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Gdowski B., Pluciński E. – Zbiór zadań z rachunku wektorowego i geometrii analitycznej Teoria, przykłady, zadania – Oficyna Wydawnicza PRz, Rzeszów. W. Dubnicki, L. Filus, H. Sosnowska, Algebra liniowa w zadaniach. PWN B. Gdowski, E. Pluciński, Zadania z rachunku wektorowego i geometrii analitycznej. Analiza matematyczna w zadaniach. PWN Warszawa Gdowski B., Pluciński E., Zbiór zadań z rachunku wektorowego i geometrii analitycznej. Oficyna.

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Set theory Lists of exercises prepared for the lecture Introduction to mathematics for the specialization Mathematics and Mathematics and Economy Quantifiers Mathematical induction Elements of the set theory Relations Short sketches of chosen issues Relations – basic definitions Seminars Bachelor seminar: Graph algorithms and their applications Abstract algebra group and ring theory Lists of exercises prepared for the lecture Algebra for the specialization Computer Science lists also contain chosen basic definitions, facts and hints List 1: Abstract Bibliography, related topics, historical remarks ginflations program and other projects Appendix: Complex numbers List 2: Linear spaces List 4: Graph algorithms and their applications for Computer Science Informatics.

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A more detailed presentation of the material of Part 3 above, together with algorithm simulations in polish. Rings, ideals, isomorphism aadania for rings; invertible, indecomposable elements Computational data for Nakayama bigraphs Horario: Representations of groups, decomposition of finitely generated abelian groups List 3: Groups – basic examples; isomorphism theorem for groups List 2: About seminar – abstract [pl] Prerequisites [pl] Recommended literature [pl] Basic course on graph algorithms: Principal ideal rings, Euklidean rings, Chinese Remainder Theorem Computer algebra Short sketches of chosen issues Diagonalization of polynomial matrices Linear algebra Lists of exercises prepared for the lecture Linear algebra with racchunku for the specialization Mathematics and Economy List 1: Network sniffing – Wireshark presentation Project 4: Elements of graph theory, graph representations [slides] [printable] Basic graph algorithms and their applications DFS, BFS [slides] [printable] Shortest paths problems Dijkstra, Bellman-Ford [slides] [printable] Minimum spaning tree Kruskal, Prim, disjoint sets structures [slides] [printable] Maximum flow Ford-Fulkerson, bipartite matchings [slides] [printable] NEW: Basis and dimension of a linear space List 5: Part 1 Part 2 Part 3 Part 4 Theory of graphs and graph algorithms.

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Security of www – IP blocking, authentication with a password Project 2: