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- Introduction
- 1. PLURALITY
- 1.1. Definitions and examples
- 1.2. Ways to Define Sets
- 1.3. Set Operations
- 1.4. Set Operations Properties
- 1.5. Euler-Venn Diagrams
- 1.6. Characteristic functions
- 1.7. Relationships
- 1.8. Functions
- 1.9. Algebraic operations
- 1.10. Hasse diagrams
- 1.11. Theorem
- 1.12. Algebraic structure
- 1.13. Theory
- 1.14. Algebras with one operation (semigroups)
- 1.15. Algebra with two operations two operations
- 1.16. Vector spaces
- 1.17. Modular arithmetic
- 1.18. Commutative semiring
- 1.19. Group
- 1.20. Boolean functions
- 1.21. Equivalent formulas
- 1.22. Algebra of Boolean functions
- 1.23. The principle of duality
- 1.24. Perfect normal forms
- 1.25. Closed classes of Boolean functions
- 1.26. Completeness of a system of Boolean functions
- 2. COMBINATORY
- 2.1. The basic principles of combinatorics
- 2.2. Placements
- 2.3. Combinations
- 2.4. Number of permutations
- 2.5. Inclusion and exclusion formula (main theorem)
- 2.6. The concept of a lattice, a distributive lattice
- 2.7. The principle of mathematical induction
- 2.8. The Cantor diagonal method
- 2.9. The principle of transfinite induction
- 2.10. Newton’s binomial
- 2.11. The Dirichlet Principle
- 2.12. FermatSmall Theorem
- 2.13. Chinese remainder theorem
- 2.14. Prufer Code
- 2.15. Fibonacci
- 2.16. Bene formula
- 2.17. Euclidean Lemma
- 2.18. Stirling numbers
- 2.19. Bell Number
- 2.20. Generating functions
- 2.21. Generalized recurrence relations
- 2.22. Zhegalkin polynomial
- 2.23. The problem of Hanoi towers
- 2.24. The general problem of sticker stamps
- 2.25. Return search method
- 2.26. full search
- 3. GRAPH THEORY
- 3.1. Simple graphs and their properties
- 3.2. Metric spaces
- 3.3. Trees and forest
- 3.4. Eulerian graphs
- 3.5. Parts Count
- 3.6. Hamiltonian graphs
- 3.7. Graph operations
- 3.8. Incidence matrix
- 3.9. Chromatic number of a graph
- 3.10. Five-color theorem
- 3.11. Flat graphs
- 3.12. Counts of Kuratovsky
- 3.13. Platonic solids
- 3.14. Mobius function
- 3.15. Adjacency matrix
- 3.16. Inversion formula
- 3.17. Product
- 3.18. Cyclomatic number of a graph
- 3.19. Independence and coverings
- 3.20. Dominant sets
- 3.21. Dijkstra’s
- 3.22. Kruskal (Kruskal) Algorithm
- 3.23. Prima Algorithm
- 3.24. Bipartite graphs and matching
- 3.25. Transport networks
- 3.26. The problem of finding a spanning tree of minimum weight
- 4. ENCODING AND MATHEMATICAL MODELING
- 4.1. Encoding
- 4.2. Alphabetical encoding
- 4.3. Coding with minimal redundancy
- 4.4. Noise-tolerant coding
- 4.5. Code distance (Hamming distance)
- 4.6. Separable schemes
- 4.7. Prefix schemes
- 4.8. Macmillan Inequality
- 4.9. Automata
- 5. Examples of execution
- 5.1. Tasks for an independent solution
- 6. Examples of calculation and graphic tasks
- 6.1. Settlement and graphic work 1
- 6.2. Settlement and graphic work 2
- 6.3. Settlement and graphic work 3
- CONCLUSION
- List of references