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Алгебра, Аналитикалық геометрия және сызықтық алгебра, Математикалық талдау, сандар теориясы

This course is designed to prepare undergraduates majoring «6M060100 – Mathematics "

In the course of implementing the requirements of the following tasks: building a strong system of theoretical knowledge, skills, problem solving, ability to work with educational and scientific literature.

Undergraduates need knowledge of algebra and mathematical logic in the volume of a university course.

Model theory is an area of mathematical logic which analyzes mathematical structures using first-order logic. This course will provide a basic introduction to model theory, with a strong focus on several mathematical applications.

Languages, Structures and Theories. Up and Down L¨owenheim–Skolem Theorem. Elementary Equivalence and Isomorphism. Types and Stone’ space. Realizing and Omitting Types. Prime and Atomic Models. Countable Saturated, Universal and Homogeneous Models. -categorical Theories. Unaccountably Categorical Theories. ω-Stable Theories.

This course is designed to prepare undergraduates majoring «6M060100 – Mathematics"

Model theory is an area of mathematical logic which analyzes mathematical structures using first-order logic. The aim of this course and these notes is to present an exposition of the

basics of stability theory.

Definability

Particular cases of stability theories

Other examples of stable theories

Other equivalent concepts of stability

Examples related to algebra

The course covers the following topics: Basic topics include the compactness theorem, the Löwenheim-Skolem theorem, quantifier elimination, types, prime and saturated models, count ably categorical models, and a brief introduction to omega-stable theories.

Course objective: undergraduate should acquire basic knowledge of the Model Theory, using modern apparatus for the study of these discipline. Study of the theory, as well as problem solving, should contribute to the expansion of concepts of this discipline, the development of sustainable skills with objects from one and, as a consequence, the ability to analyze and recognize the possibility of using the acquired knowledge to solve various mathematical problems.

Objectives of the course: implementation of the requirements established by the State Compulsory Standard of Higher Education, Master degree in mathematics.

In the course of implementing the requirements of the following tasks: building a strong system of theoretical knowledge, skills, problem solving, ability to work with educational and scientific literature.

Prerequisites course:

Undergraduates need knowledge of algebra, mathematical logic and model theory in the volume of a university course.

Writing the thesis of Master’s student dissertation.

General information about the Jonsson Theories. T - Universal T - homogeneous models. Criteria perfect ness of Jonsson Theories. Сompanions of the Jonsson Theory. Elimination of quantifiers. Properties of the kosemantichnost models Jonsson Theories. About similarities in the Jonsson Theories. Communication Jonsson Theories and universal Jonsson

This course is designed to prepare undergraduates majoring «6M060100 – Mathematics"

Model theory is an area of mathematical logic which analyzes mathematical structures using first-order logic. The aim of this course and these notes is to present an exposition of the

basics of stability theory.

Definability

Particular cases of stability theories

Other examples of stable theories

Other equivalent concepts of stability

Examples related to algebra

The course covers the following topics: Basic topics include the compactness theorem, the Löwenheim-Skolem theorem, quantifier elimination, types, prime and saturated models, countably categorical models, and a brief introduction to omega-stable theories.

Course objective: undergraduate should acquire basic knowledge of the Model Theory, using modern apparatus for the study of these discipline. Study of the theory, as well as problem solving, should contribute to the expansion of concepts of this discipline, the development of sustainable skills with objects from one and, as a consequence, the ability to analyze and recognize the possibility of using the acquired knowledge to solve various mathematical problems.

Objectives of the course: implementation of the requirements established by the State Compulsory Standard of Higher Education, Master degree in mathematics.

In the course of implementing the requirements of the following tasks: building a strong system of theoretical knowledge, skills, problem solving, ability to work with educational and scientific literature.

Prerequisites course:

Undergraduates need knowledge of algebra, mathematical logic and model theory in the volume of a university course.

Writing the thesis of Master’s student dissertation.

Notation and preliminaries from Model Theory’s course. Notation and preliminaries from Model Theory’s course. Order property. Order property. Indiscernible elements. Definability. Particular cases of stability of the theories. Examples related to algebra. Other equivalent concepts of stability. Strongly minimal sets

Лебег кеңістігінде жуықтау теориясының негізгі есептерін, тура және кері теоремалары айта білу.

Негізгі теоремаларды қолдана отырып Лебег кеңістігіндегі функциялардың ең жақсы жуықтауының және үзіліссіздік модулінің реттерін анықтай білу.