Applied Mathematics and Computer Science

Department of Mathematics offers programs of graduate study leading to the degree Doctor of Philosophy (Ph.D.). This program has been established to enable students with strong research motivation to develop their interests through advanced study. The programs of study and courses are designed as flexible as possible, in order to enable students to shape their studies as far as possible in accordance with their own specific interests. Research activities are conducted in collaboration with prominent universities and institutes in Turkey, Europe the rest of the world.

Ph.D. Programs involves eight semesters of study, comprising seven courses, and completion of a thesis, which must be defended under oral examination conditions.

Admission Requirements

Ph.D. in Applied Mathematics and Computer Science Applicants for admission to the Ph.D. Program are required to have completed an M.S. degree in Mathematics, Computer Science, or a related field. Candidates with insufficient background are required to take prerequisite preparatory courses.

Research Interests

Mathematics Mathematical analysis, differential equations, approximation theory, stochastic processes, optimal control, functional analysis Applied Mathematics and Computer Science Operational research, numerical methods, modelling and simulation with Petri Nets, bioinformatics, artificial intelligence, soft computing, decision making, neural networks, quantum computation, information data security, geographic information systems

Contact

Tel: +90 392 630 1227
Fax: +90 392 365 1314
E-mail: math@emu.edu.tr
Web: http://math.emu.edu.tr

 

 ​​​​Ph.D in Mahematics and Computer Science

Ph.D in Mathematics and Computer Science requires a minimum of 21 credit-hours from at least 7 courses, seminar and a Ph.D thesis. Stud​ents can take the​ follwing courses:

Compulsory Courses

  1. COMP600 Thesis
  2. MATH698 Seminar
  3. MATH699 Ph.D Qualifying Exam

Basic Courses (Mathematics)​

  1. MATH501 Analysis - 1
  2. MATH502 Complex Analysis
  3. MATH505 Theory of Partial Differential Equations
  4. MATH505 Theory of Partial Differential Equations
  5. MATH507 Algebra I
  6. MATH516 Measure and Integration
  7. MATH520 Group Theory
  8. MATH521 Probability Theory
  9. MATH535 Topology
  10. MATH536 Algebraic Topology
  11. MATH539 Differentiable Manifolds
  12. MATH561 Functional Analysis I
  13. MATH564 Special Functions
  14. MATH566 Linear Algebra
  15. MATH569 Numerical Linear Algebra
  16. MATH578 Theory of Finite Difference Schemes
  17. MATH583 Real Analy​sis
  18. MATH585 Theory of Optimal Control
  19. MATH586 Stochastic Differential Equations
  20. MATH587 Mathematical Statistics
  21. MATH590 Nonlinear Differential Equations and Dynamical Systems

Basic Courses (Computer Sciecne)

  1. COMP512 Theory of Algorithms
  2. COMP535 Digital Geometry
  3. COMP542 Introduction to Quantum Computing
  4. COMP544 Petri Nets
  5. COMP551 Combinatorics
  6. COMP552 Graph Theory
  7. COMP558 Parallel Processing
  8. COMP587 Artificial Intelligence
  9. COMP588 Computational Intelligence
  10. COMP585 Decision Making
  11. COMP586 Cryptography and Data Security
  12. COMP589 Data Mining​​

Ph.D. Thesis (COMP600)

Credit: 0 | Lecture Hour (hrs/week): 0 | Lab (hrs/week​): 0 | Tutorial (hrs/week): 0 | ECTS:

​P​​​​h. D. thesis in computer science. Presentation is required for the completion of the thesis.​

Seminar (COMP698)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): 0 | Tutorial (hrs/week): 0 | ECTS:

Seminar about the research field in Ph. D. study. ​

Ph.D. Qualifying Exam (COMP699)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): 0 | Tutorial (hrs/week): 0 | ECTS: - ​​

Qualifying exam on compulsory topics and on minor subjects.


Combinatorial Optimization (COMP506)

Credit: 3 | Lecture Hour (hrs/week): 0 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

Theory of Algorithms (COMP512)

Credit: 3 | Lecture Hour (hrs/week): 0 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

Automata, languages, complexity, computability. Finite automata, 2-head finite automata, pushdown automata, Turing machine. Chomsky hierarchy. Time complexity: class P, NP, NP completeness, NP complete problems.Space complexity: S​avitch ​theore​​m, class PSPACE. Hierarchy theorems and circuit complexity

​Selected Topics in Computer Programming (COMP521)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

Selected Topics in Computer Programming - II (COMP522)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

Introduction to Geographic Information Systems (COMP525)

Credit: 3 | Lecture Hour (hrs/week): 0 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

Selected Topics in Computer Science - I (COMP531)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

Selected Topics in Computer Science - II (COMP532)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

Computational Statistict in Bioinformatics (COMP533)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

Digital Geometry (COMP535)

Credit: 3 | Lecture Hour (hrs/week): 0 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

Introduction to Quantum Computing (COMP542)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

Classical and Quantum Information Theory (COMP543)

Credit: 3 | Lecture Hour (hrs/week): 0 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:
​​

Petri Nets (COMP544)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

It is the purpose of this course to provide a coherent description of the theoretical and practical aspects of Petri Nets by showing how Petri Nets have been developed – from being a promising theoretical model to being a full-fledged language for the design, specification, simulation, validation and implementation of large discrete event systems.

Combinatorics (COMP551)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS: - ​​

bsets, partitions, permutations. Recurrence relations and generating functions. Stirling numbers. Latin squares. Extremal set theory. Steiner triple systems. Finite geometry. Posets, lattices and matroids. Designs. Error-correcting codes.

Graph Theory (COMP552)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 0 | ECTS:

aphs, trees. Bipartite graphs. 0-1 matrices. Coloring. Algebraic methods of graph theory. Planarity, duality, embeddings. Hypergraphs. Graph algorithms: minimum spanning trees, graph-search algorithms: backtracking, breadth-first, depth-first search. Dijkstra algorithm. ​

Statistical Applications With Modern Techniques (COMP555)

Credit: 3 | Lecture Hour (hrs/week): 0 | Lab (hrs/week​): - | Tutorial (hrs/week): 0 | ECTS:

Regression analysis is a widely used suite of analytical techniques particularly suited to natural resources data. One of the strengths of regression is the conceptual simplicity of using an equation to represent a relationship between predictor variables and their associated response. This is also a weakness: drum into your mind the phrase “correlation does not imply causation” and you'll overcome (part of) this weakness. The goal in this course is to give you some experience with basic regression techniques that you can apply in your research, expose you to situations where regression analysis is useful (and perhaps not useful), and most of all give you enough understanding that you can evaluate regression in papers your read. The course is going to focus on underlying theory and also use of some selected software packages to for regression. However, also you need to know enough about how regression works to be able to evaluate a regression solution in a particular research situation.

Parallel Processing (COMP558)

Credit: 3 | Lecture Hour (hrs/week): 0 | Lab (hrs/week​): - | Tutorial (hrs/week): 0 | ECTS:

Introduction to parallel computers. Taxonomy of parallel computers. Array of processors, pipelining, multiprocessing. Systolic arrays. Complexity and efficiency of parallel algorithms. Principles of optimal parallel algorithm design.

Theory of Computing (COMP559)

Credit: 3 | Lecture Hour (hrs/week): 0 | Lab (hrs/week​): - | Tutorial (hrs/week): 0 | ECTS:
​​

Theory of Regression Analysis and Applications (COMP569)

Credit: 3 | Lecture Hour (hrs/week): 0 | Lab (hrs/week​): - | Tutorial (hrs/week): 0 | ECTS: - ​​

Regression analysis is a widely used suite of analytical techniques particularly suited to natural resources data. One of the strengths of regression is the conceptual simplicity of using an equation to represent a relationship between predictor variables and their associated response. This is also a weakness: drum into your mind the phrase “correlation does not imply causation” and you'll overcome (part of) this weakness. The goal in this course is to give you some experience with basic regression techniques that you can apply in your research, expose you to situations where regression analysis is useful (and perhaps not useful), and most of all give you enough understanding that you can evaluate regression in papers your read. The course is going to focus on underlying theory and also use of some selected software packages to for regression. However, also you need to know enough about how regression works to be able to evaluate a regression solution in a particular research situation.

Da​​tabase Management Systems (COMP574)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): - | Tutorial (hrs/week): 0 | ECTS:

Theory of Computing (COMP579)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): - | Tutorial (hrs/week): 0 | ECTS:

Decision Making (COMP585)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): - | Tutorial (hrs/week): 0 | ECTS: - ​​

Introduction to decision making. Decision making process. Decision Trees. Decision making under uncertainty. Utility theory. Decision making under conflict. Risk theory. Decision making under risk. Prospect theory. Group decision making. Paired comparison analysis in decision making. Queuing theory. Linear regression model in decision making. Time series model in decision making. Neural network based decision making. Markov model in decision making process. Monte Carlo analysis in decision making.

Cryptography and Data Security (COMP586)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): 0 | Tutorial (hrs/week): 0 | ECTS:

​​​En​​crypt and decrypt messages using classical and modern conventional ciphers including block ciphers as well as public cry​ptographic ciphers, sign and verify messages using well known signature generation and verification algorithms. 2. Analyze existing authentication and key agreement protocols, identify the weaknesses of these protocols. 3. Download and install an e-mail and file security software, PGP, and efficiently use the code to encrypt and sign messages. 

Artificial Intelligence (COMP587)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): 0 | Tutorial (hrs/week): 0 | ECTS:

Introduction to Artificial Intelligence (AI). AI history. Search strategies. State space search. Heuristic search. Control strategies. Knowledge representation. Rule-based representation, semantic networks, frame knowledge representation. Logi​​cal reasoning. Knowledge base and inference. Bayesian probability. Planning. Inference in first order logic. Introduction to learning. Decision trees. Game theory. Expert systems (ES). Building of ES. Main properties of ES. Prolog programming language in AI. Constraint satisfaction problems. Pattern recognition. Robotics. Distributed AI ​​​​

Computational Intelligence (COMP588)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): 0 | Tutorial (hrs/week): 0 | ECTS:

Data Mining (COMP589)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): 0 | Tutorial (hrs/week): 0 | ECTS:

Dat​a types, data pre-processing, measures of similarity, classification, classifier evaluation and comparison techniques, basic concepts in association, clustering analysis, cluster evaluation, anomaly detection, issues in multimedia mining and text mining.

Mathematical&Computational Modeling of Biological Systems (COMP645)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): 0 | Tutorial (hrs/week): 0 | ECTS:

Introduction for developing, analyzing and interpreting mathematical and computational models in systems biology. Throughout this course,our general goal is to use ODE and Petri nets as a tool for gaining a deeper understanding of biological systems and their dynamics. This course covers both qualitative and quantitative models and introduces corresponding modeling techniques demonstrated for various biological networks in Snoopy, CPNTools and matlab frameworks wherever and whenever it is convenient. It is assumed that the students have working knowledge in basic mathematical and computer science concepts. Otherwise the course is self-contained.

Network Science (COMP646)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): 0 | Tutorial (hrs/week): 0 | ECTS:


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