Bilgi Paketi & Ders Kataloğu
Türkçe English Curriculum Key Learning Outcomes
Mathematics Integrated PhD Program
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.
2
Qualification Awarded
Third Cycle (Doctorate Degree). This is a third cycle degree program in the science of Mathematics (300 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 45 credits (150 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 150 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.
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Mode of Study
Full-Time
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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
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.
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Curriculum
1. Semester
Course Code Course Title Type of Course T1 U2 L3 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 T1 U2 L3 ECTS
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. 24
Total 30
3. Semester
Course Code Course Title Type of Course T1 U2 L3 ECTS
MAT6183 ADVANCED TOPICS IN PHD THESIS III Compulsory 4 0 0 5
MAT6193 THESIS CONSULTANTS III Compulsory 0 1 0 1
Click to choose optional courses. 24
Total 30
4. Semester
Course Code Course Title Type of Course T1 U2 L3 ECTS
FEN5000 RESEARCH TECHNIQUES AND PUBLICATION ETHICS Compulsory 2 0 0 2
FEN6002 TECHNOLOGY TRANSFER, R-D AND INNOVATION Compulsory 2 0 0 2
MAT6174 SEMINAR Compulsory 0 2 0 2
MAT6184 ADVANCED TOPICS IN PHD THESIS IV Compulsory 4 0 0 5
MAT6194 THESIS CONSULTANTS IV Compulsory 0 1 0 1
Click to choose optional courses. 18
Total 30
5. Semester
Course Code Course Title Type of Course T1 U2 L3 ECTS
MAT6185 ADVANCED TOPICS IN PHD THESIS V Compulsory 4 0 0 5
MAT6195 THESIS CONSULTING V Compulsory 0 1 0 15
YET6177 PHD PROFICIENCY EXAMINATION Compulsory 0 0 0 10
Total 30
6. Semester
Course Code Course Title Type of Course T1 U2 L3 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 T1 U2 L3 ECTS
MAT6187 ADVANCED TOPICS IN PHD THESIS 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 T1 U2 L3 ECTS
MAT6188 PHD SPECIALISED FIELD COURSE VIII Compulsory 4 0 0 5
MAT6198 THESIS CONSULTING VIII Compulsory 0 1 0 25
Total 30
9. Semester
Course Code Course Title Type of Course T1 U2 L3 ECTS
MAT6189 ADVANCED TOPICS IN PHD IX Compulsory 4 0 0 5
MAT6199 PHD THESIS IX Compulsory 0 1 0 25
Total 30
10. Semester
Course Code Course Title Type of Course T1 U2 L3 ECTS
MAT6190 SPECIAL TOPICS IN PHD THESIS X Compulsory 4 0 0 5
MAT6200 PHD THESIS CONSULTING X Compulsory 0 1 0 25
Total 30
1. Semester Optional Courses
Course Code Course Title Type of Course T1 U2 L3 ECTS
MAT5101 REEL ANALYSIS I Optional 3 0 0 6
MAT5105 COMPLEX ANALYSIS I Optional 3 0 0 6
MAT5107 ADVANCED ANALYSIS I Optional 3 0 0 6
MAT5111 MULTI VARIABLE ANALYSIS I Optional 3 0 0 6
MAT5113 ADVANCED FUNCTIONAL ANALYSIS I Optional 3 0 0 6
MAT5117 FIELD THEORY I Optional 3 0 0 6
MAT5119 RING THEORY I Optional 3 0 0 6
MAT5121 DIOPHANT EQUATIONS I Optional 3 0 0 6
MAT5123 GEOMETRIC FUNCTION THEORY I Optional 3 0 0 6
MAT5125 ANALYTICAL NUMBER THEORY I Optional 3 0 0 6
MAT5127 ADVANCED QUADRATIC FORMS I Optional 3 0 0 6
MAT5203 NUMBER THEORY I Optional 3 0 0 6
MAT5205 ALGEBRA I Optional 3 0 0 6
MAT5207 ALGEBRAIC NUMBER THEORY I Optional 3 0 0 6
MAT5209 OTOMORF FUNCTIONS I Optional 3 0 0 6
MAT5211 INTRODUCTIONS TO ALGEBRAIC GEOMETRY I Optional 3 0 0 6
MAT5215 MODULAR FORMS I Optional 3 0 0 6
MAT5217 GRAPH THEORI I Optional 3 0 0 6
MAT5219 TOPOLOGICAL GRAPH INDICES I Optional 3 0 0 6
MAT5305 GEOMETRIC MODELLING OF CURVES AND SURFACES I Optional 3 0 0 6
MAT5309 ADVENCED PROJECTIVE GEOMETRY I Optional 3 0 0 6
MAT5311 LINEAR SPACES I Optional 3 0 0 6
MAT5313 TAXICAB GEOMETRY Optional 3 0 0 6
MAT5315 THEORY OF SUB-MANIFOLDS I Optional 3 0 0 6
MAT5317 DIFFERENTIABLE MANIFOLDS I Optional 3 0 0 6
MAT5319 FUNDAMENTAL CONCEPTS OF GEOMETRY Optional 3 0 0 6
MAT5321 MAPLE APPLICATIONS Optional 3 0 0 6
MAT5323 COORDINATE GEOMETRY I Optional 3 0 0 6
MAT5325 GENERALIZED POLYGONS I Optional 3 0 0 6
MAT5327 GLOBAL LORENTZIAN GEOMETRY I Optional 3 0 0 6
MAT5329 DIFFERENTIAL GEOMETRY APPLICATIONS I Optional 3 0 0 6
MAT5331 ADVANCED LINEAR ALGEBRA I Optional 3 0 0 6
MAT5405 ADVANCED NUMERICAL ANALYSIS I Optional 3 0 0 6
MAT5409 BOUNDARY VALUE PRABLEMS I Optional 3 0 0 6
MAT5411 PARTIAL DIFFERENTIAL EQUATIONS I Optional 3 0 0 6
MAT5415 TRANSFORMATION GROUPS AND LIE ALGEBRAS I Optional 3 0 0 6
MAT5417 GRAFS AND MATRICS Optional 3 0 0 6
MAT5419 MODERN GEOMETRIC METHODS AND APPLICATOUNS-I Optional 3 0 0 6
MAT5421 DIFFERANTIAL FORMS AND APPLICATIONS Optional 3 0 0 6
MAT5425 INTRODUCTION TO MODULE THEORY I Optional 3 0 0 6
2. Semester Optional Courses
Course Code Course Title Type of Course T1 U2 L3 ECTS
MAT5102 REAL ANALYSIS II Optional 3 0 0 6
MAT5106 COMPLEX ANALYSIS II Optional 3 0 0 6
MAT5108 ADVANCED ANALYSIS II Optional 3 0 0 6
MAT5112 MULTI VARIABLE ANALYSIS II Optional 3 0 0 6
MAT5114 ADVANCED FUNCTIONAL ANALYSIS II Optional 3 0 0 6
MAT5118 FIELD THEORY II Optional 3 0 0 6
MAT5120 RING THEORY II Optional 3 0 0 6
MAT5122 DIOPHANT EQUATIONS II Optional 3 0 0 6
MAT5124 GEOMETRIC FUNCTION THEORY II Optional 3 0 0 6
MAT5126 ANALYTICAL NUMBER THEORY II Optional 3 0 0 6
MAT5128 ADVANCED QUADRATIC FORMS II Optional 3 0 0 6
MAT5204 NUMBER THEORY II Optional 3 0 0 6
MAT5206 ALGEBRA II Optional 3 0 0 6
MAT5208 ALGEBRAIC NUMBER THEORY II Optional 3 0 0 6
MAT5210 OTOMORF FUNCTIONS II Optional 3 0 0 6
MAT5212 INTRODUCTIONS TOALGEBRAIC GEOMETRY II Optional 3 0 0 6
MAT5216 MODULAR FORMS II Optional 3 0 0 6
MAT5218 GRAPH THEORI II Optional 3 0 0 6
MAT5220 TOPOLOGICAL GRAPH INDICES II Optional 3 0 0 6
MAT5302 ANALYSIS ON MANIFOLDS Optional 3 0 0 6
MAT5306 GEOMETRIC MODELING OF CURVES AND SURFACES II Optional 3 0 0 6
MAT5310 ADVENCED PROJECTIVE GEOMETRY II Optional 3 0 0 6
MAT5316 THEORY OF SUB-MANIFOLDS II Optional 3 0 0 6
MAT5318 DIFFERANTIABLE MANIFOLDS II Optional 3 0 0 6
MAT5320 REAL PROJECTIVE GEOMETRY Optional 3 0 0 6
MAT5324 COORDINATE GEOMETRY II Optional 3 0 0 6
MAT5326 GENERALIZED POLYGONS II Optional 3 0 0 6
MAT5328 GLOBAL LORENTZIAN GEOMETRY II Optional 3 0 0 6
MAT5330 DIFFERENTIAL GEOMETRY APPLICATIONS II Optional 3 0 0 6
MAT5332 ADVANCED LINEAR ALGEBRA II Optional 3 0 0 6
MAT5406 ADVANCED NUMERICAL ANALYSIS II Optional 3 0 0 6
MAT5410 BOUNDARY VALUE PROBLEMS II Optional 3 0 0 6
MAT5412 PARTIAL DIFFERENTIAL EQUATIONS II Optional 3 0 0 6
MAT5414 ELLIPTIK PARTIAL DIFFERANTIAL EQUATIONS Optional 3 0 0 6
MAT5416 TRANSFORMATION GROUPS AND LIE ALGEBRAS II Optional 3 0 0 6
MAT5418 GRAFS AND LINEAR ALGEBRA Optional 3 0 0 6
MAT5420 MODERN GEOMETRIC METHODS AND APPLICATOUNS-II Optional 3 0 0 6
MAT5422 SINGULARITY THEORY IN DIFRERANTIAL GEOMETRY Optional 3 0 0 6
MAT5424 APPLICATIONS OF RIEMAIAN TRANSFORMS Optional 3 0 0 6
MAT5426 INTRODUCTION TO MODULE THEORY II Optional 3 0 0 6
3. Semester Optional Courses
Course Code Course Title Type of Course T1 U2 L3 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
4. Semester Optional Courses
Course Code Course Title Type of Course T1 U2 L3 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
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