Cycle of education: 2019/2020
Course outcomes
Speciality: ......................................
| Symbol | Contents | Reference to the PRK learning outcomes |
|---|---|---|
| K_W01 | has in-depth knowledge of the basic branches of mathematics | P7S_WG |
| K_W02 | understands well the role and importance of the construction of mathematical reasoning | P7S_WG P7S_WK |
| K_W03 | knows the most important theorems and hypotheses of the main branches of mathematics | P7S_WG |
| K_W04 | has in-depth knowledge in a selected field of theoretical or applied mathematics | P7S_WG |
| K_W05 | has in-depth knowledge in the chosen field of mathematics: knows most of the classic definitions and theorems and their proofs | P7S_WG |
| K_W06 | is able to understand the wording of issues remaining at the research stage | P7S_WG |
| K_W07 | knows the connections between the issues of the chosen field and other branches of theoretical and applied mathematics | P7S_WG |
| K_W08 | knows advanced computational techniques that support the work of the mathematician and understands their limitations | P7S_WG |
| K_W09 | knows the basics of stochastic modeling in financial and actuarial mathematics or in natural sciences, in particular in physics, chemistry or biology | P7S_WG |
| K_W10 | knows the numerical methods used to find approximate solutions to mathematical problems (e.g. differential equations) posed by applied fields (e.g. industrial technologies, management, etc.) | P7S_WG |
| K_W11 | knows the mathematical foundations of information theory, algorithm theory and cryptography as well as their practical applications, e.g. in programming and computer science in its broadest sense | P7S_WG |
| K_W12 | knows well at least one software package for symbolic computation and one package for statistical data processing | P7S_WG |
| K_W13 | has knowledge of English at the intermediate level (B2), and another foreign language at a level sufficient to read professional literature | P7S_WK P7S_UK |
| K_W14 | has sufficient knowledge of the principles of occupational health and safety in order to be able to work independently in the profession of a mathematician | P7S_WK |
| K_U01 | has the ability to construct mathematical reasoning: to prove theorems and to refute hypotheses by constructing and selecting counter-examples | P7S_UW |
| K_U02 | has the ability to express mathematical content in speech and in writing, in mathematical texts of various character | P7S_UW P7S_UK P7S_UO |
| K_U03 | has the ability to check the correctness of conclusions in building formal proofs | P7S_UW |
| K_U04 | notices formal structures related to the basic branches of mathematics and understands the importance of their properties | P7S_UW |
| K_U05 | uses tools of mathematical analysis without difficulty, including differential and integral calculus (in particular line and surface integral), elements of complex and Fourier analysis | P7S_UW |
| K_U06 | is familiar with methods of solving ordinary and partial differential equations, can apply them in typical theoretical and practical problems | P7S_UW |
| K_U07 | knows the construction of Lebesgue measure and integral; can apply the concepts of measure theory in typical theoretical and practical problems | P7S_UW |
| K_U08 | has the ability to recognize topological structures in mathematical objects occurring e.g. in geometry or mathematical analysis; can use the basic topological properties of sets, functions and transformations | P7S_UW |
| K_U09 | uses the language and methods of functional analysis in mathematical analysis and its applications, in particular uses the properties of classical Banach and Hilbert spaces | P7S_UW |
| K_U10 | is able to use algebraic methods (with emphasis on linear algebra) to solve problems in various branches of mathematics and practical tasks | P7S_UW |
| K_U11 | knows the basic probability distributions and their properties, can apply them in practical matters | P7S_UW |
| K_U12 | has knowledge of the basics of statistics (issues of estimation and testing of hypotheses) and the basics of statistical data processing | P7S_UW |
| K_U13 | is able, at an advanced level and including contemporary mathematics, to apply and present, both in speech and in writing, methods of at least one selected branch of mathematics: mathematical analysis and functional analysis, theory of differential equations and dynamic systems, algebra and number theory, geometry and topology, probability calculus and statistics, discrete mathematics and graph theory, logic and set theory | P7S_UW P7S_UK |
| K_U14 | can carry out proofs in a selected field, in which he/she uses, if necessary, tools from other branches of mathematics | P7S_UW |
| K_U15 | can identify and develop his/her interests; in particular, he/she is able to establish contact with specialists in his/her field, e.g. understands their lectures intended for young mathematicians | P7S_UK P7S_UO P7S_UU |
| K_U16 | is able to construct mathematical models, used in specific advanced applications of mathematics | P7S_UW P7S_UU |
| K_U17 | recognizes mathematical structures (e.g. algebraic, geometric) in physical theories | P7S_UW |
| K_U18 | can use stochastic processes as a tool for modeling phenomena and analyzing their evolution | P7S_UW |
| K_U19 | understands the mathematical basis of the analysis of algorithms and computational processes | P7S_UW |
| K_U20 | is able to construct algorithms with good numerical properties to solve typical and atypical mathematical problems | P7S_UW |
| K_U21 | can use methods of computer-aided proof of theorems and logical support of verification and specification of programs | P7S_UW |
| K_K01 | knows the limitations of his/her own knowledge and understands the need for further education | P7S_KK |
| K_K02 | is able to formulate precise questions in order to deepen his/her understanding of a given topic or find missing elements of reasoning | P7S_KK P7S_KO |
| K_K03 | can work in a team; understands the need for systematic work on all projects that are long-term in nature | P7S_KO P7S_KR |
| K_K04 | understands and appreciates the importance of intellectual integrity in his/her own or other people’s actions and acts ethically | P7S_KO P7S_KR |
| K_K05 | understands the need for popular presentation of selected achievements of higher mathematics | P7S_KO |
| K_K06 | can independently search for information in literature, also in foreign languages | P7S_KK P7S_KR |
| K_K07 | can formulate opinions on basic mathematical issues | P7S_KK P7S_KO P7S_KR |