Courses in registration (in Polish) Rejestracja na przedmioty całoroczne i z semestru zimowego 2024/25 1000-2024

Academic year 2024/25

• Monographic seminar - 60 hours

No brief description found, go to course home page to get more information.

Academic year 2024/25

• Monographic seminar - 60 hours

No brief description found, go to course home page to get more information.

Academic year 2024/25

• Monographic seminar - 60 hours

See the description of 1000-1D11AM.

Winter semester 2024/25

• Classes - 60 hours
• Lecture - 30 hours

(in Polish) Pierwsza część wykładu i ćwiczeń wprowadza studenta w teorię i praktykę

formalizmu matematycznego: elementy teorii mnogości są fundamentem na

którym zbudowany jest dalszy wykład algebry liniowej. Podstawy teorii

przestrzeni liniowych rozwinięte są nad dowolnym ciałem skalarów. Zarówno

teoria przestrzeni jak i przekształceń liniowych stosowane są nie tylko do

badania układów równań liniowych w kartezjańskich przestrzeniach

współrzędnych ale również do innych naturalnych przestrzeni i odwzorowań

między nimi, które pojawiają się naturalnie w innych działach matematyki

(przestrzenie wielomianów, ciągów i funkcji).

Winter semester 2024/25

• Classes - 45 hours
• Lecture - 30 hours

This is an extended version of the course Algebra 1; enriched by additional material on group and ring theory.

Fundamental algebraic structures: groups, commutative rings with 1 and fields. Group theory: normal subgroups, factor groups, group actions on sets, information about Sylow’s theorems and the classification of finitely generated abelian groups. Ring theory: divisibility, unique factorization, the notions of an ideal and of the factor ring. Field theory: field extensions obtained by adding roots of a polynomial and information on the existence of the algebraic closure.

Winter semester 2024/25

• Classes - 30 hours
• Lecture - 30 hours

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.

Winter semester 2024/25

• Classes - 30 hours
• Lab - 30 hours
• Lecture - 30 hours

Design and analysis of algorithms. Survey of fundamental algorithms and data structures. Practical improving programming and algorithm development skills. Applying ready to use libraries of algorithms and data structures.

Winter semester 2024/25

• Classes - 30 hours
• Lecture - 30 hours

The notion of amenability is one of the fundamental notions in group theory and harmonic analysis which is connected to the existence of invariant measures and paradoxical decompositions of groups. The goal of the lecture is to present a possibly broad spectrum of applications of some methods concerning amenability and to study analogies between amenability and cohomology theory for Banach algebras, as well as stability problem in the sense of Ulam.

Winter semester 2024/25

• Classes - 30 hours
• Lecture - 30 hours

Basic properties of analytic functions of one complex variable. A beautiful part of analysis with many applications all throughout mathematics.

Winter semester 2024/25

• Classes - 30 hours
• Lecture - 30 hours

Auctions are a widely used mechanisms for resource exchange and allocation, that finds application in real world (e.g. internet auctions) as well as computational applications (e.g. resource allocation in multi-agent systems and eCommerce). Which auctions are best for the seller and which for the buyers? What is the impact of knowledge of others' valuations? How bad is collusion? Is it hard to determine the winner when bundles of several interdependent objects are being sold? Does it depend on the bidding language?

The aim of this course is to introduce and present the basic issues and problems of arising in auctions and to deepen their understanding via game theory and computational complexity theory.

Winter semester 2024/25

• Classes - 30 hours
• Monographic lecture - 30 hours

(in Polish) Wykład "Algebry Banacha" ma na celu zaznajomienie uczestników z podstawową teorią algebr Banacha ze szczególnym uwzględnieniem przypadku przemiennego.

Winter semester 2024/25

• Classes - 30 hours
• Lecture - 30 hours

The subject consolidates both theoretical and practical knowledge about machine learning and data mining methods in applications related to large, heterogeneous, distributed and dynamically growing data. We discuss problems concerning reliability and quality of data in tasks of teaching effective models for classification, prediction and related applications as well as maintaining the effectiveness of such models applied as components of larger IT systems. We refer to a wide range of practical sources and shapes of data, in particular machine-generated data. We cover a wide range of practical tasks in machine learning and data analysis, e.g. anomaly detection or recognition of similarities. Based on practical examples, we discuss the full life cycle of data and information in processing and analysis systems, including properly integrated solutions based on machine learning and data analysis.

Winter semester 2024/25

• Classes - 15 hours
• Lecture - 15 hours

The goal of the course is to present the set of common mathematical notions necessary to understand contemporary techniques of machine learning as well as to instil the mathematical apparatus necessary to efficiently use them.

Winter semester 2024/25

• Classes - 60 hours
• Lecture - 30 hours

Learning the basic concepts, theorems and methods of mathematical analysis, with particular emphasis on the differential and integral calculus of functions of one variable. Applications of these methods to problems in natural sciences.

Winter semester 2024/25

• Classes - 15 hours
• Lecture - 30 hours

"Biology of the Cell" covers the current knowledge of cell structure and function including: basic cytological and molecular biology methods, differences between pro- and eukaryotic cells, structure and function of cellular organelles, cellular transport, intracellular contact and interactions, signal transduction, replication and expression of genetic material.