Studies and Programmes:

The Department of Mathematics offers the following postgraduate programmes:

• Master’s Programme in Pure, Applied, and Financial Mathematics
  This is a two-year MSc programme consisting of 10-12 courses in the first year, followed by a research thesis project in the second year.


• PhD Degree Programme in Analysis, Algebra, Geometry, Graph Theory and Combinatorics, Numerical Analysis, Financial Mathematics, and Optimisation
  This is a four-year doctoral programme that includes at least 6 courses and a comprehensive examination in the first two years. The final two years are dedicated to a research thesis project, with the expectation that the results will be publishable in reputable international journals.


• Seamless Direct MSc-PhD Programme in Pure and Applied Mathematics (for undergraduate degree holders)
  This five-year programme involves completing 13-15 courses and a comprehensive examination in the first two years. The remaining three years are focused on research, with the expectation that the findings will be publishable in reputable international journals.

Department	Subject	Field	Master’s (2 years)	PhD (4 years)	Direct PhD (MSc-PhD) (5 years)	CT-PhD (BSc-MSc-PhD) (7 years)
Mathematics	Pure Mathematics	Algebra	✹	✹	✹	–
		Analysis	✹	✹	✹	–
		Geometry	✹	✹	✹	–
		Graph Theory	✹	✹	✹	–
	Applied Mathematics	Numerical Analysis	✹	✹	✹	–
		Operations Research	✹	✹	✹	–
		Scientific Computing	✹	✹	✹	–
		Cryptography and Code	✹	✹	✹	–
	Financial Mathematics		✹	✹	✹	–

The following list of optional courses is indicative. Not all options may be offered every year and new courses may be added to this list for next years.

• Algebra
  
  

  Name of the Course
  Advanced Algebra I, II
  Commutative Algebra I, II
  Algebraic Geometry I, II, III
  Combinatorial Commutative Algebra
  Computational Commutative Algebra I, II
  Homological Algebra I, II
  Field and Galois Theory
  Category Theory
  Finite Groups I, II
  Algebraic Graph Theory
  Semigroup Theory I, II
  Group Theory
  Linear Groups I, II
  Symmetric Groups
  Graded Ring Theory
  Lattice Theory
  Universal Algebra
  Homology of Semigroups
  Representation Theory of Groups I, II
  Convex Geometry and Associated Algebras
  Finite Solvable Groups
  Computational Group Theory
  Free Presentation of Groups
  Geometric Group Theory I, II
  Infinite Dimensional Lie Algebras I, II
  Infinite Groups I, II
  Permutation Groups I, II
  Permutation Groups and Their Applications
  Representation of monoids
  Combinatorial Group Theory
  Finite Dimensional Lie Algebras I, II

• Mathematical Analysis
  
  

  Name of the Course
  Real Analysis I, II
  Approximation Theory
  Fourier Analysis I, II
  Functional Spaces and Applications
  Matrix Analysis
  Inequality Theory
  Non-linear Analysis
  Probability Theory
  Ergodic Theory
  Complex Analysis
  Harmonic Analysis
  Functional Analysis
  Convex Analysis
  Banach Algebra
  C*-Algebra
  Operator Theory

• Geometry and Topology
  
  

  Name of the Course
  Riemannian Geometry I, II, III
  Finsler Geometry I, II
  Metric Geometry I, II
  Topological Algebra I, II
  Vector Bundles I, II
  Lie Groups and Algebras
  Salitons and Non-linear Wave Equations
  Geometry of Manifolds I, II
  Symplectic Geometry

• Graph Theory and Combinatorics
  
  

  Name of the Course
  Riemannian Geometry I, II, III
  Graph Theory I, II
  Combinatorial Analysis
  Algorithmic Graph Theory
  Probabilistic Graph Theory
  Algebraic Graph Theory
  Theory of Social Networks
  Combinatorial Optimization
  Advanced Combinatorial Analysis
  Extremal Combinatorics
  Enumerative Combinatorics
  Topological Methods in Combinatorics
  Advanced Graph Theory
  Computational Complexity
  Combinatorial Geometry

• Applied Mathematics
  
  

  Name of the Course
  Riemannian Geometry I, II, III
  Advanced Numerical Analysis
  Applied Real Analysis
  Applied Functional analysis
  Numerical Solution of Integral Equations
  Theory of Integral Equations
  Finite Element Methods
  Numerical Solution of Partial Differential Equations
  Approximation Theory
  Inverse Problems in Differential Equations
  Boundary Element Methods
  Elliptic Differential Equations
  Numerical Methods in Linear Algebra
  Iterative Methods for Large Matrix Problems
  Numerical Linear Algebra and Data Mining
  Partial Differential Equations I, II
  Ordinary Differential Equations I, II
  Fractional Differential Equations
  Wavelets and Their Application
  Control Theory
  Numerical Solution of Ordinary Differential Equations
  Dynamical Systems 1, II
  Numerical Solution of Stochastic Differential Equations
  Interval Analysis
  Variational Method in Differential Equations
  Delay Differential Equations I, II
  Spectral Methods
  Advanced Linear Optimization I, II
  Network Optimization
  Stochastic Optimization
  Dynamic Programming
  Location Theory
  Combinatorial Optimization
  Integer Programming
  Multiple-Objective Optimization
  Mathematical Modeling
  Convex Optimization
  Interior Point Methods
  Advanced Nonlinear Optimization I, II

• Cryptography and Code
  
  

  Name of the Course
  Cryptography I, II
  Coding I
  Topics in Cryptography
  Information Theory
  Advanced Math software
  Cryptographic Protocols
  Combinatorial Analysis
  Topics in the Advanced Mathematics
  Advanced Linear Optimization
  Algorithm and Computation

• Financial Mathematics
  
  

  Name of the Course
  Advanced Stochastic Processes I, II
  Financial Mathematics I, II
  An Introduction to Financial Markets
  Financial Mathematics I, II
  Numerical Methods in Finance I, II
  Financial Time Series
  Simulation Methods in Finance I, II
  Optimization Problems in Finance I, II
  An Introduction to Financial Credit Risk
  Optimal Control Problems in Finance
  Analysis of Financial Statements
  Special Topics in Financial Mathematics

• Scientific Computing
  
  

  Name of the Course
  Advanced Algorithms
  Matrix Computations
  Computational Data Mining
  Sparse Matrix Technology
  Algorithmic Graph Theory
  Approximation Algorithms
  Cryptography I, II
  Special Topics in Scientific Computing
  Numerical linear Programming I, II
  Advanced Mathematical Software