General Description
The Graduate School was established in 1982 as a unit dependent to the Rectorate of Uludağ University, according to the Article 19 of the Law on Higher Education, Law Number 2547.
Department of Mathematics began to give instructions for 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.
Second Cycle (Masters Degree). This is a second cycle degree program in the science of Mathematics (120 ECTS).
You will be awarded, on successful completion of the programme and gain competencies, a degree of Masters in Mathematics.
Second 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
Master´s degree in the Mathematics field are given that students: taking at least 21 credits (60 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 70 point of 100 points for the courses, and finally defending successfully the thesis (60 ECTS) related to his/her subject in front of the selected jury.
7
Profile of The Programme
Being master of their subject, learning of the last devolopmant about own subject, and applications of them.
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.
 has an advanced level of critical thinking skills.
 solves advanced problems using standard mathematical techniques.
 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.
 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 the ability to conduct original research and independent publication.

KNOWLEDGE 
Theoretical  Conceptual 
 evaluates the fundamental notions, teories and data with academic methods, and so solves the encountered problems.
 uses mathematic as the language of science.
 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.
 applies problem solving abilities in the interdisciplinary studies and evaluate the results by taking into account the quality process in area 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.

COMPETENCES 
Field Specific Competence 
 writes a software programme for mathematical calculations.
 evaluates the fundamental notions, teories and data with academic methods, and so solves the encountered problems.
 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.

COMPETENCES 
Competence to Work Independently and Take Responsibility 
 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.
 applies the digested knowledge and problem solving ability in the collaborations between different groups.
 solves advanced problems using standard mathematical techniques.
 uses mathematic as the language of science.
 has the ability to conduct original research and independent publication.
 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.
 transfers systematically the current developments, studies to other people as verbal or written form confidently.

COMPETENCES 
Communication and Social Competence 
 uses mathematic as the language of science.
 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 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.
 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.

COMPETENCES 
Learning Competence 
 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.
 uses mathematic as the language of science.
 evaluates the fundamental notions, teories and data with academic methods, and so solves the encountered problems.
 transfers systematically the current developments, studies to other people as verbal or written form confidently.
 solves advanced problems using standard mathematical techniques.
 has the ability to conduct original research and independent publication.
 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.

9
Occupational Profiles of Graduates With Examples
Education field, Researcher in Universities
10
Access to Further Studies
Upon a successful completion of the programme, student may continue with doctoral study in the same or similar scientific areas, which may accept students from the science of Mathematics.
11
Examination Regulations, Assessment and Grading
In Master Program, each student has to enrol in the school and since he sits for a final examination, he has to attend at least % 70 of the courses and %80 of the practice. Examination is evaluated on the basis of 100. Students general grade point average has to be at least 70 for to be successful from Master Program. Students, who get one of AA, BA, BB, CB, or CC 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 60 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 
MAT5172 
SEMINAR 
Compulsory 
0 
2 
0 
6 
MAT5192 
THESIS CONSULTING II 
Compulsory 
0 
1 
0 
1 

Click to choose optional courses.





23 
Total 

30 
3. Semester 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
ECTS 
MAT5183 
ADVANCED TOPICS IN MSC THESIS III 
Compulsory 
4 
0 
0 
5 
MAT5193 
THESIS CONSULTING III 
Compulsory 
0 
1 
0 
25 
Total 

30 
4. Semester 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
ECTS 
MAT5184 
ADVANCED TOPICS IN MSC THESIS IV 
Compulsory 
4 
0 
0 
5 
MAT5194 
THESIS CONSULTING IV 
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 
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 
MAT5181 
ADVANCED TOPICS IN MSC THESIS I 
Optional 
4 
0 
0 
5 
MAT5203 
NUMBER THEORY 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 
MAT5307 
BASIC DIFFERENTIAL GEOMETRY 
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 SUBMANIFOLDS I 
Optional 
3 
0 
0 
6 
MAT5317 
DIFFERENTIABLE MANIFOLDS I 
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 
MAT5405 
ADVANCED NUMERICAL ANALYSIS I 
Optional 
3 
0 
0 
6 
MAT5409 
BOUNDARY VALUE PRABLEMS I 
Optional 
3 
0 
0 
6 
MAT5415 
TRANSFORMATION GROUPS AND LIE ALGEBRAS I 
Optional 
3 
0 
0 
6 


Optional 




MAT5205 
ALGEBRA I 
Optional 
3 
0 
0 
6 
MAT5319 
FUNDAMENTAL CONCEPTS OF GEOMETRY 
Optional 
3 
0 
0 
6 
MAT5411 
PARTIAL DIFFERENTIAL EQUATIONS I 
Optional 
3 
0 
0 
6 
2. Semester Optional Courses 
Course Code 
Course Title 
Type of Course 
T^{1} 
U^{2} 
L^{3} 
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 
MAT5182 
ADVANCED TOPICS IN MSC THESIS II 
Optional 
4 
0 
0 
5 
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 
MAT5312 
LINEAR SPACES II 
Optional 
3 
0 
0 
6 
MAT5316 
THEORY OF SUBMANIFOLDS 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 
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 
MAT5424 
APPLICATIONS OF RIEMAIAN TRANSFORMS 
Optional 
3 
0 
0 
6 