This lecture includes the following topics: Discrete groups of motions; Abstract group actions.
This lecture includes the following topics: Introduction to the course; Review: Linear algebra; Definition of groups.
This lecture includes the following topics: Group actions. Basic properties and constructions. Groups acting on themselves by left multiplication. Groups acting on themselves by conjugation.
This lecture includes the following topics: Group actions. Basic properties and constructions. Groups acting on themselves by left multiplication. Groups acting on themselves by conjugation.
This lecture includes the following topics: Group actions. Basic properties and constructions. Groups acting on themselves by left multiplication. Groups acting on themselves by conjugation.
This lecture includes the following topics: A5 and the symmetries of an icosahedron. Sylow theorems. Study of permutation groups.
This lecture includes the following topics: A5 and the symmetries of an icosahedron. Sylow theorems. Study of permutation groups.
This lecture includes the following topics: A5 and the symmetries of an icosahedron. Sylow theorems. Study of permutation groups.
This lecture includes the following topics: Rings. Examples of rings. Basic properties and constructions.
This lecture includes the following topics: Rings. Examples of rings. Basic properties and constructions.
This lecture includes the following topics: Rings. Examples of rings. Basic properties and constructions.
This lecture includes the following topics: Quotient rings, extensions of rings. Integral domains, fields of fractions.
This lecture includes topics from a special lecture.
This lecture includes topics from a special lecture.
This lecture includes the following topics: Administrative notes; Generalities on groups; Symmetric groups on n letters; A stabilizer subgroup; The subgroups of Z; Cyclic subgroups gen by element.
This lecture includes topics from a special lecture.
This lecture includes the following topics: Euclidean domains, PIDs, UFDs. Gauss' lemma. Eisenstein's criterion. Algebraic integers.
This lecture includes the following topics: Euclidean domains, PIDs, UFDs. Gauss' lemma. Eisenstein's criterion. Algebraic integers.
This lecture includes the following topics: Euclidean domains, PIDs, UFDs. Gauss' lemma. Eisenstein's criterion. Algebraic integers.
This lecture includes the following topics: Structure of ring of integers in a quadratic field. Dedekind domains. Ideal class groups.