Selected topics in Mathematics

Functional analysis 

Metric spaces (notion of distance, properties of matric spaces, examples of different metrics on vector spaces and on functional spaces). Normed vector spaces (notion of norm, relations between norms and metrics). Spaces with scalar product (Hilbert space). Bounded linear operators, matrices (contraction mapping principle and fixed point, spectral theory, eigenvalues and eigenvectors). Cryptography (RSA public-key). 

Discrete mathematics 
Graphs, basics. Paths any Cycles (Euler cycle, Hamiltonian cycle, the traveling salesman problem). 

Flow in networks (maximum flow and minimum cut). Trees (decision trees, game trees). 

Numerical solution of partial differential equations by the finite element method 

Finite element method for second order boundary value problem. Variational (weak) form of the problem (appropriate functional spaces, equivalence of classical and variational form). Discretization (triangulation, bases with local support, matrix form notation). Numerical integration. Numerical solution using FeeFEM++ open source package. 

Presentation of mathematical notions and methods which are frequently used in formulation and in solution of different problems which arise in electrical engineering. Deeper understanding of mathematical concepts and correct usage of mathematical methods are emphasized. 

Lectures cover all three listed topics. Student choose one of the topic. Deeper understanding of the chosen topic and basic knowledge about the other two topics are required.