Study field description
2ND LEVEL DEGREE IN MATHEMATICS. The 2-year period of studies includes: calculus, complex and functional analysis, logic, algebra and number theory, topology, differential equations, stochastic processes, and computational mathematics, i.e. packages Mathematica and Statistica. Students are prepared to continue their studies to obtain doctorate degree.
A graduate of applied mathematics acquires the basic knowledge in theoretical and applied mathematics. He is enabled to do mathematical proofs, present and formulate mathematical problems, investigate mathematical models necessary in the field of applications, apply IT knowledge. The graduates are prepared to work in commercial and financial companies, computing centers and statistical offices.
A graduate of financial mathematics acquires the basic knowledge in theoretical and applied mathematics in economy and finance. He is enabled to do mathematical proofs, present and formulate mathematical problems, investigate mathematical models and estimate, predict and simulate economical processes. He is prepared to financial management and apply IT knowledge. The graduates can work in financial companies, banks, stock markets, insurance and commercial industry.
The University reserves the right not to open a department or specialty when the number of accepted candidates is too low.
The procedure includes:
diploma results - in the case of graduates of the same or related field of study;
an interview covering major subjects appropriate for the undergraduate course of the Department of national security -in the case of candidates with a degree in other fields of study (sample topics are posted below - as ADDITIONAL INFORMATION).
In the qualifying procedure the following grading system is applied: very good (5), good plus (4+), good (4), satisfactory plus (3+), satisfactory (3), unsatisfactory (2). The candidate who gets an unsatisfactory grade in the interview cannot be accepted.
Rozmowa kwalifikacyjna odbędzie się w budynku Wydziału Nauk Ścisłych i Przyrodniczych przy ul. 3 Maja 54 w sali 15 (parter), w terminie określonym na stronie startowej programu IRK.
Announcement of results
The results of the recruitment will be available on the IRK account of each registered candidate.
Kandydat po dokonaniu rejestracji w systemie IRK zobowiązany jest do złożenia kompletu wymaganych dokumentów.
Niespełnienie tego warunku oznacza rezygnację z ubiegania się o przyjęcie na studia - mimo, iż kandydat dokonał ważnej rejestracji i wniósł wymaganą opłatę rekrutacyjną.
Dokumenty przyjmowane są w Centralnym Punkcie Obsługi Kandydata przy ul. Żytniej 39, w budynku Wydziału Humanistycznego w terminach określonych na stronie startowej programu IRK.
Wykaz wymaganych dokumentów można pobrać tutaj.
Addidional information for candidates
There is a fee required.
1. Propositional calculus. Functors and quantifiers. Basic laws of propositional calculus.
2. Algebra of sets. Basic operations on sets and their properties. Relations and their properties; an equivalence relation, an order relation; functions as relations.
3. Real numbers and their properties. Subsets of reals, bounded sets, limits of sets.
4. Complex numbers and their properties. Algebraic, trigonometric and exponential representations of complex numbers. Power and square root in the set of reals.
5. Numerical sequences. Limit of a sequence. Properties of convergent sequences and their examples.
6. Numeric series. The concept of convergence, convergence criteria, geometric and
7. Elementary functions. Examples, properties, graphs of basic functions.
8. A limit and continuity of functions. Properties of limits, basic theorems about continuous functions.
9. Differentiable functions. Derivative of a function and its basic properties. Derivatives of elementary functions. Basic theorems of a differential calculus. Taylor’s scheme. The use of differential calculus for function studies.
10. Indefinite and definite integrals. Definition and properties of integrals. Basic
integration methods. Newton's Leibniz scheme. Applications of integrals.
11. Sequences and function series. Point convergence and uniform convergence. Convergence criteria. Power series. Examples of expanding functions into a power series.
12. Differential equations. The concept of ordinary differential equation. General and detailed solution, geometric interpretation. Basic examples of differential equations.
13. Matrices and determinants. Operations on matrices. Inverse matrix. Properties of determinants. A matrix raw.
14. Linear spaces. Definition and basic examples of linear spaces. Basis and space dimension.
15. Linear transformations. Definition and examples of transformations. Matrix of a linear transformation.
16. Systems of linear equations. Methods of solving systems of linear equations. Kronecker – Capelli Theorem. Cramer’s systems.
18. Polynomials. Polynomial roots. Decomposition of polynomials. Bezout Theorem. The fundamental theorem of algebra.
19. Metric spaces. Definition and examples of metric spaces. A concept of a ball in a metric space. Open and closed sets. Complete, compact and consistent spaces. Homeomorphisms.
20. Elements of combinatorics. Permutations, variations and combinations. Definitions and examples.
21. Foundations of probability theory. A concept of probability. Operations on events. Properties. Conditional and total probability. Independence of events. Bernoulli scheme. Random variables. Examples of discrete and continuous distributions. Expected value and variance of random variable.