Linear algebra (esp. for n = 2). Solving of systems by elimination method, pivots. Matrix operations, properties. Linear (in)dependence of a system of vectors. Rank, Frobenius theorem of compatibility of Slaes. Unit matrix, inverse matrix.
Determinants, basic properties and calculation. Dets of order 2 and 3. Cramer's rule.
Modular arithmetic. Properties of congruencies. Finite fields/rings Z2, Z5, Z7, spaces (Zm)r, esp. for m = 2 and small r. Small systems in finite fields.
(Un)directed graphs, geometric model, vertices, edges. Complete graph, regular graph. Isomorphism of graphs, operations with graphs. Degree of a vertex. Walk, trail, path, cycle. Subgraph, factor. Connectedness and components. Tree and spanning tree. Incidence and adjacency matrices. Relationship between matrices, graphs and binary relations.
- Učitel: Daniela Bittnerová