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Study programmes > All studies > Computer Mathematics > Computer Mathematics, full-time, first-cycle

Computer Mathematics, full-time, first-cycle (WMI-0118-1SO)

(in Polish: Matematyka komputerowa, stacjonarne pierwszego stopnia)
first-cycle
full-time, 3 years
Language: Polish
No description for the programme.

Qualification awarded:

(in Polish) Licencjat na matematyce komputerowej

Access to further studies:

second-cycle programmes, postgraduate programmes

Access requirements

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

A written aptitude test for the candidates with the "old" Matura. Candidates with the "new" Matura are selected and admitted on the basis of marks awarded in the Matura school-leavers' examination and certificate

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 - Knowledge of the significance of mathematics in contemporary science and technology, and in the development of an information society; - Knowledge and comprehension of the key concepts and theorems in the foundations of contemporary mathematics: logic and theory of multiplicity, linear algebra and geometry; - Knowledge and comprehension of the key concepts and theorems in continuous mathematics: geometry and topology, differential and integral calculus, ordinary differential equations, probability theory and statistics; - Knowledge and comprehension of the key concepts and theorems in discrete mathematics: combinatorics, graph theory, the combinatorial aspects of algebra, geometry, topology, the theory of numbers, and the theory of probability; - Knowledge of why the mathematical theories he/she has learned have been developed, and of their applications in the solution of problems in the natural, technological, and/or economic sciences; - Knowledge and comprehension of the concept of mathematical proof; - Knowledge and comprehension of the concept of the algorithm, and the key concepts and ideas of algorithmics; - Knowledge of the principal problems which may be solved algorithmically with the use of mathematical tools and computer techniques; - Knowledge and appreciation of the chief limits to the solution of algorithmic problems; - Knowledge of the fundamental data structures used in algorithmics, and the operations performed on them; - Knowledge of the fundamental construction and analytical techniques for algorithms; - Knowledge of the key algorithms in discrete mathematics; - Knowledge of the key algorithms in continuous mathematics (numerical methods); - Knowledge of programming techniques, including procedural, structural, object-oriented, functional, and generic programming in scripting languages and the principal contemporary programming languages; - Knowledge of the process of designing and developing of professional software; - Knowledge of the operational environment of modern software, including the principal concepts of operational systems and network technologies; - Knowledge of the basic software for computer operations; - Knowledge of selected mathematical software packages for discrete mathematics and continuous mathematics; - A foundation knowledge of the social aspects of computer science and the ethical and legal issues associated with the mathematician’s and computer scientist’s profession; - A foundation knowledge of the principles of safety and hygiene at work with computers and computer networks. SKILLS - Ability to correctly express mathematical definitions and theorems learned during his /her period of study, both orally and in writing; - Ability to use examples to demonstrate that he/she understands the mathematical concepts and theorems learned during his/ her period of study; - Ability to formulate the correct definitions for selected simple mathematical theorems; - Ability to successfully communicate with members of the engineering, scientific, and business communities on Computer Mathematics and its applications; - Ability to correctly express a problem in mathematical language, and assess the possibility of, and limits to its solution using the algorithmic approach; - Ability to successfully apply the mathematical software he/she has been taught about during his/her period of study to solve typical problems in discrete and continuous mathematics; - Ability to select the right algorithmic techniques and data structures to design algorithms for the solution of typical problems in discrete and continuous mathematics; - Ability to perform a critical analysis of the algorithms he/she has designed for computational correctness and complexity; - Ability to successfully and efficiently implement the classical algorithms, and algorithms he/she has designed for discrete and continuous mathematics, applying them in the solution of a problem using an appropriately selected programming language; and to present the solution in a clear way, if need be with the use of graphical means; - Ability to apply the required concepts and objects such as functions, relations, and recursively defined sequences, in the solution of a problem; - Ability to design algorithms, analyse their computational correctness and complexity, and implement them using the basic algorithmic techniques and data structures; - Ability to apply the concept of numbers, including natural, whole, rational, real, and complex numbers; represent them in the memory of a computer; and assess the outcome of their imperfect representation; ability to apply the principle of mathematical induction to examine the recursive properties of defined sequences and recursive algorithms; - Proficiency in the application of the concepts of linear space, vectors, linear transformations, and matrices; and their representation in typical mathematical packages and programming languages; - Ability to apply an effective algorithm for the reduction of a matrix to selected canonical forms, and to apply appropriate algorithms to calculate the determinant, rank, eigenvalues, and eigenvectors of matrices; - Ability to find numerical solutions to systems of linear and non-linear equations; - Ability to apply the concept of the boundary for the approximation and definition of numbers and functions; and to make a critical evaluation of the effects of the numerical approximation of numbers and functions; - Proficiency in the application of the concept of the derivative and integral of a function with one or more variables; ability to apply these concepts to examine a function, in optimisation problems, and to determine the surface area of the faces and the volume of polyhedral figures; - Ability to interpret the graphs of functions obtained using mathematical software, in the language of differential and integral calculus; - Ability to find the numerical solution to the initial value problem in an ordinary differential equation; - Ability to analyse the topological properties of the subsets of a linear space, in particular for large sets of data, using the methods of general and combinatorial topology, and algorithmic methods; - Ability to apply probability theory to analyse the mathematical model of a random experiment and provide a numerical simulation for it; - Ability to derive simple statistical conclusions using the appropriate software; - Ability to find solutions to problems involving combinatorics, graphs, and number theory, using algorithmic methods; - Proficiency in the use of the software required in the computer mathematician’s profession, including the fundamental tools for editing and presenting documents, spreadsheets, mathematical packages for symbolic, numerical, and graphic transformations, as well as the typical tools for operational systems and the computer programmer’s environment; - Ability to speak on Computer Mathematics using language that is clear and easy to understand; - Ability to compile written presentations and papers on detailed problems and issues in Computer Mathematics; - Ability to compile oral presentations in Polish and a foreign language on detailed problems and issues in Computer Mathematics; - Ability to collect information from the professional/scientific literature, the internet, and other reliable sources; integrate and interpret them; and on this basis draw conclusions and formulate an opinion; - Ability to study individually and in a group; - Proficiency in a foreign language at the B2 intermediate level, allowing him/her to read and understand software documentation, textbooks, and scientific papers in that language; - Proficiency in programming using modern programming languages; ability to design software in compliance with the object-oriented method. SOCIAL COMPETENCES - Awareness of his/her own limitations, and willingness to enhance his/her knowledge and practical skills; appreciation of the need for continuing enhancement of his/her qualifications; - Ability to conduct a dialogue to develop and increase the precision of his/her comprehension of the subject under discussion; - Capacity for teamwork, as team leader, as a subordinate member, and as a partner in the team; - Appreciation of the need for systematic work in long-term projects; - Ability to define the priorities for the achievement of tasks he/she has set him/herself, or which have been assigned him/her by others; - Appreciation of the value of intellectual integrity in his/her own and other people’s activities; adherence to the ethical principles in his/her conduct; - Awareness of the legal and social aspects of computerisation; and ability to observe the principles associated with them in his/her professional activities; - Appreciation of the ethical requirement of objectivity in the interpretation and presentation to the best of his/her knowledge of the results he/she obtains in his/her professional activities; - An attitude of reservation on opinions and claims which have not received sufficient verification.