0 | 6 | |

MAT6402 | GENERALIZED ANALYTIC FUNCTIONS II | Optional | 3 | 0 | 0 | 6 | |

MAT6406 | ADVANCED SPECIAL FUNCTIONS | Optional | 3 | 0 | 0 | 6 | |

MAT6416 | LIE GROUPS AND CONSEVATION LAWS II | Optional | 3 | 0 | 0 | 6 | |

MAT6418 | GRAFS AND COLORING | Optional | 3 | 0 | 0 | 6 | |

MAT6420 | GRAPH INDICES RESPECT TO DISTANCE | Optional | 3 | 0 | 0 | 6 | |

MAT6426 | P-ADIC NUMBER THEORY II | Optional | 3 | 0 | 0 | 6 | |

MAT6428 | COMPUTATIONAL ALGEBRAIC NUMBER THEORY II | Optional | 3 | 0 | 0 | 6 |