MAT-60056 Algebra, 5 cr
Lisätiedot
This is an English version of the Algebra 1B course MTTMA3B. The course will be lectured in English every second year.
Vastuuhenkilö
Mika Mattila
Opetus
| Toteutuskerta | Periodi | Vastuuhenkilö | Suoritusvaatimukset |
| MAT-60056 2019-01 | 3 |
Mika Mattila |
Final exam. |
Osaamistavoitteet
After passing the course the student - possesses an ability of abstract thinking - recognizes and understands basic algebraic structures such as groups, rings and fields - understands the content of the fundamental theorems of abstract algebra and is able to prove them if necessary
Sisältö
| Sisältö | Ydinsisältö | Täydentävä tietämys | Erityistietämys |
| 1. | GROUP THEORY: Groups, subgroups, group homomorphisms and isomorphisms. | Normal subgroups and quotient groups. | Congruence gruops, cyclic groups, permutation groups, matrix groups, dihedral groups. |
| 2. | RINGS AND FIELDS: Rings, subrings, integral domains and fields, ideals, polynomials of one variable. | Quotient rings, field extensions. | Matrix rings, field of fractions. |
Ohjeita opiskelijalle osaamisen tasojen saavuttamiseksi
Active participation in the weekly exercise sessions is very much recommended. It will also result as a significant number of bonus points that will be taken into account in the grading of the course.
Arvosteluasteikko:
Numerical evaluation scale (0-5)
Oppimateriaali
| Tyyppi | Nimi | Tekijä | ISBN | URL | Lisätiedot | Tenttimateriaali |
| Book | An Introduction to Essential Algebraic Structures | M.R. Dixon, L.A. Kurdachenko and I.Y. Subbotin | No | |||
| Book | Johdatus Abstraktiin Algebraan | J. Häsä & J. Rämö | Alternative Finnish material | No |
Esitietovaatimukset
| Opintojakso | P/S | Selite |
| MAT-01366 Mathematics 3 | Mandatory | |
| MAT-01566 Mathematics 5 | Advisable | |
| MAT-02106 Multivariable Calculus | Advisable |
Vastaavuudet
| Opintojakso | Vastaa opintojaksoa | Selite |
| MAT-60056 Algebra, 5 cr | MAT-41156 Algebra 1, 5 cr | |
| MAT-60056 Algebra, 5 cr | MAT-60050 Algebra, 5 cr |