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The graduate receives a thorough education in the field of mathematics and computer science enabling him or her to use acquired knowledge in various disciplines depending on the chosen specialty. The graduate is able to use mathematical models essential in applications of mathematics, is able to use information technology tools to solve theoretical and practical mathematical problems. Studies of first degree prepare its graduates for studies of second degree.
Specialties offered within the major
Mathematical Computer Science
The graduate has mathematical and computer science skills which allow him or her to work as an independent computer scientist and enable an interdisciplinary cooperation with those who use mathematics and computer science in their professional activities. The graduate in this area of specialization acquires knowledge essential for constructing and implementation of software, for designing, maintaining and administration of databases, and statistical data processing. Employment prospects: graduates of this specialisation can find employment in computer companies and IT centers.
Mathematics and Computer Science in Economics
The graduate receives a thorough education in the field of mathematics and computer science, and acquires basic knowledge of economics allowing him or her to take part in solving practical and theoretical problems in economics. The graduate in this area of specialisation is prepared to process and analyze data, to prepare forecasts and analyses of business activities, to construct and implement software which facilitates economic activity. The graduate has skills in mathematical modeling of economic phenomena, in solving control problems and in optimization of economic activity. Employment prospects: graduates of this specialisation can find employment in economics, planning and management departments of manufacturing and trading companies, in departments of state budget entities, and in consulting companies.
Mathematics and Computer Science in Finance and Insurance
The graduate receives a thorough education in the field of mathematics and computer science enabling him or her to prepare - in cooperation with economists, investment and insurance consultants – capital strategies. The graduate in this area of specialisation demonstrates skills and knowledge of actuarial calculus, financial evaluation of investment projects and statistical elaboration of data. He or she is able to apply mathematical methods both to capital and insurance markets, and can use adequate computer packages to solve the above-mentioned issues. Employment prospects: graduates of this specialisation can find employment in companies where capital decisions are of special importance, i.e. banks or insurance companies.
Mathematical Modelling
The graduate is ready to begin interdisciplinary cooperation with economists, engineers and social scientists. The graduate acquires knowledge necessary for the development of mathematical models which effectively solve problems whose sources can be traced to natural, technical, financial, and social processes. He or she is able to apply information technology tools which are used to solve problems in the above-mentioned disciplines. Employment prospects: graduates of this specialisation can find employment in industrial plants, financial and insurance institutions, and in consulting companies.
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Outcome symbol |
After completing first-cycle studies in mathematics, the graduate: |
Reference to |
|
KNOWLEDGE |
||
|
K_W01 |
understands significance of mathematics and its applications to the development of modern civilization |
P6S_WG-O1 |
|
K_W02 |
understands the importance of proof and assumptions in mathematics |
P6S_WG-O1 |
|
K_W03 |
knows methods of mathematical analysis, linear algebra, probability theory and mathematical statistics, enabling to build models of medium complexity in other branches of science |
P6S_WK-O2.1 |
|
K_W04 |
knows basic theorems of previously studied branches of mathematics |
P6S_WG-O1 |
|
K_W05 |
knows basic examples which present mathematical concepts and enable to refute wrong hypotheses or invalid reasoning |
P6S_WG-O1 |
|
K_W06 |
knows selected concepts and methods of mathematical logic, set theory, discrete mathematics included in fundamentals of other branches of mathematics |
P6S_WG-O1 |
|
K_W07 |
knows fundamentals of differential and integral calculus of functions of one and many variables; knows other branches of mathematics used in the calculus, linear algebra and topology in particular |
P6S_WG-O1 |
|
K_W08 |
knows fundamentals of computing techniques and programming which help mathematicians to carry out their tasks, and is aware of their limitations |
P6S_WG-O1 |
|
K_W09 |
has basic knowledge of at least one software package used for symbolic calculations |
P6S_WG-O1 |
|
K_W10 |
has achieved English language proficiency equivalent to level B2 of European Framework of Reference for Languages and is familiar with specialist terminology from selected branches of mathematics |
P6S_UK-O4.3 |
|
K_W11 |
knows principles of occupational health and safety |
P6S_WK-O2.2 |
|
K_W12 |
has basic knowledge of the law and ethics relating to scientific research activities and teaching, as well as to forms of individual entrepreneurship and copyright law |
P6S_WK-O2.2 |
|
SKILLS |
||
|
K_U01 |
is able to present in a clear manner, both in speech and writing, correct mathematical reasoning, and formulate theorems and definitions |
P6S_UW-O3 |
|
K_U02 |
demonstrates the ability to use propositional logic and quantifiers; can properly use quantifiers in colloquial language |
P6S_UW-O3 |
|
K_U03 |
demonstrates the ability to perform mathematical proofs by complete induction; can define functions and recurrence relations |
P6S_UW-O3 |
|
K_U04 |
is able to support mathematical reasoning using simple diagrams, such as Vienna or Hasse diagrams, or graphs |
P6S_UW-O3 |
|
K_U05 |
is able to create new objects by means of constructing quotient spaces or Cartesian products |
P6S_UW-O3 |
|
K_U06 |
uses the language of multiplicity theory to interpret problems relating to different branches of mathematics |
P6S_UW-O3 |
|
K_U07 |
understands issues concerning different types of infinity and orders in sets |
P6S_UW-O3 |
|
K_U08 |
can use the concept of real number; can give examples of irrational numbers and leap numbers |
P6S_UW-O3 |
|
K_U09 |
is able to define functions, also using boundary crossings, and describe their properties |
P6S_UW-O3 |
|
K_U10 |
can use in different contexts the concept of convergence and limit; is able to – on easy and medium difficulty levels – calculate limits of sequences and functions, determine absolute and conditional convergence of series |
P6S_UW-O3 |
|
K_U11 |
can interpret and explain functional dependencies presented in the form of formulae, charts, graphs, schemes and apply them to practical problems |
P6S_UW-O3 |
|
K_U12 |
can apply theorems and methods of differential calculus of functions of one and many variables to problems relating to optimization, to finding local and global extrema, and to function investigation; can give precise justification of their reasoning |
P6S_UW-O3 |
|
K_U13 |
can use the definition of an integral of a function of one and many real variables; can explain analytical and geometric sense of the concept |
P6S_UW-O3 |
|
K_U14 |
can integrate functions of one and many variables by parts and substitution; can change order of integration; can present areas of plane surfaces and volumes in forms of integrals |
P6S_UW-O3 |
|
K_U15 |
can apply numeric tools and methods to solving selected problems of differential and integral calculus, including those basing on its applications |
P6S_UW-O3 |
|
K_U16 |
uses the concepts of linear space, vector, linear transformation, matrix |
P6S_UW-O3 |
|
K_U17 |
notices algebraic structures (group, ring, body, linear space) in different mathematical issues, not necessarily associated directly with algebra |
P6S_UW-O3 |
|
K_U18 |
can compute determinants and know their properties; can give a geometric representation of a determinant and understands its relation to mathematical analysis |
P6S_UW-O3 |
|
K_U19 |
solves sets of linear equations with constant coefficients; can use geometric interpretation of solutions |
P6S_UW-O3 |
|
K_U20 |
finds matrices of linear transformations with respect to different bases; computes eigenvalues and eigenvectors of matrices; can explain geometric sense of these concepts |
P6S_UW-O3 |
|
K_U21 |
reduces matrices to a canonical form; can use this skill to solve linear differential equations with constant coefficients |
P6S_UW-O3 |
|
K_U22 |
is able to interpret a system of ordinary differential equations in the language of geometry by means of vector field and phase space |
P6S_UW-O3 |
|
K_U23 |
recognizes and determines most important topological properties of subsets of Euclidean space and metric spaces |
P6S_UW-O3 |
|
K_U24 |
applies topological properties of sets and functions to solving problems relating to quality |
P6S_UW-O3 |
|
K_U25 |
recognizes problems, including practical issues, which can be solved using algorithms; can specify this type of problem |
P6S_UW-O3 |
|
K_U26 |
can construct and analyze an algorithm in accordance with a specification and write it in a selected programming language |
P6S_UW-O3 |
|
K_U27 |
is able to compile, start and test an independently written computer program |
P6S_UW-O3 |
|
K_U28 |
is able to use computer programs for data analysis |
P6S_UW-O3 |
|
K_U29 |
is able to model and solve discrete problems |
P6S_UW-O3 |
|
K_U30 |
uses the concept of probabilistic space; is able to construct and analyze a mathematical model of a random experiment |
P6S_UW-O3 |
|
K_U31 |
can give various examples of discrete and continuous probability distributions and discuss selected random experiments and mathematical models in which these distributions occur; knows practical applications of basic distributions |
P6S_UW-O3 |
|
K_U32 |
knows how to use formula of total probability and Bayes formula |
P6S_UW-O3 |
|
K_U33 |
can identify parameters for the distribution of a discrete and continuous random variable; can apply boundary theorems and law of large numbers to probability evaluation |
P6S_UW-O3 |
|
K_U34 |
knows how to use statistical characteristics of a population and the equivalent sample |
P6S_UW-O3 |
|
K_U35 |
is able to conduct simple statistical inference, also with the use of computer tools |
P6S_UW-O3 |
|
K_U36 |
is able to present mathematical problems and issues in a simple colloquial language |
P6S_UK-O4.1 |
|
K_U37 |
has acquired English language proficiency in the field of mathematics according to the requirements for level B2 of European Framework of Reference for Languages |
P6S_UK-O4.3 |
|
K_U38 |
can write a short paper and deliver an oral presentation, both in English and Polish, relating to previously studied problems; uses relevant resources to fulfill the task |
P6S_UK-O4.3 |
|
K_U39 |
can prepare a longer presentation discussing a selected problem in mathematics and its applications |
P6S_UW-O3 |
|
SOCIAL COMPETENCES |
||
|
K_K01 |
understands the need for lifelong education |
P6S_UU-O6 |
|
K_K02 |
demonstrates the ability to formulate precise questions to deepen his understanding of a given topic or to find missing elements of reasoning |
P6S_UU-O6 |
|
K_K03 |
can interact and work in a team; understands the need of systematic work on long term projects |
P6S_KR-O9 |
|
K_K04 |
understands the significance of intellectual honesty, both in his own and in other people’s activities; demonstrate ethical behavior |
P6S_KK-O7.2 |
|
K_K05 |
understands the need to popularize selected achievements in the field of higher mathematics |
P6S_KK-O7.1 |
|
K_K06 |
deepen his knowledge and abilities relating to the scope of his interests; is able to obtain information from specialist literature independently, also in foreign languages |
P6S_UU-O6 |
|
K_K07 |
demonstrates the ability to formulate opinions concerning important mathematical issues |
P6S_KO-O8.1 |
The graduate acquires in-depth knowledge in the field of mathematics and computer science, demonstrates the ability to construct mathematical models and can apply advanced information technology tools to solving mathematical problems. The graduate is able to use acquired knowledge and skills in various disciplines depending on the chosen specialty.
Specialties offered within the major
Mathematical Computer Science
The graduate of this specialization receives a thorough education in the field of mathematics and computer science enabling him or her to work as an independent computer scientist, and to begin interdisciplinary cooperation with those who in their professional activity use mathematics and computer science. Students who major in mathematical computer science acquire knowledge essential for data processing, solving optimization problems, constructing algorithms and analyzing their computational complexity, modeling and computer simulations, as well as skills required to administer and use local and wide area computer networks. Employment prospects: graduates of this specialisation can find employment in computer companies, IT centers or in research institutions which use information technologies.
Mathematics and Computer Science in Economics
The graduate acquires in-depth knowledge in the field of mathematics and its applications in economics and management; the graduate also receives a thorough education in the field of computer science enabling him or her to solve practical economic problems using quantitative methods. The graduate of this specialisation is able to construct and analyze mathematical models of economic processes, construct and verify econometric models, collect, analyze and use data to facilitate economic decisions. Employment prospects: graduates of this specialisation are ready to work independently and creatively for companies and institutions which use advanced quantitative analysis of economic processes, as well as in research institutions.
Mathematics and Computer Science in Finance and Insurance
The graduate receives a thorough education in the field of mathematics and computer science. The graduate acquires interdisciplinary knowledge enabling him or her to participate in processes of making capital decisions. The graduate of this specialisation demonstrates skills and knowledge of actuarial calculus, financial evaluation of investment projects and statistical elaboration of data and is able to use adequate computer packages for the above purposes, the graduate shows the ability to construct mathematical models of both capital and insurance markets issues. Employment prospects: graduates of this specialisation can find employment in big companies where capital decisions are of special importance, i.e. banks, insurance companies, companies operating on capital market, and in research institutions.
Mathematical Modeling
The graduate of this specialization receives a thorough education in the field of mathematics, statistics and computer science necessary for interdisciplinary cooperation with economists, engineers and social scientists. The knowledge acquired during the course enables the graduate to develop and analyze mathematical models for problems whose sources can be traced to natural, technical, financial, and social processes. Employment prospects: the graduates of this specialisation can find employment in industrial plants, financial and insurance institutions, centers for implementing advanced technology, universities, research institutions, and consulting companies.
|
Outcome symbol |
After completing second-cycle studies in mathematics, the graduate: |
Reference to |
|
KNOWLEDGE |
||
|
K_W01 |
demonstrates deepened knowledge of basic branches of mathematics |
P7S_WG-O1.1 |
|
K_W02 |
knows different proving techniques; understands the significance of proof in mathematics |
P7S_WG-O1.1 |
|
K_W03 |
is familiar with basic theorems from main branches of mathematics |
P7S_WG-O1.1 |
|
K_W04 |
demonstrates in-depth knowledge of a selected branch of theoretical or applied mathematics, in particular: 1) knows most of classical definitions and theorems and proofs for them |
P7S_WG-O1.1 |
|
K_W05 |
2) understands concepts and issues of research in progress |
P7S_WG-O1.1 |
|
K_W06 |
3) knows relations between a selected academic discipline and other branches of theoretical and applied mathematics |
P7S_WG-O1.1 |
|
K_W07 |
is familiar with and understand basic concepts of real complex analysis, such as: Lebesgue measure and integral, Laurent and Fourier series, residue |
P7S_WG-O1.1 |
|
K_W08 |
is familiar with and understands basic concepts of functional analysis, such as: Hilbert space, Banach space, linear continuous spectrum operator |
P7S_WG-O1.1 |
|
K_W09 |
is familiar with and understands basic concepts of algebraic topology and differential geometry, such as: simplicial division, basic group, Euler characteristics, parallel transport, curvature |
P7S_WG-O1.1 |
|
K_W10 |
is familiar with and understands basic concepts and methods of solving partial differential equations; knows applications of such equations |
P7S_WG-O1.1 |
|
K_W11 |
knows numerical methods used to find approximate solutions to mathematical problems (e.g. differential equations) raised by applied sciences, such as: industrial technologies, management |
P7S_WG-O1.1 |
|
K_W12 |
is familiar with basic concepts and methods of discrete mathematics used in computer science; knows what a Turing machine is and understands the significance of the concept |
P7S_WG-O1.1 |
|
K_W13 |
has achieved English language proficiency equivalent to level B2 of European Framework of Reference for Languages and is familiar with specialist terminology used in mathematical papers |
P7S_UK-O4.3 |
|
K_W14 |
demonstrates knowledge of principles of occupational health and safety sufficient to carry out tasks of a mathematician |
P7S_WK-O2.2 |
|
K_W15 |
has basic knowledge of the law and ethics related to scientific research activities, teaching, and copyright law |
P7S_WK-O2.2 |
|
SKILLS |
||
|
K_U01 |
demonstrates the ability to construct a line of mathematical reasoning; proves theorems and refutes hypotheses by means of generating and choosing counterarguments |
P7S_UW-O3.1 |
|
K_U02 |
demonstrates the ability to present mathematical issues, both in speech and writing, in mathematical texts of different types |
P7S_UW-O3.1 |
|
K_U03 |
demonstrates the ability to check correctness of conclusions established while constructing formal proofs |
P7S_UW-O3.1 |
|
K_U04 |
recognizes, in mathematical problems, formal structures relating to basic branches of mathematics and understands the significance of their properties |
P7S_UW-O3.1 |
|
K_U05 |
can effectively use tools of analysis, such as differential and integral calculus (in particular curvature and area integral), elements of complex and Fourier analysis |
P7S_UW-O3.1 |
|
K_U06 |
knows methods of solving classical ordinary and partial differential equations, can apply them to typical practical issues |
P7S_UW-O3.1 |
|
K_U07 |
is familiar with Lebesgue measure and integral; can apply concepts of measure theory to typical theoretical and practical issues |
P7S_UW-O3.1 |
|
K_U08 |
recognizes topological structures in mathematical objects occurring in geometry or mathematical analysis; has the ability to use basic topological properties of sets, functions and transformations |
P7S_UW-O3.1 |
|
K_U09 |
uses the language and methods of functional analysis and demonstrates the ability to apply them to problems in mathematical analysis and its applications, in particular uses the properties of classical Banach and Hilbert spaces |
P7S_UW-O3.1 |
|
K_U10 |
can apply algebraic methods (in particular linear algebra) to solving problems relating to different branches of mathematics and practical problems |
P7S_UW-O3.1 |
|
K_U11 |
can find simple characteristic numbers, local and global, of a surface, such as Ricci curvature, Gauss curvature, Euler characteristic |
P7S_UW-O3.1 |
|
K_U12 |
has achieved English language proficiency relevant to the language of mathematics and equivalent to level B2 of the Common European Framework of Reference for Languages |
P7S_UK-O4.2 |
|
K_U13 |
can - on an advanced level including modern mathematics – apply and present both in speech and writing methods of at least one of the following branches of mathematics: mathematical analysis, functional analysis, differential equation and dynamic system theories, algebra, number theory, geometry and topology, probability theory and statistics, discrete mathematics and graph theory, logic and multiplicity theory |
P7S_UW-O3.1 |
|
K_U14 |
is able to construct proofs in a selected branch of mathematics, and if necessary uses tools from other branches of mathematics |
P7S_UW-O3.1 |
|
K_U15 |
can apply tools used in computer science to solve mathematical problems, e.g. partial differential equations problems |
P7S_UW-O3.1 |
|
K_U16 |
recognizes mathematical structures (e.g. algebraic, geometric) in physical theories |
P7S_UW-O3.1 |
|
K_U17 |
demonstrates the ability to popularize achievements in the field of higher mathematics |
P7S_UW-O3.1 |
|
K_U18 |
is able to obtain information concerning latest achievements in mathematics independently, also in foreign languages |
P7S_UK-O4.3 |
|
K_U19 |
is able to precisely formulate questions which will be used to deepen his understanding of a given topic or to find missing elements of reasoning |
P7S_UW-O3.1 |
|
SOCIAL COMPETENCES |
||
|
K_K01 |
understands the need for lifelong education; is able to organize learning process of other people |
P7S_UU-O6 |
|
K_K02 |
is able to work in a team; understands the importance of systematic work on long term projects |
P7S_UO-O5.1 |
|
K_K03 |
understands the significance of intellectual honesty, both in his own and in other people’s activities; demonstrates ethical behavior |
P7S_KK-O7.2 |
|
K_K04 |
demonstrates the ability to formulate opinions concerning important mathematical issues |
P7S_KO-O8.1 |
