Set theory (including function), number theory foundation, algorithm design, combinatorial analysis, discrete probability, relation theory, graph theory and tree, abstract algebra (including algebraic system, group, ring, field, etc. ), Boolean algebra, computational models (languages and automata) and so on. The application of discrete mathematics covers many fields of modern science and technology.

Synthesis of binary relations R and S (also called synthesis)

For example:

R = { & lt 1，2 & gt； ，& lt2，3 >，& lt 1，4 & gt； ，& lt3， 1 & gt； }

S = { & lt2，3 >，& lt3，4 >，& lt 1，2 & gt； ，& lt4， 1 & gt； }

r .S = { & lt 1，3 & gt； ，& lt2，4 >，& lt 1， 1 & gt； ，& lt3，2 >}

s .R = { & lt2， 1 & gt； ，& lt 1，3 & gt； ，& lt4，2 >，& lt4，4 >}

Discrete mathematics is divided into three courses, namely set theory and graph theory, algebraic structure and combinatorial mathematics, and mathematical logic. The teaching method is mainly classroom teaching, supplemented by written homework after class, courseware release through the school network teaching platform and teacher-student communication.

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.