Принадлежность элемента множеству

Lecture



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Lectures and tutorial on "Discrete Math. Set theory. Graph theory. Combinatorics."

Terms: Discrete Math. Set theory. Graph theory. Combinatorics.

Theory of finite and infinite sets
Graph and graph theory: history, classification, description, applications
Propositional algebra
Graph decomposition. Paths in graphs. Shortest paths. Paths in an acyclic graph. The decomposition approach with examples
Hasse diagram with examples briefly
The continuum in set theory
Glossary of graph theory
Inclusion-exclusion formula or exclusion-exclusion principle and examples
Subfactorial
Factorial superfactorials hyperfactorial primalial
Combinatorics sum rule and work rule
Combination and placement permutations (with and without repetitions)
Combination rearrangement and placement and Newton binom examples
Summary of formulas for all types of combinatorics connections - permutations and placement with repetitions and without repetitions with examples
Earl (mathematics)
Incidence and adjacency matrix
Path (graph theory)
Hamilton graph
Euler cycle graph chain (path)
Connected graph, Non-connected graph, strongly connected graph of definition and theorem
Edge graph (“derived graph covering graph)
Numerical characteristics of graphs Chromatic number of graphs
Hypergraph
kograf, or additionally reducible graph, or P4-free graph
Reachability matrix
Union and intersection of graphs
Standard deviation
Elements of binary logic
Set in mathematics: concept, types, history and methods of defining relations between sets
Принадлежность элемента множеству
Basic identities of set algebra
Venn Diagram and Euler Circles
Binary relation Bijection. Surgery. Injection
Direct or Cartesian product of two sets
Equivalence relation
General properties of relationships
Order relationship
Strict order relationship
Matrices of order relations
The structure of ordered sets
Mappings
Functional relationship
Relationship tolerance
Splitting set. Sets of sets. Classification. Breaking up into classes. Examples
Count internal stability number
The external stability number of the graph
Graph connectivity component
Connected graph
Tree (graph theory)
Binary tree
Planar graph Pontryagin-Kuratovsky theorem
The problem of four colors
Coloring graphs
Practical application of graph coloring
Wheel (graph theory)
Абстрактная теория зависимости: роль матроидов в дискретной математике
Verge of flat graph
Types of finite graphs
Multigraph and pseudograph
Bichrophic Earl (Bigraph)
Regular graph Homogeneous graph
Tournament (graph theory)
Graph properties
Minimum spanning tree
The Dirichlet principle (pigeonhole principle) in combinatorics
Edge contraction and vertex identification
The blossom algorithm: cutting and contracting blossoms
Functional completeness of a set of logical operations, and its criteria
Block graph (clique tree) and related classes of graphs
Clique (graph theory) of an undirected graph
Methods of graph visualization. Force-directed graph drawing algorithms
Difference and similarities between Venn diagram and Euler diagram
Integer partitions in combinatorics
Probabilistic combinatorics, random permutations
Ordinal number
Cardinality of a set; the cardinal number (cardinal) of a set
Transfinite number
Диаграмма паука
Genus, thickness, coarseness and crossing number of a graph, and embedding a graph on the torus
Kosaraju's algorithm — finding strongly connected components in a directed graph
The Bron–Kerbosch algorithm — a branch-and-bound method for finding all cliques of an undirected graph
The Havel–Hakimi algorithm for checking whether a sequence is graphic
Perfect graph
Combinatorial objects
Bit vector
The antimatroid as a system in which a set is built by adding elements one at a time
Random permutation
Primorial and compositorial as functions over the natural numbers
Friedman's SSCG function
Falling and rising factorials
Reflexive and irreflexive (antireflexive) relations
Transitive relation in mathematics
Symmetric relation in mathematics
Rel — the category of correspondences (relations) between sets in mathematics