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Discrete Math. Set theory. Graph theory. Combinatorics.

All lectures: All lectures at the Academy of Intelligence on the discipline: discrete math. set theory. graph theory. combinatorics.. These fascinating lectures provide us with the opportunity to explore the deep principles and phenomena underlying our knowledge and our desire to understand the world.

Subsections and categories

Ecology 14 lectures
1. Theory of finite and infinite sets
2. Graph and graph theory: history, classification, description, applications
3. Propositional algebra
4. Graph decomposition. Paths in graphs. Shortest paths. Paths in an acyclic graph. The decomposition approach with examples
5. Hasse diagram with examples briefly
6. The continuum in set theory
7. Glossary of graph theory
8. Inclusion-exclusion formula or exclusion-exclusion principle and examples
9. Subfactorial
10. Factorial superfactorials hyperfactorial primalial
11. Combinatorics sum rule and work rule
12. Combination and placement permutations (with and without repetitions)
13. Combination rearrangement and placement and Newton binom examples
14. Summary of formulas for all types of combinatorics connections - permutations and placement with repetitions and without repetitions with examples
15. Earl (mathematics)
16. Incidence and adjacency matrix
17. Path (graph theory)
18. Hamilton graph
19. Euler cycle graph chain (path)
20. Connected graph, Non-connected graph, strongly connected graph of definition and theorem
21. Edge graph (“derived graph covering graph)
22. Numerical characteristics of graphs Chromatic number of graphs
23. Hypergraph
24. kograf, or additionally reducible graph, or P4-free graph
25. Reachability matrix
26. Union and intersection of graphs
27. Standard deviation
28. Elements of binary logic
29. Set in mathematics: concept, types, history and methods of defining relations between sets
30. Принадлежность элемента множеству
31. Basic identities of set algebra
32. Venn Diagram and Euler Circles
33. Binary relation Bijection. Surgery. Injection
34. Direct or Cartesian product of two sets
35. Equivalence relation
36. General properties of relationships
37. Order relationship
38. Strict order relationship
39. Matrices of order relations
40. The structure of ordered sets
41. Mappings
42. Functional relationship
43. Relationship tolerance
44. Splitting set. Sets of sets. Classification. Breaking up into classes. Examples
45. Count internal stability number
46. The external stability number of the graph
47. Graph connectivity component
48. Connected graph
49. Tree (graph theory)
50. Binary tree
51. Planar graph Pontryagin-Kuratovsky theorem
52. The problem of four colors
53. Coloring graphs
54. Practical application of graph coloring
55. Wheel (graph theory)
56. Абстрактная теория зависимости: роль матроидов в дискретной математике
57. Verge of flat graph
58. Types of finite graphs
59. Multigraph and pseudograph
60. Bichrophic Earl (Bigraph)
61. Regular graph Homogeneous graph
62. Tournament (graph theory)
63. Graph properties
64. Minimum spanning tree
65. The Dirichlet principle (pigeonhole principle) in combinatorics
66. Edge contraction and vertex identification
67. The blossom algorithm: cutting and contracting blossoms
68. Functional completeness of a set of logical operations, and its criteria
69. Block graph (clique tree) and related classes of graphs
70. Clique (graph theory) of an undirected graph
71. Methods of graph visualization. Force-directed graph drawing algorithms
72. Difference and similarities between Venn diagram and Euler diagram
73. Integer partitions in combinatorics
74. Probabilistic combinatorics, random permutations
75. Ordinal number
76. Cardinality of a set; the cardinal number (cardinal) of a set
77. Transfinite number
78. Диаграмма паука
79. Genus, thickness, coarseness and crossing number of a graph, and embedding a graph on the torus
80. Kosaraju's algorithm — finding strongly connected components in a directed graph
81. The Bron–Kerbosch algorithm — a branch-and-bound method for finding all cliques of an undirected graph
82. The Havel–Hakimi algorithm for checking whether a sequence is graphic
83. Perfect graph
84. Combinatorial objects
85. Bit vector
86. The antimatroid as a system in which a set is built by adding elements one at a time
87. Random permutation
88. Primorial and compositorial as functions over the natural numbers
89. Friedman's SSCG function
90. Falling and rising factorials
91. Reflexive and irreflexive (antireflexive) relations
92. Transitive relation in mathematics
93. Symmetric relation in mathematics
94. Rel — the category of correspondences (relations) between sets in mathematics
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