Obligatory courses for 2nd grade JSIM (3M+4I) (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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| 1000-113bAG1a |
 
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Classes
Winter semester 2023/24
Groups
Brief description
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. |
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| 1000-113bAG1* |
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Classes
Winter semester 2023/24
Groups
Brief description
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. |
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| 1000-213bCPP |
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Classes
Winter semester 2023/24
Groups
Brief description
(in Polish) Celem tego przedmiotu jest pokazanie studentom nowoczesnego i efektywnego stylu programowania w języku C++. |
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| 1000-213bPW |
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Classes
Winter semester 2023/24
Groups
Brief description
The goal of the lecture is to present basic problems and techniques of programming in concurrent and distributed systems. The course is focused on two key issues: correctness and performance. In connection with fundamental problems of synchronisation such as mutual exclusion and readers-writers problem, the course presents solutions based upon shared variables and ones that require higher-level language support. |
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| 1000-213bBD |
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Classes
Winter semester 2023/24
Groups
Brief description
Structures and functions of database systems and a survey of data model. Relational databases. Relational query languages (relational algebra, first order calculus, SQL and Datalog). Database design, functional dependencies and normal forms. Entity-relationship modelling. Physical data storage and physical query execution. Query optimisation. Transaction processing. |
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| 1000-212bMD | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Mathematical concepts essential for design and analysis of algorithms: combinatorics, graph theory and number theory. |
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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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| 1000-113bAM3a |
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Classes
Winter semester 2023/24
Groups
Brief description
Many-variable differential calculus, measure and integration theory. |
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| 1000-113bAM3* |
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Classes
Winter semester 2023/24
Groups
Brief description
Multivariable differential calculus, measure and integration theory. This is an extended course and therefore it may be harder and more comprehensive than the normal course of Mathematical Analysis II.1. |
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| 1000-114bAM4a | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
(in Polish) Przedmiot jest kontynuacją Analizy matematycznej II.1, obejmuje dalszy ciąg teorii całki Lebesgue'a, funkcje całkowalne w sensie Lebesgue'a oraz rachunek różniczkowy i całkowy na podrozmaitościach R^n. |
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| 1000-114bAM4* | n/a |
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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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| 1000-114bRRZa | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
The lecture presents basic informations on existence, uniqueness and properties of ODE solutions. Elements of the qualitative analysis of solutions are also included. A number of important applications of ODE is discussed. |
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| 1000-114bRRZIb | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Ordinary differential equations (ODEs), their properties and applications. Solution methods for ODEs: using paper and pencil, and using numerical schemes. Computer lab experiments: numerical and symbolic ODE packages. |
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| 1000-114bRP1a | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Kolmogorov axioms. Basic probabilities. Random variables, probability distributions, and their parameters. Independence. Convergence of random variables. Basic limit theorems: Poisson theorem, weak and strong laws of large numbers, de Moivre-Laplace theorem. |
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| 1000-114bRP1* | n/a |
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Classes
Summer semester 2023/24
Groups
Brief description
Kolmogorov axioms. Basic probabilities. Random variables, probability distributions, and their parameters. Independence. Convergence of random variables. Basic limit theorems: Poisson theorem, weak and strong laws of large numbers, de Moivre-Laplace theorem. |
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| 1000-213bPYT |
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Classes
Winter semester 2023/24
Groups
Brief description
(in Polish) Wprowadzenie do języka Python, omówienie wybranych bibliotek i narzędzi. Po tym kursie studenci będą przygotowani do udziału w bardziej specjalistycznych zajęciach np. ze Sztucznej inteligencji czy Aplikacji WWW. |
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| 1000-113bTP1a |
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Classes
Winter semester 2023/24
Groups
Brief description
This course presents basic notions of topology: metric and topological spaces, continuous maps, homeomorphisms, Cartesian products, complete metric spaces, compactness, connectedness and path connectedness, homotopy of maps and loops, contractibility, quotient spaces. |
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| 1000-113bTP1* |
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Classes
Winter semester 2023/24
Groups
Brief description
The course presents basic notions of topology: metric and topological spaces, continuous maps, homeomorphisms, Cartesian products, complete metric spaces, compactness, connectedness and path connectedness, homotopy of maps and loops, contractibility, quotient spaces. The course is addressed to students with deeper interest in the subject, who like to work on related problems. |
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