Research course


Koç University · Graduate School of Sciences and Engineering

Entry requirements

  1. Personal and Educational Background Information (CV)
  2. Recommendation Letters
  3. TOEFL Requirement (for those whose native language is not English) – New Internet Based: Minimum Score 80
  4. GRE scores
  5. Official transcripts from all the universities attended
  6. Statement of Purpose

Months of entry

September, February

Course content

The Department of Mathematics offers graduate courses leading to M.Sc., and eventually to Ph.D., degree in Mathematics.

The Master of Science program aims to provide a sound foundation for the students who wish to pursue a research career in mathematics as well as other related areas. The department emphasizes both pure and applied mathematics.

Research in the department covers algebra, number theory, combinatorics, differential equations, functional analysis, abstract harmonic analysis, mathematical physics, stochastic analysis, biomathematics and topology.

Department specialisms

• Ring Theory and Module Theory, especially Krull dimension, torsion theories, and localization • Algebraic Theory of Lattices, especially their dimensions (Krull, Goldie, Gabriel, etc.) with applications to Grothendieck categories and module categories equipped with torsion theories • Field Theory, especially Galois Theory, Cogalois Theory, and Galois cohomology • Algebraic Number Theory, especially rings of algebraic integers • Iwasawa Theory of Galois representations and their deformations, Euler and Kolyvagin systems, Equivariant Tamagawa Number Conjecture • Combinatorial design theory, in particular metamorphosis of designs, perfect hexagon triple systems • Graph theory, in particular number of cycles in 2-factorizations of complete graphs • Coding theory, especially relation of designs to codes • Random graphs, in particular, random proximity catch graphs and digraphs • Partial Differential Equations • Nonlinear Problems of Mathematical Physics • Dissipative Dynamical Systems • Scattering of classical and quantum waves • Wavelet analysis • Molecular dynamics • Banach algebras, especially the structure of the second Arens duals of Banach algebras • Abstract Harmonic Analysis, especially the Fourier and Fourier-Stieltjes algebras associated to a locally compact group • Geometry of Banach spaces, especially vector measures, spaces of vector valued continuous functions, fixed point theory, isomorphic properties of Banach spaces • Differential geometric, topologic, and algebraic methods used in quantum mechanics • Geometric phases and dynamical invariants • Supersymmetry and its generalizations • Pseudo-Hermitian quantum mechanics • Quantum cosmology • Numerical Linear Algebra • Numerical Optimization • Perturbation Theory of Eigenvalues • Eigenvalue Optimization • Mathematical finance • Stochastic optimal control and dynamic programming • Stochastic flows and random velocity fields • Lyapunov exponents of flows • Unicast and multicast data traffic in telecommunications • Probabilistic Inference • Inference on Random Graphs (with emphasis on modeling email and internet traffic and clustering analysis) • Graph Theory (probabilistic investigation of graphs emerging from computational geometry) • Statistics (analysis of spatial data and spatial point patterns with applications in epidemiology and ecology and statistical methods for medical data and image analysis) • Classification and Pattern Recognition (with applications in mine field and face detection) • Arithmetical Algebraic Geometry, Arakelov geometry, Mixed Tate motives • p-adic methods in arithmetical algebraic geometry, Ramification theory of arithmetic varieties • Topology of low-dimensional manifolds, in particular Lefschetz fibrations, symplectic and contact structures, Stein fillings • Symplectic topology and geometry, Seiberg-Witten theory, Floer homology • Foliation and Lamination Theory, Minimal Surfaces, and Hyperbolic Geometry

Information for international students

There is no separate application process for the full scholarship. You apply to the program and if admitted will be offered the full scholarship. The program is taught in English and there are a full range of student support services for our international students.

Fees and funding

KU Graduate Fellowship

KU Graduate Fellowship is a unique and highly competitive MS and PhD scholarship opportunity for outstanding applicants. Candidates having outstanding academic record and/or having high impact scientific publications are considered for KU Graduate Fellowship.

The KU Graduate Fellowship for both MSc and PhD admitted international candidates includes:

  • Monthly stipend
  • Full tuition waiver
  • Free furnished housing nearby campus or housing aid
  • Private health insurance
  • Travel awards
  • Other benefits

Qualification and course duration


full time
48 months

Course contact details

Global Recruitment Team