Mathematics

Department of Mathematics offers programs of graduate study leading to the degrees of Master of Science (M.S.) and Doctor of Philosophy (Ph.D.). These programs have 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 Mathematics Applicants for admission to the Ph.D. Program are required to have completed an M.S. degree in Mathematics, 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 Mathematics

Ph.D in Mathematics 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. MATH600 Thesis
  2. MATH698 Seminar
  3. MATH699 Ph.D Qualifying Exam

Basic Courses

  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​

Ph.D. Thesis (MATH600)

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

Ph. D. thesis in mathematics. Presentation is required for the completion of the thesis.

Seminar (MATH598)

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

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

Ph.D. Qualifying Exam (MATH699)

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

Qualifying exam in compulsory courses and minor topics. ​​

Analysis - I (MATH501)

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

Set theory. Construction of real numbers. Convergence. Continuous functions. Differentiation. Riemann integral. Introduction to metric spaces. Spaces of continuous functions. ​

Complex Analysis (MATH502)

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

Recap of undergraduate complex analysis: holomorphic/analytic functions, Cauchy’s theorem, residue theorem. Conformal mappings, local degree. Möbius transformations. Techniques for evaluating complex integrals. Equivalent conditions for analyticity. The d-bar derivative. Plemelj and Pompeiu formulae. Weierstrass canonical product formula. Analytic continuation, and its uses in defining complex functions. Gamma, beta, and zeta functions. Jordan’s lemma. The inverse Laplace transform. Partial differential equations. The unified transform method.

​Theory of Partial Differential Equations (MATH505)

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

Algebra - I (MATH507)

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

Group theory, ring theory; polynomials, modules. Fields and simple field extensions. Construction with ruler and compass, the elements of Galois theory. Solvability by radicals. Finite fields.


Analysis - II (MATH512)

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

Measure and Intergration (MATH516)

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

Group Theory (MATH520)

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

Probability Theory (MATH521)

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

Random Processes (MATH522)

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

Statistical Data Analysis (MATH523)

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

Essential probability concepts in statistics. Sampling methods, data validation. Sample statistics, sampling distributions. Estimation problems and estimation errors. Hypothesis testing of the means, and variances. Simple linear regression and correlation. Multiple linear regression.


Linear Programming (MATH529)

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

Topology (MATH535)

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

Topological spaces, continuous functions; Connectedness, countability, separation axioms, compactness and Tchykonoff theorem; metric spaces and metrizability; topological groups; Homotopy of maps, fundamental groups, covering spaces; Simplicial complexes and singular complexes, homology groups.

Algebraic Topology (MATH536)

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

Selected Topics in Random Processes (MATH540)

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

Selected Topics in Probability Theory (MATH541)

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


Principal Component Analysis (MATH542)

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


Selected Topics in System Theory (MATH543)

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

Selected Topics in Algebraic Topology (MATH547)

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

Selected Topics in Differential Equations (MATH549)

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

Mathematical Statistics (MATH550)

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

Selected Topics in Analysis (MATH551)

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

Selected Topics in Analysis - II (MATH552)

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

Approximation Properties of Linear Positive Operators (MATH553)

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

Special Functions by Continued (MATH554)

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

Select Topics Differencial Geometry (MATH555)

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

Quantum Calculus (MATH556)

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


Function of Several Variables (MATH557)

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

Selected Topics in Applied Mathematics (MATH558)

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

Functional Analysis (MATH561)

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

Set Theory, Zorn's lemma. Topological spaces. Metric spaces. Linear spaces, Banach spaces, Hilbert spaces, Dual space. Completeness, separability, compactness. Linear operators and functionals, Riesz representation theorem. Hahn-Banach theorem. Contraction mapping. Strong and weak convergences. ​

Selected Topics in Functional Analysis (MATH563)

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

Special Functions (MATH564)

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

Fourier Analysis - I (MATH565)

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

Linear Algebra (MATH566)

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

Vector Spaces, Linear Transformations and Their Properties, Elementary Matrices, Determinants, Eigenvalues, Eigenvectors, Diagonalization, Inner Product Spaces; Gram- Schmidt Orthogonalization Process, Adjoint Forms, Brief Introduction to Canonical Forms.

Numerical Linear Algebra (MATH569)

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

Selected Topics in Numerical Analysis (MATH571)

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

Difference schemes for time-dependent equations with constant coefficients, Stability theory of difference schemes, Homogeneous difference schemes for time-dependent equations of mathematical physics, Economical difference schemes for multidimensional problems in mathematical physics are the main topics that will be considered in this course.

Computational Methods in PDE for Science and Engineering (MATH572)

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

Basic linear algebra. Method for designing difference schemes. Explicit, implicit formulae, convergence and stability for parabolic equations in one space dimension. ADI and LOD methods for parabolic eqautions in two space dimensions. ADI and LOD methods, the Neumann and Robbin’s problems for Laplace’s equation in a square. Laplace’s equation in three variables. Explicit, implicit and LOD methods for Hyperbolic equations.

Numerical Solutions of E.B.V.P. (MATH573)

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

Advanced Numerical Analysis (MATH574)

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

Fractional Calculus (MATH576)

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

Special functions for fractional calculus: gamma, beta, hypergeometric, Mittag-Leffler functions. The Riemann-Liouville model of fractional calculus, with properties including semigroup law, differentiation of series, Leibniz rule, and Laplace transforms. The Caputo, Weyl, Cauchy, and Grunwald-Letnikov models of fractional calculus, and their relationships with the Riemann-Liouville model. Some simple ordinary differential equations solved using transform methods. Fractional calculus defined using special-function kernels; basic properties of these models and their relationships with the Riemann-Liouville model.

Fractional Differential Equations (MATH577)

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

Banach Fixed Point Theory, Schauder Fixed Point Theorem, Fractional Differentiation and Integration, Application of Fixed Point Theory, Existence and Uniqueness of Solutions of various types of Fractional Differential Equations.

Theory of Finite Difference Schemes (MATH578)

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

Block Method for solving the Laplace equation (MATH580)

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

Real Analysis (MATH583)

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

Review on Riemann integral. Infinite sets. Countable and continuum sets. Equivalent sets. Cardinality. Point set topology. Systems of sets. Algebras, sigma-algebras and semi-algebras. Monotonic class theorem. Measure and measurable sets. Construction of measures. Caratherodory theorem. Hahn theorem. Lebesgue and Stieltjes measures. Measurable functions. Lebesgue Iitegral and its properties. Comparison of Lebesgue and Riemann integrals. The spaces of Lebesgue integrable functions. Product measure. Tonelli and Fubini theorems. Absolute continuity. Radon-Nikodym theorem.

Differential Geometry (MATH584)

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

Theory of Optimal Control (MATH585)

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

Recent Developments in Computational Fluid Dynamics (MATH586)

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

Advanced Engineering Mathematics (MATH587)

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

Fourier series, complex Fourier series, Approximation by trigonometric polynomials, Fourier integral, Fourier transforms, discrete and fast Fourier transforms, wave equation, solution by separating variables, D’Alembert solution of the wave equation, characteristics, heat equation: solution by Fourier series, solution by Fourier integrals and transforms, two-dimensional wave equation, rectangular membrane, double Fourier series, Laplacian in polar coordinates, circular membrane, Fourier-Bessel series, potentials, solutions of PDEs by Laplace transforms.

Numerical Sol. of Parabolic PDE and Inverse Control Prob. (MATH588)

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

Linear Programming (MATH589)

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

Nonlinear Differential Equations and Dynamic Systems (MATH590)

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

Dynamical Systems: Introduction to Bifurcation (MATH591)

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

Introduction to Nonlinear Programming (MATH592)

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

Introduction to Bifurcation II (MATH593)

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

Problem solving in Analysis, Algebra, and Topology (MATH597)

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

Mathematical Achievements In Antiquity (MATH599)

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

Korovkin Type Approximation Theory (MATH653)

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

Advanced Numerical Linear Algebra (MATH669)

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

This course aims to study iterative solution methods for solvıng linear systems mainly using preconditioning methods. As a Krylov subspace iterative method accelerated over relaxation method and the convergence theorems of this method for L- matrices, ırreducible matrices, consistently ordered matrices will be given. Preconditioning of linear systems will be studied by incomplete factorization preconditioning methods, approximate matrix inverses and corresponding preconditioning methods, block diagonal and Schur complement preconditionings. Estimates of eigenvalues and condition numbers for preconditioned matrices will be analyzed .

Nabla Fractional Calculus (MATH670)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week​): 0 | Tutorial (hrs/week): 1 | ECTS:

Orthogonal Polynomials On Non Uniform Lattices (MATH672)

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

In this course the q-Analogs of the Hahn, Meixner, Kravchuk,and Charlier Polynomials on the lattices x(s) = exp(2ws) and x(s) = sinh(2ws) will be investigated. Also, the q-Analogs of the Racah and Dual Hahn polynomials on the lattices x(s) = cosh(2ws) and x(s) = cos(2ws) will be considered. Asymptotic properties of the Racah and Dual Hahn polynomials and construction of some orthogonal polynomials on non-uniform lattices by means of the Darboux-Christoffel formula will be studied.

Fractional Abstract Evolution Equations (MATH677)

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

Advanced methods of Applied Mathematics (MATH687)

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

The Sturm Liouville theory with engineering applications such as elastic vibration, buckling of beams and vibration of circular membrane will be studied. Finite Difference numerical methods that are based on the principle of discretization which results in generated numerical values of the solution at a discrete set of points will be investigated. Finally after investigating the structure of Green’s function, the solutions of Dirichlet’s and Neumann problems will be given with the help of Conformal mappings.

Undergraduate Programs

Application and registration system for international students and TRNC citizens with GCE scores.

Apply Online

Postgraduate Programs

Application and registration system for master and doctorate programs.

Apply Online

Agency Login

Agency login for online application and registration system.

Agency Login

Mathematics