Forventet læringsutbytte

After the course, the students should acquire:

1. understanding of the most important topics of abstract algebra

2. understanding of the most important topics of combinatorics, including fundamentals of graph theory and combinatorial optimization algorithms.

Emnets temaer

- Enumeration concepts: Fundamental coefficients,
formal series and infinite matrices, generating
functions, hypergeometric summation, and sieve
methods.
- Abstract algebra: Groups, rings, module and
vector spaces, algebraic extensions of fields,
normal and separable extensions
- Graphs: Matching, covering, and packing,
connectivity, coloring, flows
- Algebraic systems

Pedagogiske metoder

Forelesninger
Oppgaveløsning

Vurderingsformer

Skriftlig eksamen, 3 timer

Karakterskala

Bokstavkarakterer, A (best) - F (ikke bestått)

Sensorordning

Evaluated by the lecturer.

Gjennomføring av kontinuasjon

The whole subject must be repeated.

Tillatte hjelpemidler (gjelder kun skriftlig eksamen)

Approved calculator

Obligatoriske arbeidskrav

None.

Læremidler

- R. Diestel:
Graph Theory, 3rd ed.
Graduate Texts in Mathematics, Vol. 173
Springer-Verlag, Berlin, Germany (2005).
- P. B. Bhattacharya, S. K. Jain, and S. R. Nagpaul:
Basic Abstract Algebra, 2nd ed.
Cambridge University Press, Cambridge, UK (1994).
- M. Aigner:
A Course in Enumeration.
Graduate Texts in Mathematics, Vol. 238
Springer-Verlag, Berlin, Germany (2007).
- M. Aigner:
Combinatorial Theory.
Springer-Verlag, Berlin, Germany (2004).