After this course, students should be able to use the methods of abstract algebra to analyse situations with a high degree of symmetry and those where the rationality domain plays an important role, such as questions of solvability by radicals, and ruler and compass constructions. A special emphasis will be laid on techniques which use the representation of symmetry groups as groups of vector space transformations.
Galois theory: field extensions and their automorphisms; translation of field extensions properties in terms of the associated groups and applications to some classical problems (solvability by radicals, ruler and compass constructions).Group representations: character of a linear representation; group algebras and induced representations.
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)
Precursorycourses A first course in linear algebra
Support J. Rotman : Galois theory (2d edition), Springer 1998J-P. Serre : Représentations linéaires des groupes finis, Hermann 1971
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