Obligatory courses for 4th grade JSIM (3I+4M) (course group defined by Faculty of Mathematics, Informatics, and Mechanics)
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2024Z - Winter semester 2024/25 2024L - Summer semester 2024/25 2025Z - Winter semester 2025/26 2025L - Summer semester 2025/26 (there could be semester, trimester or one-year classes) |
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| 1000-113bAG1a |
 
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Classes
Winter semester 2024/25
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 2024/25
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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| 1000-134FAN |
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Classes
Winter semester 2024/25
Groups
Brief description
Basic properties of analytic functions of one complex variable. A beautiful part of analysis with many applications all throughout mathematics. |
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| 1000-134FAN* |
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Classes
Winter semester 2024/25
Groups
Brief description
Basic properties of analytic functions of one complex variable. A beautiful part of analysis with many applications all throughout mathematics. |
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| 1000-114bRRZa | n/a |
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Classes
Summer semester 2024/25
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 2024/25
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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| 1000-116bST |
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Classes
Winter semester 2024/25
Groups
Brief description
The lecture serves as an introduction to classical mathematical statistics, focusing on a rigorous presentation of the theory behind the statistical techniques used in data analysis. The course centers on parametric statistical models, with a particular emphasis on exponential families. During the course, methods for parameter estimation, confidence intervals, hypothesis testing, and the theoretical properties of these techniques are introduced. The section on prediction is limited to a thorough discussion of linear models. Alternatively, you may choose 1000-714SAD, which has a more practical orientation. |
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