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Study programmes > All studies > Mathematics > Mathematics, Second Cycle of Courses

Mathematics, Second Cycle of Courses (WMI-0050-2SO)

(in Polish: Matematyka, stacjonarne drugiego stopnia)
full-time, 2 years
Language: Polish
No description for the programme.

Qualification awarded:

(in Polish) Magisterium na matematyce

Access to further studies:

education in doctoral school, postgraduate programmes

Professional status:

In compliance with the educational level the graduate has achieved.

Access requirements

ATTENTION: this information may be not up to date. Valid admission requirements can be found on www.erk.uj.edu.pl

attainment of sufficient score on the basis of requisite application documents

Teaching standards

ATTENTION: this information may be not up to date. Valid admission requirements can be found on www.erk.uj.edu.pl

Graduates who complete the programme of study have acquired the learning outcomes specified in Resolution No. 34/III/2012 adopted by the Senate of the Jagiellonian University on 28th March 2012 on the introduction of learning outcomes for particular fields of study conducted at the Jagiellonian University as of the 2012/2013 academic year, with later amendments. Graduates hold the following qualifications as regards knowledge, skills, and social competences: KNOWLEDGE - An advanced level of knowledge of the fundamental areas of mathematics. - Appreciation of the role and significance of the construction of mathematical reasoning. - Knowledge of the principal theorems and conjectures in the main areas of mathematics. - An advanced level of knowledge in a selected area of theoretical or applied mathematics. - An advanced level of knowledge in a selected area of mathematics: 1) knowledge of the majority of the classical definitions and theorems, along with their proofs. - An advanced level of knowledge in a selected area of mathematics: 2) a capacity to understand the formulation of problems still at the research stage. - An advanced level of knowledge in a selected area of mathematics: 3) a knowledge of the connections between issues in their selected area and other areas of theoretical and applied mathematics. - Knowledge of the advanced computational techniques which assist the mathematician in his work, and an awareness of their limitations. - Knowledge of the principles of modelling and computational methods applied in selected areas of mathematics. - Knowledge of the numerical methods applied to find approximate solutions to mathematical problems (e.g. differential equations). - A good knowledge of at least one software system for symbolic computation. - Proficiency in a foreign language at the B2 intermediate level, sufficient to read the professional literature. - A knowledge of the principles of hygiene and safety at work to a satisfactory level for independent work as a mathematician. SKILLS - Ability to construct mathematical reasoning to prove theorems and disprove conjectures by constructing and selecting counterexamples. - Ability to express mathematical content orally and in writing, in a variety of types of mathematical texts. - Ability to verify the correctness of reasoning applied to construct formal proofs. - Ability to identify formal structures associated with the basic areas of mathematics and to understand the significance of their properties. - Proficient use of advanced analytical tools, including differential and integral calculus. - A knowledge of the methods applied to solve classical differential equation, and the ability to apply them in typical practical problems. - Ability to use the language and methods of complex analysis in issues involving mathematical analysis and its applications. - Ability to identify topological structures in mathematical objects occurring in e.g. geometry or mathematical analysis; ability to apply the basic topological properties of sets, functions, and transformations. - Ability to use the language and methods of functional analysis in issues involving mathematical analysis and its applications; particularly to apply the properties of the classical Banach and Hilbert spaces. - Ability to apply algebraic methods to solve problems from various areas of mathematics and in practical tasks. - Ability to apply and give an oral and written presentation of the methods of at least one selected area of mathematics, at an advanced level of current mathematical practice. - Ability to conduct proofs for a selected area of mathematics, using tools from other branches of mathematics whenever the need arises. - Ability to define and develop their individual interests; in particular to establish contacts with specialists in their area of mathematics, e.g. the ability to follow lectures or reviews. - Ability to construct the mathematical models required for specific applications in mathematics. - Ability to find and adapt mathematical models for practical tasks, including tasks formulated outside mathematics. SOCIAL COMPETENCES - Awareness of the limitations on their knowledge and appreciation of the need for continuing education. - Ability to precisely formulate questions to further their understanding of a given problem, or to find the missing components in a process of mathematical reasoning. - A capacity for team-work; appreciation of the need for systematic work on long-term projects. - An appreciation of intellectual integrity in their own and other people’s work; adherence to the ethical code. - An appreciation for the need to present selected issues in higher mathematics in an accessible manner to the non-specialist general public. - Ability to conduct an independent search for information in the literature, including foreign-language publications. - A critical attitude with respect to theorems, observations, and conclusions, particularly those which are not based on logical grounds. - Appreciation of the need for critical analysis of information, including statistical and financial data, and of decision-making on the basis of an appropriate analysis of the data available. - Appreciation of the need to formulate objective opinions on issues which are described by means of mathematics.