| Center |
| Faculty of Mathematics |
| Departament |
| Algebra |
| Lecturers in charge |
| Sin datos cargados |
| Met. Docent |
| In the theoretical sessions, the active part of its development corresponds basically to the professor. One will harness the participation and the work in the classroom of the students, particularly in the practical exercises. |
| Met. Avaluació |
| A theoretical-practical examination will be made. In the final qualification the resolution of questions will be able also to be valued, problems and the exhibition of subjects that possibly can consider. |
| Bibliografia |
| Amstrong, M. A., Groups and Symmetry, Springer-Verlag, 1988 Biggs, N. L., “Discrete Mathematics”, Clarendon Press, 1989. Gilbert, W. J., “Modern Algebra with Applications”, Wiley, 1976. Hill, R., “A first course in coding theory”, Clarendon Press, 1986. R. Lidl, R., Pilz, G., “Applied Abstract Algebra”, Springer-Verlag, 1984. |
| Continguts |
| Hamming distance. Hamming and Singleton bounds. Codes and designs. Perfect codes, MDS-codes. Existence and unicity of finite fiels of determined order. Linear codes. Hamming and Golay codes. Boolean functions and Boolean polynomials. Reed-Muller codes. Cyclic codes. Generator matrix and parity-check matrix of a cyclic code. Error trapping. BCH-codes, Reed-Solomon codes. Group actions on sets: cyclic index.. Burnside’s theorem on the number of orbits. Sets of colourings and their generating functions. Pólya-Redfield method of enumeration. Symmetry groups: Finite rotation groups in the plane. Finite rotation groups in the space: proper rotations of regular solids. Automata, semigroups and connections between them. |
| Objetius |
| -Algebraic knowledge acquired in a first course of Algebra will be applied to particular problems of the real life: -Data transmission. Error-correcting. -Symmetries in the nature and groups of transformations. -Combinatorial problems. -Algebraic models in computer sciences. -Visualize algebraic structures. -Extension of the algebraic knowledge through the study of finite fields, polynomials over finite fields, semigroups, group actions and movements in the plane and the space. |
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