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

Overview of the data processing pipeline; collection and storage of raw data; processing, cleaning, and storage of processed data; scaling tools for the data processing system.

(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.

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.

The aim of the lecture is to introduce fundamental algebraic structures: groups, commutative rings with 1 and fields, and to discuss their basic properties. The properties of rings are presented as a natural extension of the properties of the ring of integers and the ring of polynomials over a field. In particular,

the following topics are discussed: divisibility, unique factorization, the notions of an ideal and of the quotient ring. The part of the lecture devoted to fields includes field extensions obtained by adding roots of a polynomial and the

information on the algebraic closure. The construction of the quotient field of a domain is presented. The part of the lecture concerning group theory covers basic properties of groups but it also includes information about the classification of finitely generated abelian groups and about actions of finite groups on sets and their simplest applications.

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.

Algorithmic problems and methods of analysis of high-throughput sequencing data and other large-scale experimental techniques of modern genomics. Topics will include the problems of mapping reads to reference genomes, reconstructing sequenced genomes from reads, classifying and quantifying reads. Methods handling data from different experiments and sequencing technologies, as well as approaches using different types of data together will be presented.

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

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.

Students perform tasks contributing to their bachelor's thesis under the promoter supervision.

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.

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.

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.

"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.

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.

An overview of fundamental problems and techniques of interpreter and compiler construction. The central topics of the course are methods and tools of semantic analysis of programs as well as code generation and optimisation for various platforms (JVM, LLVM, assembly).

The course builds upon knnowledge and abilities from the course "Programming Languages and Paradigms" (or an equivalent course).

Completing the course should enable students to create a compiler for a simple programming language.