### What is applied mathematics?

Applied mathematics is an important branch of mathematics that combines mathematical knowledge, programming and knowledge from a specific application area. Where theoretical mathematics can no longer help, methods of approximate problem solving, optimization and simulation are used. With the advent of the computer, applied mathematics has seen enormous progress. Numerical methods, optimization methods, and simulations are the most important tools, along with mathematical modeling, in numerous fields, for example in:

- meteorology (weather forecasting, study of the greenhouse effect, tornado forecasting),
- astronomy and astrophysics (study of the life cycle of galaxies),
- aeronautical industry (study of turbulence around objects),
- astronautical industry (study of rocket performance, spacecraft navigation)
- robotics (study of constraint forces in the optimal movement of a robotic system)
- armies (selection of combat equipment and strategy, missile navigation)
- technological processes (improvement and monitoring),
- manufacturing industry (problems of production planning, determination of the optimal plan)
- construction (testing the stability of the building),
- economy (modelling of market evolution, prediction of stock evolution, insurance),
- medicine (new materials for implants, ECG and EEG signals, tomography),
- genetics (study of the influence of radiation on genetic changes),
- signal processing (analysis, compression, signal and image transmission),
- computer networks and telecommunications (optimization of data flow and parallelization of processing).

Without numerical methods and simulations, it would be impossible to design nuclear reactors, build major structures, plan space travel, determine an accurate GPS position, obtain an image from a scanner, etc.

**What is taught in this module?**

The program of the module is aligned with the Applied Mathematics programs of the universities of the world. In addition to the usual theoretical mathematical education, this program of study teaches how to describe real-world problems in mathematical language (mathematical modeling), how to approximate the solutions of these models (numerical mathematics), how to obtain optimal solutions to problems (optimization), how to study the behavior of models in advance ( simulation). Since computers are used extensively for these tasks, computer topics are also covered in this module. Electives provide the student with the opportunity to choose additional content from the areas that appeal more to him/her.

**Where can I get a job?**

Experts in the field of applied mathematics are highly valued all over the world, as they form the backbone of the development teams of industrial, software and other companies. A theoretical mathematics education enables applied mathematicians to model and solve existing problems better and more efficiently, and to more easily acquire new knowledge, of which there is always more. Computer science education enables them to design and implement computer software themselves, not only in the field of applied mathematics, but also, as experience shows, in the field of information systems (databases) and Internet technologies. Applied mathematicians are involved in both development and data analysis in business, banking, insurance, software companies, industry, etc. Many applied mathematicians have made remarkable careers in foreign companies or universities. If they earn the appropriate number of credits in methodological subjects during their bachelor's and master's degrees, applied mathematicians can also work as teachers of mathematics and computer science in elementary and secondary schools. One semester of professional practice in schools is part of the undergraduate degree.

**What will I experience in the module?**

(general part)

- Basic math courses (calculus, algebra, geometry)
- At least 4 semesters of computer courses
- At least 1 semester of discrete mathematics
- At least 2 semesters differential equations
- At least 2 semesters of probability and statistics
- 1 semester of mathematical physics
- 1 semester of professional practice in an elementary or secondary school
- 1 semester of a foreign language

(close professional part)

- At least 5 semesters of numerical mathematics
- At least 4 semesters of discrete optimization (2 semesters of mathematical programming, 1 semester of operations research, 1 semester of heuristic methods)
- At least 1 semester of optimization in functional domains
- At least 1 semester mathematical modeling

**What will I definitely learn?**

(general part)

- Standard mathematical content found in related modules in universities worldwide: Real, functional and complex calculus, theory of measures and integrals, algebra and logic, analytic and synthetic Euclidean geometry, theory of curves and surfaces.
- Basic and advanced programming techniques, object-oriented programming, computer systems organization and architecture, at least 2 programming languages (at least 1 object-oriented).
- Elements of discrete mathematics: sets, combinatorics, basic number theory, graph theory, and code theory.
- Basic types of differential equations, systems of differential equations, boundary value problems, partial differential equations, dynamical systems, Fourier transforms.
- Probability models, limit theorems of probability, basic mathematical statistics, typical statistical distributions and applications.
- Standard equations of mathematical physics. Solving with Fourier transforms.

(close professional part)

- Interpolation, numerical solution of problems in linear algebra, nonlinear equations and systems. Numerical solution of problems with eigenvalues and eigenvectors of matrices. Numerical differentiation and integration. Approximation of functions. Numerical solution of differential, partial and integral equations. Software implementations and applications of numerical computations.
- Linear and nonlinear mathematical programming: simplex method, integer programming, conditional and unconditional optimization methods. Backpack problem. Methods of dynamic programming. Cutting plane methods, branching and bounding, implicit enumeration. Network optimization. Maximum flow, shortest path, covering, matching, minimum spanning tree and traveling salesman problems. Basic heuristic and metaheuristic methods of optimization and application in solving mathematical optimization problems. Software implementations and applications of discrete optimization methods.
- The simplest variational calculus problems and their applications. Problems with higher order derivatives, isoperimetric problems of variational calculus.
- Creating and solving mathematical models in demography, economics, astronomy and mechanics. Modeling with ordinary and partial differential equations. Dynamical systems. Probabilistic and stochastic models.
- At least 1 general mathematical software package and at least 3 software packages focused on mathematical optimization.

**What else can I learn?**

The knowledge acquired in the compulsory content of the program is extended through the selection of specific subjects in general mathematics, computer science, astronomy, mechanics, financial mathematics, statistics, software packages in mathematics, and additional narrow professional profiling in the form of a selection of advanced courses in numerical mathematics, discrete and continuous optimization, mathematical modeling and its applications. Each student chooses 6 subjects spread over 3 academic years. The master's program of the Applied Mathematics module naturally follows the bachelor's program of the same module.