Elective courses for Mathematics (course group defined by Faculty of Mathematics, Informatics, and Mechanics)
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2023Z - Winter semester 2023/24 2023L - Summer semester 2023/24 2024Z - Winter semester 2024/25 2024L - Summer semester 2024/25 (there could be semester, trimester or one-year classes) |
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| 2023Z | 2023L | 2024Z | 2024L | |||||||
| 1000-134AG2 | n/a |
 
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n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Elements of group theory, field theory, theory of noncommutative rings and modules. Group theory: free groups, solvable groups, semidirect products of groups. Fields: Galois theory and applications. Modules: finitely generated modules over principal ideal domains. Noncommutative rings: matrix algebras, division algebras, Frobenius theorem, algebras of skew polynomials and Weyl algebras. |
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| 1000-135ALP |
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n/a |
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n/a |
Classes
Winter semester 2023/24
Groups
Brief description
This lecture class provides an introduction to commutative algebra; it is required for algebraic geometry lecture. The topics concern commutative rings and modules over such rings. An important class of rings considered are noetherian rings. |
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| 1000-135AGL | n/a |
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n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Classical linear groups, abstract Lie groups, compact groups. Classical Lie's theory: correspondence between Lie groups and Lie algebras. The exponential map. Abstract approach to Lie algebras. Classification of simple Lie algebras. Representations of classical Lie groups and Lie algebras by the highest weight. Homogeneous spaces. |
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| 1000-135ASW |
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n/a |
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Classes
Winter semester 2023/24
Groups
Brief description
The lecture aims to present the classical results concerning the structure and linear representation theory of finite dimensional algebras over fields. The following will be discussed: correspondence between theory of modules and representation theory, simple modules, radical algebras and classification of semi-simple associative algebras. Applications will be given to the representation theory of finite groups, through results concerning group algebras and the theory of group characters. Examples of applications will be discussed. Basic information on finite dimensional Lie algebras and their representations will be given. As a tool in this theory, universal enveloping algebras and their properties will be discussed |
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| 1000-135AMD | n/a | n/a | n/a |
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Classes
Summer semester 2024/25
Groups
- (from 2024-10-01) Elective courses for 1st degree studies in mathematics
Brief description
(in Polish) Wykład jest wprowadzeniem do algorytmiki opartym na prezentacji wybranych problemów obliczeniowych oraz algorytmów związanych z klasycznymi strukturami matematyki dyskretnej takimi jak grafy, drzewa, sieci przepływowe oraz języki regularne. |
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| 1000-135AF |
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Classes
Winter semester 2023/24
Groups
Brief description
This is a fundamental course in functional analysis. The course starts with basic notions on Banach and Hilbert spaces and their properties. The next topic of the course concerns linear functionals and operators in these spaces and their properties. The course gives also basic information on spectra and spectral oroperties of linear operators. Spectra of compact operators on Hilbert spaces are discussed. |
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| 1000-135AF* |
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n/a | n/a |
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Classes
Winter semester 2023/24
Groups
Brief description
This is a fundamental course in functional analysis. The course gives a basic knowledge on Banach and Hilbert spaces and their geometric properties. The next topic of the course concerns linear functionals and operators in these spaces and their properties. The course gives also basic informations on spectra and spectral properties of linear operators. In particular, spectra of compact operators in Hilbert spaces are discussed. |
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| 1000-135AN |
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n/a |
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n/a |
Classes
Winter semester 2023/24
Groups
Brief description
Numerical solution of important computational problems of applied mathematics: the eigenproblem, large sparse linear systems, systems of nonlinear equations and multidimensional quadrature. |
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| 1000-135AP | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The course will present economic basis and mathematical technique required in selecting optimal investments under uncertainty. The topics discussed will include: solutions to the classical Markowitz problem for risky assets, risky assets with riskless asset, both with short sale constraints and without that constraints; risk measures Value-at-Risk and Conditional-Value-at-Risk, their properties and applications in portfolio optimization. |
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| 1000-135ANZ | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Main topics: Weierstrass theorem, Mittag-Leffler theorem, Runge theorem. Many-valued functions, analytical extensions, monodromy. Analytical functions on Riemann surfaces; Problems in Riemann surface theory: basic information and examples. Fundamental notions of the theory of analytic functions in many complex variables, Cauchy-Riemann equations, power series expansions, analytical extensions, Cousin problems. |
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| 1000-135APZ |
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n/a |
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Classes
Winter semester 2023/24
Groups
Brief description
Introduction to two key concepts in numerical analysis: approximation and complexity. Classical polynomial approximation of smooth functions. Approximation based on partial information. Construction of optimal algorithms in prescribed model of computation. |
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| 1000-134BAD |
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n/a |
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Classes
Winter semester 2023/24
Groups
Brief description
Database concepts and role. Data models. Relational databases. Relational query languages. SQL. Database dasign theory, normal forms, modeling using entity-relationship models. Transaction processing. Physical models, query optimization. Databases based on non-standard data models: object-oriented, deductive (Datalog) and distributed. |
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| 1000-135EKN | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The aim of the course is to present the theoretical background, main concepts and basic methodology of modern econometrics. We will discuss classification and examples of econometric models, in particular one equation linear model, estimation with least squares, applications in non-linear models, large sample theory, time series: stationarity, ARIMA,heteroskedasticity and forecasting. |
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| 1000-135EAR | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
(in Polish) Splot funkcji i jego zastosowania do aproksymacji. Szeregi Fouriera i badanie ich zbieżności. Przestrzeń Schwartza i transformata Fouriera. Funkcja maksymalna Hardy’ego-Littlewooda. Funkcje monotoniczne, o wahaniu ograniczonym i absolutnie ciągłe. Funkcje lipszycowskie: ich rozszerzenia i własności aproksymacyjne. Przykłady powiązań pomiędzy teorią równań cząstkowych, teorią aproksymacji, analizą harmoniczną i zespoloną oraz teorią interpolacji. |
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| 1000-135GEA | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
This is an introductory course in algebraic geometry. The aim is to introduce students to algebraic varieties and their basic geometric properties. At the end of the course examples of applications of algebraic geometry will be shown. |
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| 1000-135GM1 |
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Classes
Winter semester 2023/24
Groups
Brief description
The lecture presents selected properties of Euclidean figures and transformations. |
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| 1000-135GM2 | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
(in Polish) Inwersja, przekształcenia afiniczne oraz stożkowe w ujęciu czysto geometrycznym. Ogniska i kierownice stożkowych, własności izogonalne stożkowych, przekroje stożka obrotowego. Liczne zastosowania i geometryczne dowody najsłynniejszych twierdzeń m.in.: Gaussa-Bodenmillera, Brianchona, o motylku, Ponceleta (dla trójkąta), Feuerbacha, o łańcuchach Steinera, Newtona oraz formuł Kartezjusza, Eulera i Fussa. |
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| 1000-135GR | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Abstract smooth manifolds, smooth maps. Tangent vectors and derivative of a smooth map. Vector fields as differentatials and flows. Lie bracket. Tangent bundle. Ventor bundles and operations on them. Tensor fields. Foliations and Frobenius theorem. Differential forms, exterior derivative and the Stokes theorem. Covariant derivative and affine connection, parallel transport and geodesics. Curvature tensor. Levi-Civita connection on Riemannian manifold. Ricci tensor.Geodesically complete manifolds. Manifolds of constantt curvature (space form problem). Lie groups and algebras. |
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| 1000-135GK |
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Classes
Winter semester 2023/24
Groups
Brief description
Our aim is to introduce the students to basic algorithms and data structures used in computer graphics. These include basic raster graphics algorithms, two- and three-dimensional geometry, elements of computational geometry, geometric modelling, visibility algorithms and illumination models. |
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| 1000-135IFI |
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Classes
Winter semester 2023/24
Groups
Brief description
The course presents fundamental financial instruments: forward rate agreements, interest rate swaps, forward and futures contracts, options - plain vanilla options, selected simple exotic options and interest rate options. For each of these instruments the following is shown: the structure of the instrument, its market role, pricing method and sensitivity analysis - all that with market practice aspects. |
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| 1000-135RRJ |
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Classes
Winter semester 2023/24
Groups
Brief description
We will address the limit behaviour of trajectories of an ordinary differential equation, its invariant sets and the approach to a differential equation seen as a dynamical system. |
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| 1000-214bJAO | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Basic computation models (automata, grammars and Turing machines). Chomsky hierarchy. Mathematical description of computability; the limits of computability; and a brief introduction to computational complexity. |
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| 1000-135LOM |
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Classes
Winter semester 2023/24
Groups
Brief description
An introduction to classical topics of mathematical logic with elements of model theory. |
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| 1000-134MAD | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Selected topics in combinatorics and graph theory, in particular: counting principles, combinatorial proofs, recurrence relations, Burnside's lemma, Eulerian circuits and Hamiltonian cycles, trees, planarity, colorings, matchings. |
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| 1000-135MUZ |
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n/a |
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Classes
Winter semester 2023/24
Groups
Brief description
This is a basic course providing theoretical principles for computation of premiums and reserves in a life insurance company. The required mathematical background comprises calculus and the first course in probability. The computational models for individual and multiple - life policies (including multiple - decrement model) are developped in a systematic way. The carefully selected problems and exercises reinforce working knowledge of theoretical issues. The course can serve as a good preparation for future actuaries. |
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| 1000-135MGT |
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Classes
Winter semester 2023/24
Groups
Brief description
Fundamental notions of the category theory, additive and abelian categories. Tensor product in the category of modules. Projective and injective modules, resolvents. Graded groups, chain complexes and their homologies. Derived functors of Hom and of the tensor product. Presheaves, sheaves and their cohomologies. Simplicial cohomologies and Cech cohomologies. Coverings and principal bundles; cohomological interpretation. |
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| 1000-135MMN |
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Classes
Winter semester 2023/24
Groups
Brief description
The aim of the lecture is to present some basic methods of dynamical systems and partial differential equations that are essential in the modern description of natural and social processes. |
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| 1000-135MOF | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The course will present methods for pricing financial assets. The following topics will be discussed: tree algorithms, Monte Carlo methods, solutions to the Black-Scholes PDE. The course will present convergence problems for SDE of Ito type, parabolic PDE and properties of their solutions, and convergence problems for numerical solutions to parabolic PDE. Mathematical content will be enlarged by examples of numerical valuation of selected instruments. |
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| 1000-135MAG |
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Classes
Winter semester 2023/24
Groups
Brief description
The course intends to systematize the fundamental notions of number theory, algebra and analysis in the scope of the national curriculum in mathematics. It will also present methods of teaching of school algebra and the good practices, at the level of an elementary school and of a high school. The course will also include topics that can inclrase the interest of students in mathematics. |
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| 1000-135MGE |
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Classes
Winter semester 2023/24
Groups
Brief description
The course presents a wide variety of methods for teaching geometry at primary and secondary school level. |
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| 1000-135MRP | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
We will discuss teaching methodology for combinatorics and theory of probability and work on developing probabilistic intuition. |
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| 1000-135MR |
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n/a | n/a |
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Classes
Winter semester 2023/24
Groups
Brief description
The goal of the lecture is an introduction to the mathematical background of the risk management. Special attention will be paid to Value at Risk. |
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| 1000-135MIE |
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n/a |
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Classes
Winter semester 2023/24
Groups
Brief description
Microeconomics is the part of economics dealing with rules governing individuals' choices and interactions between individuals in economy. The course will combine introduction to microeconomics and advanced microeconomic theory. It encompasses the general choice theory, producers and consumers optimization problems, choice under uncertainty, and various concepts of market equilibria. |
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| 1000-135MBM | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The lecture is devoted to the widely understood mathematical modelling in biology and medicine. We mainly focus on ecological models which are built using differential and difference equations. We also consider models of immune reactions and those of classical genetics (Mendel theory) based on Markov chains. |
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| 1000-135MMK | n/a |
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n/a | n/a |
Classes
Summer semester 2023/24
Groups
Brief description
No brief description found, go to course home page to get more information.
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| 1000-135IP1 | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
During this course we describe and solve problems related to the modelling of financial markets and to the pricing and hedging of financial derivatives. |
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| 1000-135IP2 |
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n/a |
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Classes
Winter semester 2023/24
Groups
Brief description
The course will desribe: Interest rate securities. Models of short rate. HJM model. Interest rate derivatives (FRA, caps, floors, swaptions etc.). Market models. Callibration of models to market data. |
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| 1000-135MMS |
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Classes
Winter semester 2023/24
Groups
Brief description
The aim of this course is to describe various models in applied mathematics in order to help students to plan their master studies and to choose a subject of a future master thesis. We will discuss several mathematical models in physics, biology, economy and social sciences. |
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| 1000-135NRR |
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Classes
Winter semester 2023/24
Groups
Brief description
The course is devoted to a construction, analysis and implementation of fundamental methods for numerical solution of initial and boundary value problems for ordinary differential equations, and for boundary and initial-boundary value problems for basic type of partial differential equations: elliptic, parabolic and hyperbolic. |
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| 1000-135ONA | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Scientific computing interactive systems e.g. Matlab, Scilab.memory hierarchy, CPUs abilities, basics of C programming, code optimization techniques, basic numerical packages and libraries, scientific visualization. |
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| 1000-135OPL | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
We will focus on solving linear programming problems mainly by applying various simplex methods . Special attention will be given to duality in linear programming and to geometric interpretations. |
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| 1000-135OPN |
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Classes
Winter semester 2023/24
Groups
Brief description
Finding minima and maxima of functions on sets given by systems of nonlinear equations and inequalities. Lagrange multipliers, Kuhn-Tucker conditions, dual techniques. Special attention is given to convex optimisation. |
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| 1000-135PS | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Main topics: Gaussian processes; Poisson processes; The theory of Markov processes; Diffusion processes and their relation to stochastic differential equations; Weak and strong solutions of stochastic differential equations; Processes with independent increments. |
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| 1000-135PSB | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Lectures on theoretical foundations of stochastic analysis (Markov chains, Poisson process, birth and death processes, Master and Fokker-Planck equations will be integrated with concrete biological models on the micro level (gene expression and regulation, ion channels) and on the macro level (evolutionary game theory). |
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| 1000-135POC |
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Winter semester 2023/24
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Brief description
The paradigm of object-oriented programming. Practical course in C++ programming. |
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| 1000-135RP2 |
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Classes
Winter semester 2023/24
Groups
Brief description
The course contains an introduction to the convergence theory for probability distributions (equivalence of various definitions, Central Limit Theorem) and to applications of harmonical analysis in the theory (properties of characteristic functions). Moreover, some elements of martingale theory and Markov chains will be discussed. |
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| 1000-135RP2* |
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Classes
Winter semester 2023/24
Groups
Brief description
The course contains an introduction to the convergence theory for probability distributions (equivalence of various definitions, the Central Limit Theorem) and to applications of harmonic analysis in the theory (properties of characteristic functions). Moreover, some elements of martingale theory and Markov chains will be discussed. The course is intended for students interested in a deeper understanding of probability theory and willing to think about various related problems and excercises. |
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| 1000-135ROZ |
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Classes
Winter semester 2023/24
Groups
Brief description
The course covers the following topics: local complex geometry, complex differential forms, Kaehler manifolds, Dolbeault cohomologies, Hodge theory, vector bundles, Chern classes. |
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| 1000-135RRC |
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Classes
Winter semester 2023/24
Groups
Brief description
Introduction to the theory of linear partial differential equations. The first part focuses on the classical theory. The second gives introduction to the theory of Sobolev spaces and weak solutions of elliptic problems. The course does not require previous experience in PDEs. However, the students are encouraged to take a basic course in Functional Analysis, at least parallelly. Certain issues, in particular concerning the theory of weak solutions, will be treated in a more detailed way compared to the course "Introduction to PDE". |
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| 1000-135STB |
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Winter semester 2023/24
Groups
Brief description
Systematic introduction to Bayesian statistics. The subject of this course is now becoming more popular, has many important applications, but is treated marginally or entirely omitted in standard courses of statistics. The course is dedicated to students of mathematics and also students of informatics who are interested in statistics. |
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| 1000-135SW |
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Classes
Winter semester 2023/24
Groups
Brief description
This course presents multivariate statistical theory and techniques. The topics covered are: 1) Asymptotic log likelihood ratio tests; Wald, Rao, Pearson; logistic regression. 2) Generalised Linear Models. 3) Model selection criteria (for example: AIC, BIC) 4) Shrinkage methods for linear regression (e.g. PCR, PSLR, Ridge and LASSO). 5) The multivariate Gaussian distribution, parameter estimation, the Wishart distribution. 6) Statistical tests for multivariate Gaussian data. (e.g. Hotelling) 7) The data matrix, geometrical representations and distances. 8) Principal Component Analysis and Canonical Correlation Analysis. 9) Non-parametric Density Estimation: histograms, kernel density estimation methods, optimal bin width, projection pursuit methods for multivariate densities. 10) Discriminant Function Analysis. 11) Clustering techniques, including logistic regression, self organising maps (SOM) and the EM algorithm as a tool for clustering and semi-supervised learning. |
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| 1000-135SST | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The course concerns computer simulation of random variables and simple stochastic processes. It comprises also an introduction to Monte Carlo (MC) methods, also known as randomized algorithms. |
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| 1000-135SYD |
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Classes
Winter semester 2023/24
Groups
Brief description
An overview of classification methods and intelligent decision support systems. Methods deriving from different approaches, such as machine learning, statistics, fuzzy set theory and rough set theory, will be presented. During practical laboratory classes decision support software will be used. There will be some takehome projects for individual investigation. |
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| 1000-135SC | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The course presents probabilistic and statistical theory for modelling time series data and forecasting. There is particular emphasis on the Box-Jenkins method of ARIMA processes, also further developments; GARCH modelling, cointegration and neural networks are also considered. The R programming language is used for implementation. |
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| 1000-135TL | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Basic lecture in number theory. Rudiments of basic abstract algebra are used and applications to number theory are explained. |
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| 1000-135TM |
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Winter semester 2023/24
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Brief description
This lecture is self-contained and is based only on the obligatory courses from the first two years of studies. We will recall some elements of measure theory. The aim of this course is to improve the knowledge of tools from Measure Theory in Functional Analysis, Partial Differential Equations, Probability Theory, and many other fields of mathematics. |
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| 1000-135TMN |
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Winter semester 2023/24
Groups
Brief description
The lecture presents basic notions of advanced set theory (ordinal and cardinal numbers, axioms of set theory) and introduces elements of infinite combinatorics. |
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| 1000-135TRU |
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Classes
Winter semester 2023/24
Groups
Brief description
The lecture is devoted to short term pricing of insurance risk. We will discuss basic premium calculation issues, individual and collective risk models, risk sharing, and ruin probability. |
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| 1000-135TST | n/a | n/a |
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Classes
Winter semester 2024/25
Groups
Brief description
It is an introduction to modern mathematical Control Theory. The theory is illustrated by numerous examples from economy, biology, medicine, physics and technology. In particular: controllability for linear and nonlinear systems, bang-bang principle, time-optimal control, Pontriagin Maximum Principle, transversality, dynamic programming. |
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| 1000-135TA | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Homotopy groups. Fibrations and cofibrations. Long exact sequence of homotopy grooups of fibration. Axioms for generalized (co-)homology. Singular (co-)homology. Degree of self-maps of spheres. Cellular (co-)homology. De Rham cohomology. Multiplicative structure in singular (co-)homology. Orientation of topological manifolds and duality theorems. Intersection number and linking number. |
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| 1000-134TP2 | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The course starts from the notion of a fundamental group of a space and its relations to the theory of covering spaces. The second part is devoted to a brief introduction to singular homology theory of topological spaces. The last few lectures should present important applications of previously introduced concepts. |
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| 1000-135TOG | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The aim of this course is to present a series of main concepts and theorems of general topology which are both important and elegant from the point of view of this field, as well as essential for applications in topology and mathematics as a whole. The notion of compactness and its variants is of central importance to the course. |
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| 1000-135UD |
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Classes
Winter semester 2023/24
Groups
Brief description
The theory of dynamical systems studies the long-term evolution of systems, which takes place under constant and deterministic rules. The evolution may thus be given (in the discrete time case) by the iterates of a certain map, or (in the continuous time case) by the solutions of an ODE, etc. The aim of the theory is to describe regular and chaotic properties of some classes of systems, study their stability and determine their invariants (such as entropy). |
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| 1000-135WAS |
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Classes
Winter semester 2023/24
Groups
Brief description
Main topics: General theory of stochastic processes, Wiener process; Introduction to the theory of continuos-time martingales; Definition and basic properties of stochastic integral; Ito's formula; Stochastic differential equations and their connections with partial differential equations. |
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| 1000-135WGR |
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Classes
Winter semester 2023/24
Groups
Brief description
Basic differential geometry: submanifolds of euclidean spaces and tangent vectors, curves and moving frames. Frenet-Serret theorem, cuvature and torsion of curves in 3-dimensional space. Surfaces in 3-dimensional space., I and II fundamental forms, principal curvatures, Gauss curvature. Theorema egregium and intrinsic geometry of surfaces. Geodesic curves on surfaces. Covariant derivative of vector fields and parallel transport. The Gauss-Bonnet-Theorem. Abstract Riemannian manifolds. Models of the hyperbolic plane. |
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| 1000-135WMF |
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n/a |
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Classes
Winter semester 2023/24
Groups
Brief description
(in Polish) Skrócony opis: wykład pełni rolę wstępu do zagadnień matematyki finansowej i ubezpieczeniowej. Przygotowuje do uczestnictwa w bardziej zaawansowanych wykładach poświęconych tej tematyce, Zakres materiału pokrywa znaczną częśc zagadnień wymaganych na państwowych egzaminach aktuarialnych w zakresie matematyki finansowej. |
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| 1000-135WPS | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Introduction of basic concepts of the theory of stochastic processes. Definition and properties of the Poisson process and the Wiener process. Preliminary information about Markov processes and continuous time martingales. |
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| 1000-135WRC | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Introduction to partial differential equations. Selected topics in theory of distributions and Sobolev spaces, applications to ellpitic, parabolic and hyperbolic problems. |
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| 1000-135WTG | n/a |
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n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The basic notions and mathematical formalism of game theory, with a particular focus on the non cooperative games, will be introduced and illustrated by selected applications in economy, social sciences and biology. The classical notions of equilibria, and dynamical systems leading to such equilibria (evolutionary game theory) will be considered. Laboratory experiments for various types of discussed games are planned during the classes. |
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| 1000-135WTL |
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n/a |
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n/a |
Classes
Winter semester 2023/24
Groups
Brief description
(in Polish) Podstawowym celem wykładu jest przedstawienie wstepu do teorii liczb, jako jednego z najwazniejszych działów matematyki. W dalszej jego czesci przedstawione sa przykłady zastosowania tej teorii do kryptografii oraz teorii kodowania. |
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| 1000-135WUD | n/a |
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n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The course is an introduction to some aspects of the dynamical systems theory based on the analysis of some model examples. This includes a description of the dynamics of transformations of the interval, circle, torus and complex plane. |
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| 1000-135ZAF | n/a |
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n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The goal of this course is to present various examples of applications of tools and methods of functional analysis in other branches in mathematics. We will present spectral theory for compact operators on Banach spaces and normal operators on Hilbert spaces, and its importance in differential equations. We will also discuss Fourier transform, theory of distribution, convolution algebras, as well as weak and weak* topologies on topological vector spaces with some examples of their natural appearance. |
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