SylabUZ
| Nazwa przedmiotu | General Algebra |
| Kod przedmiotu | 11.1-WK-MATP-GA-S22 |
| Wydział | Wydział Nauk Ścisłych i Przyrodniczych |
| Kierunek | WMIiE - oferta ERASMUS |
| Profil | - |
| Rodzaj studiów | Program Erasmus |
| Semestr rozpoczęcia | semestr zimowy 2023/2024 |
| Semestr | 1 |
| Liczba punktów ECTS do zdobycia | 4 |
| Typ przedmiotu | obieralny |
| Język nauczania | angielski |
| Sylabus opracował |
|
| Forma zajęć | Liczba godzin w semestrze (stacjonarne) | Liczba godzin w tygodniu (stacjonarne) | Liczba godzin w semestrze (niestacjonarne) | Liczba godzin w tygodniu (niestacjonarne) | Forma zaliczenia |
| Wykład | 30 | 2 | - | - | Egzamin |
| Ćwiczenia | 30 | 2 | - | - | Zaliczenie na ocenę |
In the end of this course the students know and understand the basic theorems concerning groups, rings, fields and lattices theory to applicate and use the notions and theorems from the abstract algebra in other areas of mathematics.
Linear Algebra.
1. Algebraic structures in Modern Algebra (fields, groups, rings). Isomorphisms, homomorphisms.
2. Prime numbers, divisibility, fundamental theorem of arithmetics, Euclidean algorithm, congruences of integer numbers.
3. Groups, abelian groups, cyclic groups, subgroups, permutation groups, Cayley’s theorem and Lagrange’s thorem for groups. Morphisms of groups, normal subgroups, congruences in groups. Quotient groups, Isomorphism theorem for groups.
4. Rings, subrings, ideals, congruences in rings, quotient rings. Isomorphism theorem for rings, principal ideals, prime ideals, maximal ideals. Chinese reminder theorem.
5. Polynomial rings in one and many indeterminates, polynomial roots, symmetric polynomials. Bezout’s theorem, Gauss’s theorem, Eisenstein-Shönemann’s criterion. algebraic elements over a field, minimal polynomial. Extensions of fields.
6. Fields, subfields, algebraic fields.
7. Posets, lattices, sublattices, distributive lattices, Boolean algebras.
Traditional lectures; Solving appropriate selected exercises in the class.
| Opis efektu | Symbole efektów | Metody weryfikacji | Forma zajęć |
Verifying the level of preparation of students and their activities during the classes. The student has to receive the positive grade from two tests with tasks of different difficulty which help to assess whether students have achieved effects of the course in a minimum degree (50% of the final grade). Written exam (50% of the final grade).
[1] David Joyce, INTRODUCTION TO MODERN ALGEBRA , Clark University, 2017.
[2] S. Burris, H. P. Sankappanavar , A COURSE IN UNIVERSAL ALGEBRA, ** The Millennium Edition ** , 2000.
[1] W. J. Gilbert and W. K. Nicholson, MODERN ALGEBRA WITH APPLICATIONS, A JOHN WILEY & SONS, 2003.
Zmodyfikowane przez dr Dorota Głazowska (ostatnia modyfikacja: 26-04-2023 20:22)
