<lo> <li> Sets, relations between sets; properties of relations; mappings. Ordered sets, equivalence relations, decompositions. <li> Structures with a single operation and their substructures ? groupoids, halfgroups, neutral element, inverse element, subgroupoids. Groups, subgroups. <li> Structures with two operations and their substructures ? rings, subrings, domains. Fields, subfields, numbers fields. <li> Vector spaces over number fields ? subspaces; subspaces generated by vectors. Linear combination of vectors, linear hull; dimension and basis of a vector space, vector coordinates. <li> Matrices and determinants ? definitions, computing rules for determinants. Sum of matrices, scalar multiple of a matrix, matrix multiplication. Inverse of a matrix and its computing, rank of a matrix . <li> Systems of linear equations ? introduction, solvability. Gauss elimination method, The Frobenius Theorem, Cramer?s rule. Homogeneous systems of linear equations. </lo>
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