Algebraic Structures
Algebraiska strukturer

FMAN10F, 7.5 högskolepoäng

Gäller från och med: Autumn 2013
Beslutad av: FN1/Anders Gustafsson
Datum för fastställande: 2014-01-27

Allmänna uppgifter

Avdelning: Mathematics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskoder: FMAN10, MATM11
Undervisningsspråk: English

Syfte

The course is established in order to give the doctoral students knowledge about basic concepts of abstract algebra, which is useful for further studies in mathematics as well as within digital technology and coding theory.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• be able to describe basic properties of integers and polynomials, and be able to compute with congruences modulo these objects.
• be able to describe basic properties of the important concepts in abstract algebra; ring, ideal, quotient ring, group and field.
• be able to explain, in writing and orally, the contents of some central definitions and proofs.
• be able to give examples of and illustrate some important applications of the course contents.
• have acquired basic knowledge for further studies in algebra or subjects based on algebraic methods.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• For a passing grade the student must
• be able to independently construct proofs of simple statements within the framework of the course.
• be able to show a good ability to independently, in writing and orally, explain mathematical reasoning in a well structured way, with clear logic.

Kursinnehåll

Rings: Polynomial rings. Ideals and quotient rings. Ring homomorphisms and isomorphisms. Groups: Lagrange's theorem. Permutation groups. Normal subgroups and quotient groups. Group homomorphisms and isomorphisms. Fields: Characteristic. Finite fields. Field extensions.

Kurslitteratur

Hungerford, T.: Abstract Algebra: An Introduction. Cengage Learning, 2012. ISBN 9781111573331.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, övningar

Kursens examination

Examinationsformer: Skriftlig tentamen, muntlig tentamen
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förutsatta förkunskaper: In terms of content, basic courses in calculus (in one and several variables) and linear algebra are sufficient. However, the mathematical maturity provided by one or more further courses in mathematics is helpful .

Kurstillfällesinformation

Kontaktinformation och övrigt

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