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TATA55 Kursinformation
10+10 föreläsningar (kursen går i period 1 och period 2). Några av dessa tillfällen kommer att tillägnas uppgiftsräkning. Examination genom inlämningsuppgifter, 4 omgångar. .
10+10 lectures, some of which will be used for discussing exercises. Examination is 4 sets of Hand-in exercises. The course stretches over the whole autumn semester.
Schedule/Plan
- Binary operations, associativity, semigroups. Definitions of groups, simple properties, examples.
- Integers, divisibility, greatest common denominator. Euclidean algorithm, congruences, Diophantine equations. Equivalence realtions.
- Symmetry Groups. Z_n och and Z_n^x.
- Cyclic groups
- Permutation groups. More on Symmetry groups
- Isomorphisms. Cayley's thm. Homomorphisms.
- Direct products. Structure thm for finite abelian groups.
- Normal subgroups. Cosets. Lagrange's thm.
- Quotient groups. Isomorphism theorems.
- Group actions. Burnside's thm. Sylow's theorems.
- Rings.
- Quotient rings.
- Polynomial rings.
- Euclidean rings, principal ideal domains, unique factorization domains.
- Fields. Field extensions.
- Splitting fields. Geometric constructions.
- Separable extensions. Finite fields.
- Finite fields.
Exercises
The following leaflet contain some exercises from Svensson, some from Judson, and some from other sources.
Sidansvarig: Jan Snellman
Senast uppdaterad: 2023-11-07