Courses in registration (in Polish) Rejestracja na przedmioty całoroczne i z semestru zimowego 2023/24 1000-2023

• Monographic seminar - 60 hours

• Monographic seminar - 60 hours

• 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.

• Classes - 30 hours
• Lecture - 30 hours

The lecture is an introduction to the supervised learning, in other words statistical prediction, focused on modern linear methods and largely (about 2/3) based on "The Elements of Statistical Learning" by Hastie, Tibshirani and Friedman.

• Classes - 30 hours
• Lecture - 30 hours

(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.

• Lab - 30 hours
• Lecture - 30 hours

The course will cover various issues which have not fit into the basic database course. Furthermore, the database research domain is so huge that it would not fit into any basic course. The subjects of lectures will be relational database tuning, object-relational mapping, columnar data store, NOSQL stores (key-value, wide-column, document, graph), advanced server programming and distributed databases.

• 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).

• 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.

• 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.

• Monographic seminar - 60 hours

Presentation of selected important topics in mathematical analysis. Participants will be encouraged to present their Master's theses at the seminar.

• Classes - 30 hours
• Lecture - 30 hours

The lecture is addressed to students of mathematics as well as to students of computer science interested in theoretical or applied aspects of approximate reasoning. Issues and problems discussed in the lecture are considered by many famous mathematicians and computer scientists to be among central problems of the current century, as important as deciphering the genetic code was for the second half of the 20th century. We will discuss problems important for making progress in many projects, in particular, interdisciplinary projects, in which mathematicians and computer scientists work together with specialists from other areas such as neuroscience, bioinformatics, psychology, economy, or complex adaptive systems. Different theoretical and applied aspects of methods of concept approximation from experimental data and domain knowledge will be covered.

• 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.

• Classes - 30 hours
• Lecture - 30 hours

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.

• Lab - 10 hours
• Lecture - 10 hours

The goal of the course is to present the set of elementary notions of machine learning necessary to understand contemporary, advanced techniques of machine learning as well to instil the programming techniques necessary to efficiently use them.

• Lab - 30 hours

(in Polish) Celem tego przedmiotu jest pokazanie studentom nowoczesnego i efektywnego stylu programowania w języku C++.