Let R be the equivalence relation defined on the set A, and the set of all elements related to an element A in A is called the equivalence class of A. Equivalence classes are widely used. For example, in programming languages, we use equivalence classes to determine whether identifiers represent the same thing.
Subject content
1. set theory: sets and their operations, binary relations and functions, natural numbers and natural number set, cardinality of sets.
2. Graph theory: basic concepts of graphs, Euler graphs 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.
3. Algebraic structure: the basic concepts of algebraic system, semigroup and singularity, group, ring and field, lattice and Boolean algebra.
4. Combinatorial mathematics: combinatorial existence theorem, basic counting formula, combinatorial counting method and combinatorial counting theorem.
5. Mathematical logic: propositional logic, first-order predicate calculus and resolution principle.
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.