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Master Program Computational Mathematics and Mathematical Modeling

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Period of study: three semesters
Form of study: full-time  ECTS: 90
Coordinator: Assoc. Prof. Tatyana Chernogorova, PhD University of Sofia,
Faculty of Mathematics and Informatics,
5 James Bourchier blvd., 1164 Sofia, Bulgaria, Phone: +359 2 8161506,
e-mail: chernogorova@fmi.uni-sofia.bg

This Program aims to provide the students with solid theoretical knowledge and practical skills for solving mathematical problems in one of the following areas:

  • classical and contemporary fields of Approximation theory and its applications;
  • creation and study of mathematical models of processes in Physics, Chemistry, Biology, Ecology and Engineering;
  • development and study of effective numerical methods and algorithms for solving the mathematical problems obtained through the modeling;
  • use of available software for scientific computations.

The aim of this Master Program is to prepare students to work in interdisciplinary research teams, which do research on current practical problems, to do research in the fields mentioned above, as well as to work on applications of Mathematics in natural sciences and engineering. The Program aims to provide students with a solid education in the fields of contemporary numerical methods, high-performance computing systems, development and use of software for mathematical modeling in at least one domain of science and engineering.

The students who have graduated from this program will be able to work in applied-scientific sections and industrial companies, which develop and use software for research on the basis of
mathematical models; in scientific institutes and centers; in universities. The Master Program facilitates a further PhD degree study on the same subject.

Highly skilled specialists from the Faculty of Mathematics and Informatics, from the Bulgarian Academy of Sciences and from abroad teach the students in the Master Program. The Master Program is well provided with computer laboratories, libraries and software products.

The Master program complies nicely with the branch Technomathematics of the ECMI Model Master Program in Industrial Mathematics. The latter is created on the basis of the best practices in Europe, realized after setting up The European Consortium for Mathematics in Industry (ECMI) in 1986. FMI is a member of ECMI since 2010 and an Educational teaching centre of ECMI since 2014. For our master students this provides possibilities to attend Summer Schools and Mathematical Modelling Seminars, organized by ECMI, to study at other ECMI teaching centers, to award ECMI certificate.

The courses, signed with # in the CURRICULUM, could be taught in English, if there are foreign students, following the program, as well as ECMI or Erasmus students.

CURRICULUM

Courses:

Winter Semester:
Numerical methods for differential equations (9 ECTS credits) #
Mathematical Modelling in Biology (6 ECTS credits) #
Mathematical methods of signal processing: Fourier transform and wavelets (6 ECTS credits)
Mathematical Models in Physics (8 ECTS credits)
Finite element method – algorithmic foundations (6 ECTS credits) #
Approximation Theory (6 ECTS credits) #
Theory of difference methods (7 ECTS credits) #
Numerical methods for linear systems with sparse matrices (9 ECTS credits) #
Computer Graphics (8 ECTS credits) #
Partial differential equations (10 ECTS credits) #
Applied Functional Analysis (4 ECTS credits) #
Special Functions and Approximations (6 ECTS credits) #
Hydrodynamics 1 (4.5 ECTS credits) #

Summer Semester:
Mathematical modeling seminar (4 ECTS credits) #
Spline functions and applications (6 ECTS credits)#
Numerical Methods (10 ECTS credits) #
Mathematical models and computational experiment (6 ECTS credits)
Nonlinear mathematical models (6 ECTS credits) #
Finite elements methods – theory (4 ECTS credits)#
Parallel algorithms (9 ECTS credits) #
MATLAB and its Applications in Numerical Methods (6 ECTS credits) #
Software for scientific computations (4 ECTS credits)
Sobolev spaces and applications in PDEs (8 ECTS credits) #
Numerical Integration (6 ECTS credits) #
Hydrodynamics 2 (4.5 ECTS credits) #