# ECTS - - Ph.D. in Mathematics

### Program Competencies

Course Code Course Name
MDES600 Research Methodology and Communication Skills
MATH611 Mathematical Analysis
MATH682 Seminar
MATH689 Qualification Exam
MATH691 Thesis Proposal
MATH697 Doctoral Thesis
Departmental Elective
Departmental Elective
Departmental Elective
Departmental Elective
Departmental Elective

### Program Competencies

Course Code Course Name
MATH521 Numerical Analysis I
MATH522 Numerical Analysis II
MATH524 Finite Difference Methods for PDEs
MATH543 Group Theory I
MATH552 Complex Analysis
MATH557 Functional Analysis
MATH562 Theory of Differential Equations
MATH564 Impulsive Differential Equations
MATH571 Topology
MATH575 Calculus on Manifolds
MATH577 An Introduction to Low Dimensional Topology
MATH545 Introduction to Authenticated Encryption
MATH542 Algebraic Number Theory
MATH546 Galois Theory
MATH565 Dynamic Systems on Time Scales
MATH572 Differentiable Manifolds
MATH574 Riemannian Geometry
MATH582 Approximation Theory
MATH547 Algebraic Geometry
MATH556 Applied Functional Analysis
MATH563 Difference Equations
MATH573 Algebraic Topology
MATH591 Analytical Probability Theory
MATH584 Nonlinear Problems in Applied Mathematics
MATH576 Differential Topology
MATH585 Mathematical Modeling
MFGE505 Practical Finite Elements (Linear Finite Element)
MFGE576 Nonlinear Finite Element Method
MFGE508 Boundary Element Method
MDES610 Mathematical Modeling via Differential and Difference Equations
MDES615 Analytical Probability Theory
MDES618 Probabilistic Methods in Engineering
MDES620 Numerical Solution of Differential Equations
MDES621 Numerical Linear Algebra
MATH555 Bernstein Polynomials
ME684 Finite Element Analysis of Solids and Fluids I
ME683 Boundary Element Method
ME685 Finite Element Analysis of Solids and Fluids II
MATH630 Analytic Number Theory
MATH640 Time Series Analysis
MATH651 Measure Theory and Functional Analysis
MATH670 Mathematical Models in Biology
EE611 Detection and Estimation