Uniwersytet w Białymstoku - Centralny System Uwierzytelniania
Strona główna

Algebra II 0600-MS1-2ALG2#a
Wykład (WYK) Rok akademicki 2018/19

Informacje o zajęciach (wspólne dla wszystkich grup)

Liczba godzin: 30
Limit miejsc: (brak limitu)
Efekty uczenia się: (tylko po angielsku)

Learning outcomes and verification methods:

A student knows that the algebraic structures occurs and are important in various mathematical theories; A student knows the basic concepts of general algebra II and is able to illustrate them on examples (a group action, simple groups, solvable groups, noetherian rings, algebraic sets). A student is able to formulate main theorems of general algebra II (the Sylow theorem, the Galois theorem). A student knows the importance of the Galois theorem in mathematics (i.e. non-solvability by radicals of polynomial equations, non-constructability in geometry). A student knows the contemporary problems of algebra (i.e. the classification of simple groups). - Oral/written Exam Quizzes Test/ midterm exam Homework presentation of solutions continous evaluation

A student can take advantage of the most important general theorem of general algebra II to solve classical exercises. A student can classify finite abelian groups. A student understands problems formulated in the language of abstract algebra and he can formulate problems in this language. A studen can apply euclidean rings to solve diophantine equations. - Oral/written Exam Quizzes Test/ midterm exam Homework presentation of solutions continous evaluation

A student can identify a concrete example of application of algebra in reality (i.e. counting of combinatorial objects by the Burnside lemma). - Oral/written Exam Quizzes Test/ midterm exam Homework presentation of solutions

A student can present the three famous problems of antiquity and briefly explain the main algebraic ideas which are used in the solution of these problems. - Oral/written Exam Homework continous evaluation

Zakres tematów: (tylko po angielsku)

Contents of the course

A group action, the action of a group on a set, the Sylow theorem, solvable groups, simple groups, the structure of finitely-generated abelian groups; the polynomial ring in several variables, noetherian rings, the Hilbert's basis theorem, algebraic sets, rings of formal power series; finite fields, algebraic extensions,algebraic and transcendental numbers, splitting field of a polynomial, solvability of polynomial equations, algebraically closed fields, the field of constructible numbers, the three famous problems of ancient Greek mathematics.

Metody dydaktyczne: (tylko po angielsku)

Teaching methods: lectures, consultations, studying literature, home works, discussions in groups.

Grupy zajęciowe

zobacz na planie zajęć

Grupa Termin(y) Prowadzący Miejsca Liczba osób w grupie / limit miejsc Akcje
Opisy przedmiotów w USOS i USOSweb są chronione prawem autorskim.
Właścicielem praw autorskich jest Uniwersytet w Białymstoku.
ul. Świerkowa 20B, 15-328 Białystok tel: +48 85 745 70 00 (Centrala) https://uwb.edu.pl kontakt deklaracja dostępności USOSweb 7.0.2.0-1 (2024-03-12)