Elective courses for 1st degree studies in 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 | |||||||
| 1000-135AMD | 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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| 1000-135EAR | n/a |
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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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| 1000-135OPL | n/a |
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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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| 1000-135WPS | n/a |
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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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| 1000-135WUD | 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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| 1000-135WTL |
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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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| 1000-134AG2 | 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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| 1000-134BAD |
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n/a |
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n/a |
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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| 1000-135SYD |
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n/a | n/a |
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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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| 1000-134MAD | n/a |
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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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| 1000-135GM1 |
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n/a |
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n/a |
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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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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| 1000-135WMF |
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n/a |
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n/a |
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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| 1000-135WGR |
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n/a |
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n/a |
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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| 1000-135WTG | 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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| 1000-135WRC | n/a |
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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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| 1000-135MAG |
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n/a | n/a |
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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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n/a |
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n/a |
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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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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| 1000-135MIE |
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n/a |
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n/a |
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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| 1000-135MMS |
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n/a |
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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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| 1000-135POC |
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n/a |
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n/a |
Classes
Winter semester 2023/24
Groups
Brief description
The paradigm of object-oriented programming. Practical course in C++ programming. |
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| 1000-135RP2 |
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n/a |
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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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n/a |
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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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| 1000-134TP2 | 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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