Set theory: sets and their operations, binary relations and functions, natural numbers and natural number set, cardinality of sets. Graph theory: basic concepts of graphs, Euler and hamiltonian graph, matrix representation of trees and graphs, planar graphs, graph coloring, dominating sets, covering sets, independent sets and matching, weighted graphs and their applications.
Algebraic structure: the basic concepts of algebraic systems, semigroups and uniqueness, groups, rings and fields, lattices and Boolean algebras. Combinatorial mathematics: combinatorial existence theorem, basic counting formula, combinatorial counting method and combinatorial counting theorem. Mathematical logic part: propositional logic, first-order predicate calculus, resolution principle.
The application of discrete mathematics;
Discrete mathematics can also be said to be the basic core discipline of computer science. There is a famous typical example in discrete mathematics-the four-color theorem, also known as the four-color conjecture, which is one of the three major mathematical problems in the modern world. It was put forward by the British draftsman Fernandez guthrie in 1852. When he colored the map, he found a phenomenon, "Each map can only be colored in four colors, and *.
So can this be proved mathematically? 100 years later 1976, Kenneth Appel and Wolfgang Haken used computer-aided calculation, which took 1200 hours and 1000 billion judgments, and finally proved the four-color theorem, causing a sensation in the world. This is discrete mathematics.
The above content comes from the reference: Baidu Encyclopedia-Discrete Mathematics