Discrete mathematics is a field of mathematics that studies discrete structures that arise both within mathematics itself and in its applications.
In the context of mathematics as a whole, discrete mathematics is often identified with finite mathematics - a direction that studies finite structures - finite graphs, finite groups, finite automata. And at the same time, some features that are not inherent in sections working with infinite and continuous structures can be distinguished. So, in discrete directions, as a rule, the class of solvable problems is more extensive, since in many cases a complete enumeration of options is possible, whereas in sections dealing with infinite and continuous structures, for solvability usually require significant restrictions on the conditions.
Discrete mathematics cheat sheet:
- Sets and their specifications. Subsets
- Operations on sets. Properties
- Cartesian product
- Relations. Relationship Properties
- Graphic representation of binary relations
- Binary ratio matrix
- equivalence relation
- Relationship order
- Functions. Power sets
- Representation of sets in computers
- Definition of graphs
- Adjacency, incidence, degrees
- Routes, paths, cycles
- Isomorphism of graphs
- Presentation of graphs in computers
- Complete graphs and bipartite graphs
- Operations with graphs
- Connectivity in undirected graphs
- Connectivity in digraphs
- Finding connectivity components on a computer
- Width and depth search
- Free trees
- Oriented and ordered trees
- Binary trees. Detours
- Sort trees
- Comparison of representations of associative memory
- Shortest skeleton
- Planar graphs. Pontyagin-Kuratovsky theorem
- Coloring graphs. Algorithms
- Building a fundamental set of cycles
- Euler cycles
- Hamiltonian graphs
- Graphs and binary relations
In the context of mathematics as a whole, discrete mathematics is often identified with finite mathematics - a direction that studies finite structures - finite graphs, finite groups, finite automata. And at the same time, some features that are not inherent in sections working with infinite and continuous structures can be distinguished. So, in discrete directions, as a rule, the class of solvable problems is more extensive, since in many cases a complete enumeration of options is possible, whereas in sections dealing with infinite and continuous structures, for solvability usually require significant restrictions on the conditions.
Discrete mathematics cheat sheet:
- Sets and their specifications. Subsets
- Operations on sets. Properties
- Cartesian product
- Relations. Relationship Properties
- Graphic representation of binary relations
- Binary ratio matrix
- equivalence relation
- Relationship order
- Functions. Power sets
- Representation of sets in computers
- Definition of graphs
- Adjacency, incidence, degrees
- Routes, paths, cycles
- Isomorphism of graphs
- Presentation of graphs in computers
- Complete graphs and bipartite graphs
- Operations with graphs
- Connectivity in undirected graphs
- Connectivity in digraphs
- Finding connectivity components on a computer
- Width and depth search
- Free trees
- Oriented and ordered trees
- Binary trees. Detours
- Sort trees
- Comparison of representations of associative memory
- Shortest skeleton
- Planar graphs. Pontyagin-Kuratovsky theorem
- Coloring graphs. Algorithms
- Building a fundamental set of cycles
- Euler cycles
- Hamiltonian graphs
- Graphs and binary relations
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