Third Cycle Programmes
    (Doctorate Degree)
Second Cycle Programmes
    (Master's Degree)
First Cycle Programmes
    (Bachelor's Degree)
Short Cycle Programmes
    (Associate's Degree)
 
Third Cycle Programmes (Doctorate Degree)

Graduate School of Natural and Applied Sciences - Mathematics - Fundamentals of Mathematics and Mathematical Logic - Third Cycle Programme



General Description
History
Qualification Awarded
Level of Qualification
Third Cycle
Specific Admission Requirements
The applicants who hold a Master's Degree and willing to enroll in the Doctorate programme may apply to the Directorate of Graduate School with the documents. 1-Sufficient score (at least 55 out of 100) from the Academic Staff and Graduate Study Education Exam (ALES) conducted by Student Selection and Placement Center (OSYM) or GRE Graduate Record Examination (GRE) score or Graduate Management Admission Test (GMAT) score equivalent to ALES score of 55. 2-English proficiency (at least 70 out of 100 from the Profiency Exam conducted by Ege University Foreign Language Department, or at least 55 out of 100 from ÜDS (University Language Examination conducted by OSYM) or TOEFL or IELTS score equivalent to UDS score of 55. The candidates holding Bachelor's or Master's Degree taught totally in English are exempted from English proficiency requirement. The candidates fulfilling the criteria outlined above are invited to interwiev. The assessment for admission to masters programs is based on : 50% of ALES, 15% of academic success in the undergraduate programme (cumulative grade point average (CGPA) ) 10 % of academic success in the master's programme and 25% of interview grade. The required minimum interview grade is 60 out of 100. The candidates having an assessed score of 65 at least are accepted into the Doctorate programme. The results of the evaluation are announced by the Directorate of Graduate School.
Specific Arrangements For Recognition Of Prior Learning (Formal, Non-Formal and Informal)
The rules for recognition of formal prior learning are well defined. A student who is currently enrolled in a Doctorate Degree programme in the same discipline at another institution and has successfully completed at least one semester, upon submitting all required documents before the deadline, may transfer to the Doctorate Programme at EGE University upon the recommendation of the department administration and with the approval of the Administrative Committee of the Graduate School. The decision taken will also include eligibility for exemption from some course requirements of the graduate program. Students who transfer from another university must be successful in the EGE University English Proficiency Exam or in an equivalent English examination. Recognition of prior non-formal and in-formal learning is at the beginning stage in Turkish Higher Education Institutions. Ege University is not an exception to this.
Qualification Requirements and Regulations
The doctorate programme consists of a minimum of seven courses, with a minimum of 21 national credits, a qualifying examination, a dissertation proposal, and a dissertation. The period allotted for the completion of the Doctorate programmes is normally eight semesters (four years). However, while it is possible to graduate in a shorter time, it is also possible to have an extension subject to the approval of the graduate school. The seminar course and thesis are non-credit and graded on a pass/fail basis. The total ECTS credits of the programme is 240 ECTS. A student may take undergraduate courses on the condition that the courses have not been taken during the undergraduate program. However, at most two of these courses may be counted to the Doctorate course load and credits. The PhD students are required to take the Doctoral Qualifying Examination, after having successfully completed taught courses. The examination consists of written and oral parts. The Doctoral Qualifying Committee determines by absolute majority whether a candidate has passed or failed the examination. Students who fail the Qualifying Examination may retake the examination the following semester. Students failing the Examination a second time are dismissed from the program. Students must register for thesis work and the Specialization Field course offered by his supervisor every semester following the semester, in which the supervisor is appointed. A dissertation supervisor who must hold the minimum rank of assistant professor is appointed for each PhD student. When the nature of the dissertation topic requires more than one supervisor, a joint-supervisor may be appointed. A joint-supervisor must hold a doctoral degree. Periodic monitoring of research work by a thesis monitoring committee is required to be awarded the Doctoral degree. A student who has completed work on the thesis within the time period, must write a thesis, using the data collected, according to the specifications of the Graduate School Thesis Writing Guide. The thesis must be defended in front of a jury. The thesis jury is appointed on the recommendations of the relevant Department Chairperson and with the approval of the Administrative Committee of the Graduate School. The jury is composed of the thesis supervisor and 5 faculty members. Of the appointed jury members, up to two may be selected from another Department or another University. The co-supervisor cannot be the jury member. Thesis defense by the candidate is open to all audience and a jury decides to grant/deny the Doctoral degree. A majority vote by the jury members determines the outcome of the thesis or examination. The vote can be for "acceptance", "rejection" or "correction". A student may be given, by a decision of the Administrative Committee of the Graduate School, up to six months to complete the corrections. The student must then retake the thesis examination.
Profile of The Programme
Occupational Profiles of Graduates With Examples
Access to Further Studies
Graduates who succesfully completed doctorate degree may apply to both in the same or related disciplines in higher education institutions at home or abroad to get a position in academic staff or to governmental R&D centres to get expert position.
Examination Regulations, Assessment and Grading
Graduation Requirements
Graduation requirements are explained in the section “Qualification Requirements and Regulations” .
Mode of Study (Full-Time, Part-Time, E-Learning )
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Address, Programme Director or Equivalent
Facilities

Key Learning Outcomes
1To perform the ethical responsibilities in working life.
2Ability to learn information about history of science and scientific knowledge production.
3Ability to make individual and team work on issues related to working and social life.
4Ability to use mathematical knowledge in technology.
5Ability to develop a foreign language in a sufficient level to follow the information in his/her field of interest and to communicate with the colleagues.
6Ability to use the approaches and knowledge of other disciplines in Mathematics.
7Ability to assimilate mathematic related concepts and associate these concepts with each other.
8Ability to learn scientific, mathematical perception and the ability to use that information to related areas.
9Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
10Following the developments in science and technology and gain self-renewing ability.
11Be able to access to information, make research on resources for this purpose and be able to use databases and other information resources.
12Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
13Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
14To apply mathematical principles to real world problems.
15Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.

Key Programme Learning Outcomes - NQF for HE in Turkey
TYYÇKey Learning Outcomes
000000000
KNOWLEDGE1
2
SKILLS1
2
3
4
COMPETENCES (Competence to Work Independently and Take Responsibility)1
2
3
COMPETENCES (Learning Competence)1
COMPETENCES (Communication and Social Competence)1
2
3
COMPETENCES (Field Specific Competence)1
2
3

Course Structure Diagram with Credits
T : Theoretical P: Practice L : Laboratory
1. Semester
No Course Unit Code Course Unit Title Type of Course T P L ECTS
1 MAT-SG-DOK-G ELECTIVE COURSES 1 Elective - - - 30
Total 0 0 0 30
 
2. Semester
No Course Unit Code Course Unit Title Type of Course T P L ECTS
1 9101076022013 Comprehensive Studies in Mathematics II Compulsory 3 0 0 8
2 MAT-SG-DOK-B ELECTIVE COURSES 2 Elective - - - 22
Total 3 0 0 30
 
3. Semester
No Course Unit Code Course Unit Title Type of Course T P L ECTS
1 DRUAD691 Specialization Field Compulsory 0 0 0 5
2 DRTEZ692 Thesis Study Compulsory 0 0 0 25
Total 0 0 0 30
 
4. Semester
No Course Unit Code Course Unit Title Type of Course T P L ECTS
1 FENDRSEM1 SEMINAR I Compulsory 1 0 0 6
2 DRUAD691 Specialization Field Compulsory 0 0 0 5
3 DRTEZ694 Thesis Study Compulsory 0 0 0 19
Total 1 0 0 30
 
5. Semester
No Course Unit Code Course Unit Title Type of Course T P L ECTS
1 DRUAD691 Specialization Field Compulsory 0 0 0 5
2 DRTEZ692 Thesis Study Compulsory 0 0 0 25
Total 0 0 0 30
 
6. Semester
No Course Unit Code Course Unit Title Type of Course T P L ECTS
1 FENDRSEM2 Seminar II Compulsory 1 0 0 6
2 DRUAD691 Specialization Field Compulsory 0 0 0 5
3 DRTEZ694 Thesis Study Compulsory 0 0 0 19
Total 1 0 0 30
 
7. Semester
No Course Unit Code Course Unit Title Type of Course T P L ECTS
1 DRUAD691 Specialization Field Compulsory 0 0 0 5
2 DRTEZ692 Thesis Study Compulsory 0 0 0 25
Total 0 0 0 30
 
8. Semester
No Course Unit Code Course Unit Title Type of Course T P L ECTS
1 DRUAD691 Specialization Field Compulsory 0 0 0 5
2 DRTEZ692 Thesis Study Compulsory 0 0 0 25
Total 0 0 0 30
 
ELECTIVE COURSES 1
No Course Unit Code Course Unit Title Type of Course T P L ECTS
1 9101076031998 Groups Theory Elective 3 0 0 8
2 9101076051998 Ring Theory I Elective 3 0 0 8
3 9101076092012 Selected Topics in Summability Theory I Elective 3 0 0 7
4 9101076092015 Selected Topics in Summability Theory I Elective 3 0 0 0
5 9101076112001 Graph Theory Techniques in Mathematical Modelling Elective 3 0 0 8
6 9101076132004 Complements on Advanced Analysis Elective 3 0 0 7
7 9101076132015 Complements on Advanced Analysis Elective 3 0 0 0
8 9101076151998 Fuzzy Topology I Elective 3 0 0 8
9 9101076172013 Theory of Models I Elective 3 0 0 8
10 9101076192012 Selected Topics in Ring Theory Elective 3 0 0 8
11 9101076231998 Non-Linear Differential Equations Elective 3 0 0 7
12 9101076271998 Numerical Solution of Partial Differential Equations and Boundary Value Elective 3 0 0 8
13 9101076291998 Numerical Solutions of The Ordinary Differential Equations Elective 3 0 0 8
14 9101076312005 Calculus on Time Scales Elective 3 0 0 8
15 9101076332005 Directed Graphs Elective 3 0 0 7
16 9101076332014 Directed Graphs Elective 3 0 0 0
17 9101076392005 Many-Dimensional Modal Logics I Elective 3 0 0 8
18 9101076412009 Computational Geometry I Elective 3 0 0 8
19 9101076452012 The Design and Analysis of Computer Algorithms Elective 3 0 0 8
20 9101076472002 Homotopy Theory I Elective 3 0 0 8
21 9101076552007 Near Rings Elective 3 0 0 7
22 9101076592008 Topics in Algebraic Topology Elective 3 0 0 7
23 9101076592015 Topics Algebraic Topology Elective 3 0 0 0
24 9101076612008 Dynamic Systems on Time Scales Elective 3 0 0 8
25 9101076632009 Differential Topology I Elective 3 0 0 8
26 9101076652009 Artifical Intelligent Techniquies of the Solving of the Optimization Problems I Elective 3 0 0 8
27 9101076672010 Fractional Calculus-I Elective 3 0 0 8
28 9101076692013 Line Congruence I Elective 3 0 0 8
29 9101076712010 Number-Theoretic Algorithms in Cryptography Elective 3 0 0 8
30 9101076732011 Digital Topolgy I Elective 3 0 0 8
31 9101076752011 Sequence Spaces and Summability I Elective 3 0 0 7
32 9101076752015 Sequence Spaces and Summability I Elective 3 0 0 0
33 9101076772011 Topics in Time Scales I Elective 3 0 0 7
34 9101076792013 Curves and Surfaces in Computer Aided Design I Elective 3 0 0 8
35 9101076812013 Advanced Topology I Elective 3 0 0 8
36 9101076832014 Graph Theory Wıth Applıcatıons To Computer Scıence II Elective 3 0 0 0
37 9101076852014 Graph Theory With Applications to Computer Science I Elective 3 0 0 0
38 9101076872017 Mappings Between Manifolds I Elective 3 0 0 0
39 9101076912017 Geometric Structures On Manifolds Elective 3 0 0 0
40 9101076932017 Degenerate Differential Geometry Elective 3 0 0 0
41 EBB6832017 Planning and Assesment in Education Elective 3 2 0 6
42 EBB6852017 Development and Learning Elective 3 0 0 4
ELECTIVE COURSES 2
No Course Unit Code Course Unit Title Type of Course T P L ECTS
1 9101076041998 Ring Theory II Elective 3 0 0 8
2 9101076062012 Asymptotic Methods for Partial Differential Equations Elective 3 0 0 8
3 9101076082011 Noncommutative Rings II Elective 3 0 0 8
4 9101076102011 Digital Topolgy II Elective 3 0 0 8
5 9101076122011 Sequence Spaces and Summability II Elective 3 0 0 8
6 9101076142011 Topics in Time Scales II Elective 3 0 0 8
7 9101076162012 Selected Topics in Summability Theory II Elective 3 0 0 8
8 9101076182001 Hilbert Spaces and Operators Theory Elective 3 0 0 8
9 9101076221998 Fuzzy Topology II Elective 3 0 0 8
10 9101076241998 Topological Continuities Elective 3 0 0 8
11 9101076261998 Theory of Models II Elective 3 0 0 8
12 9101076322013 Numerical Functional Analysis Elective 3 0 0 8
13 9101076342001 Perturbation Techniques Elective 3 0 0 8
14 9101076362002 Free and Moving Boundary Problems Elective 3 0 0 8
15 9101076382005 Graphs in Computer Science Elective 3 0 0 8
16 9101076402005 Many-Dimensional Modal Logics II Elective 3 0 0 8
17 9101076422009 Computational Geometry II Elective 3 0 0 8
18 9101076482012 Mathematical Elements for Analysis of Algoritms Elective 3 0 0 8
19 9101076522002 Graphical Enumeration Elective 3 0 0 8
20 9101076602009 Arithmetic of Infinity and Computer Elective 3 0 0 8
21 9101076622009 Differential Topology II Elective 3 0 0 8
22 9101076642000 Homotopy Theory II Elective 3 0 0 8
23 9101076682009 Artifical Intelligent Techniquies of the Solving of the Optimization Problems II Elective 3 0 0 8
24 9101076702006 Mathematical Foundations of Neural Networks Elective 3 0 0 8
25 9101076722006 Mathematical Theory of Inverse Problems and Their Applications Elective 3 0 0 8
26 9101076742006 Theory of Integral Equations and Their Numerical Solutions Elective 3 0 0 8
27 9101076762007 Rings with Derivations Elective 3 0 0 8
28 9101076782007 Algebra II Elective 3 0 0 8
29 9101076822012 Line Congruence II Elective 3 0 0 8
30 9101076842013 Curves and Surfaces in Computer Aided Design II Elective 3 0 0 8
31 9101076862013 Advanced Topology II Elective 3 0 0 8
 
Ege University, Bornova - İzmir / TURKEY • Phone: +90 232 311 10 10 • e-mail: intrec@mail.ege.edu.tr