REALMATHS DOUBLE MSC • INTERMATHS NETWORK

ECTS Credits: 4   |      |   Year: 2   |   Programme: Double Degrees   |   Campus: Silesian University of Technology   |   Language: English

Unit Coordinator: dr hab. inż. Edyta Hetmaniok, prof. PŚ; prof. dr hab. inż. Damian Słota

Aims:

The aim of the course is to get knowledge on numerical methods and technics of solving the problems possible to meet in engineering applications with implementation by using mathematical software.

Content:

1. Elements of the error theory.

2. Approximate solutions of the nonlinear equations and their systems.

3. Solving linear equations.

4. Approximate methods of determining the eigenvalues and eigenvectors.

5. Interpolation.

6. Approximation.

7. Numerical integration.

8. Approximate methods of solving the initial and boundary problems.

9. Approximate methods of solving integral equations.

ECTS Credits: 5   |      |   Year: 2   |   Programme: Double Degrees   |   Campus: Silesian University of Technology   |   Language: English

Unit Coordinator: dr hab. inż. Edyta Hetmaniok, prof. PŚ

Aims:

The aim of the course is to get knowledge on constructing mathematical models of selected technical and economic problems, verifying them and simulating by using Mathematica software.

Content:

1. Types of models, types of variables, selection of variables to the model.

2. Construction of the model.

3. Linear model - assumptions, estimation of parameters, verification procedures.

4. Analysis of the selected nonlinear models.

5. Analysis of the selected models described by means of differential equations.

6. Computer simulations of selected models.

ECTS Credits: 5   |      |   Year: 2   |   Programme: Double Degrees   |   Campus: Silesian University of Technology   |   Language: English

Unit Coordinator: dr hab. inż. Wojciech Kempa, prof. PŚ

Aims:

The aim of the course is to familiarize students with basic stochastic models used in technical, economic, and natural sciences, as well as with the basics of stochastic simulation.

Content:

1. Fundamentals of the theory of stochastic processes.

2. Poisson processes (simple, compound and non-stationary)

3. Elements of renewal theory. The renewal process and the renewal equation.

4. Markov chains with discrete and continuous time parameters.

5. Basics of queueing theory.

6. The Galton-Watson branching process.

7.  Basics of stochastic simulation.

ECTS Credits: 5   |      |   Year: 2   |   Programme: Double Degrees   |   Campus: Silesian University of Technology   |   Language: English

Unit Coordinator: dr inż. Witold Tomaszewski

Aims:

The aim of the course is to familiarize students with various aspects of modern cryptography, using number theory, modular arithmetic, group theory and the theory of rings and fields.

Content:

1. Number theory algorithms: Euclidean algorithm, Diophantine equations, Chinese remainder theorem.

2. Elements of group theory and commutative ring theory.

3. Modular arithmetic.

4. Classical cyphers: Caesar cypher, affine cypher, Vigenère cypher, matrix cyphers.

5. Public-key cryptography.

6. Selected cryptographic protocols.

7. Finite fields: constructions, properties and arithmetic.

8. Applications of finite fields in cryptography.

9. Elliptic-curve cryptography.

ECTS Credits: 5   |      |   Year: 2   |   Programme: Double Degrees   |   Campus: Silesian University of Technology   |   Language: English

Unit Coordinator: dr hab. Henryk Gacki, prof. PŚ

Aims:

Introduction to the concept of independence of probabilistic objects.

The gamma distribution: basic properties and applications 

Content:

ECTS Credits: 14   |      |   Year: 2   |   Programme: Double Degrees   |   Campus: Silesian University of Technology   |   Language: English

Additional info:

Students choose four courses (two for 4 ECTS and two for 3 ECTS) from among the offered courses. The courses offered will be updated each year.
The exemplary courses offer is given below:

• Queuing theory,
• Finite groups,
• Optimization theory with applications,
• Inverse problems,
• Heuristic optimization methods,
• Computational Geometry,
• Graphs and Algorithms,
• Complexity Theory,
• Introduction to modern cryptography,
• AI Security,
• Differential geometry,
• Complex analysis
• Modelling with R,
• Program specialization and metaprogramming,
• Development of computer games.

ECTS Credits: 2   |      |   Year: 2   |   Programme: Double Degrees   |   Campus: Silesian University of Technology   |   Language: English

Aims:

The aim of this course to discuss the selected problems from the various fields of mathematics, more or less connected with the chosen topics of a master thesis.

Content:

1. Literature research on the selected problems.

2. Preparation of a report on the selected topic.

3. Presentation of the prepared report.

ECTS Credits: 20   |      |   Year: 2   |   Programme: Double Degrees   |   Campus: Silesian University of Technology   |   Language: English

Aims:

The aim of this course is to prepare and complete the master’s thesis.

Content:

1. Literature research on the selected problems.

2. Execution of the calculations, simulations, analysis required to prepare the master’s thesis.

3. Verification of results.

4. Preparation of a master’s thesis.